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What is the magnitude of the momentum of a 28-g sparrow flying with a speed of 8.4 m/s?

A constant friction force of 25 N acts on a 65-kg skier for 15 s on level snow. What is the skiers change in velocity?

A 7150-kg railroad car travels alone on a level frictionless track with a constant speed of A 3350-kg load, initially at rest, is dropped onto the car. What will be the cars new speed?

A 110-kg tackler moving at meets head-on (and holds on to) an 82-kg halfback moving at What will be their mutual speed immediately after the collision?

Calculate the force exerted on a rocket when the propelling gases are being expelled at a rate of with a speed of 4.5 x 10 m/s?

A 7700-kg boxcar traveling strikes a second car at rest. The two stick together and move off with a speed of What is the mass of the second car?

(II) A child in a boat throws a 5.30-kg package out horizontally with a speed of 10.0 m/s, Fig. 7–31. Calculate the velocity of the boat immediately after, assuming it was initially at rest. The mass of the child is 24.0 kg and the mass of the boat is 35.0 kg.

An atomic nucleus at rest decays radioactively into an alpha particle and a different nucleus. What will be the speed of this recoiling nucleus if the speed of the alpha particle is Assume the recoiling nucleus has a mass 57 times greater than that of the alpha particle

An atomic nucleus initially moving at emits an alpha particle in the direction of its velocity, and the remaining nucleus slows to If the alpha particle has a mass of 4.0 u and the original nucleus has a mass of 222 u, what speed does the alpha particle have when it is emitted?

An object at rest is suddenly broken apart into two fragments by an explosion. One fragment acquires twice the kinetic energy of the other. What is the ratio of their masses?

A 22-g bullet traveling penetrates a 2.0-kg block of wood and emerges going If the block is stationary on a frictionless surface when hit, how fast does it move after the bullet emerges?

A 0.145-kg baseball pitched horizontally at strikes a bat and pops straight up to a height of 31.5 m. If the contact time between bat and ball is 2.5 ms, calculate the average force between the ball and bat during contact

Air in a 120-km/h wind strikes head-on the face of a building 45 m wide by 75 m high and is brought to rest. If air has a mass of 1.3 kg per cubic meter, determine the average force of the wind on the building.

A 725-kg two-stage rocket is traveling at a speed of away from Earth when a predesigned explosion separates the rocket into two sections of equal mass that then move with a speed of relative to each other along the original line of motion. (a) What is the speed and direction of each section (relative to Earth) after the explosion? (b) How much energy was supplied by the explosion? [Hint: What is the change in kinetic energy as a result of the explosion?]

(I) A 0.145-kg baseball pitched at 31.0 m/s is hit on a horizontal line drive straight back at the pitcher at 46.0 m/s. If the contact time between bat and ball is \(5.00 \times 10^{-3}\ s\), calculate the force (assumed to be constant) between the ball and bat.

A golf ball of mass 0.045 kg is hit off the tee at a speed of The golf club was in contact with the ball for Find (a) the impulse imparted to the golf ball, and (b) the average force exerted on the ball by the golf club.

A 12-kg hammer strikes a nail at a velocity of and comes to rest in a time interval of 8.0 ms. (a) What is the impulse given to the nail? (b) What is the average force acting on the nail?

A tennis ball of mass and speed strikes a wall at a 45 angle and rebounds with the same speed at 45 (Fig. 732). What is the impulse (magnitude and direction) given to the ball

A 125-kg astronaut (including space suit) acquires a speed of by pushing off with her legs from a 1900-kg space capsule. (a) What is the change in speed of the space capsule? (b) If the push lasts 0.600 s, what is the average force exerted by each on the other? As the reference frame, use the position of the capsule before the push. (c) What is the kinetic energy of each after the push?

Rain is falling at the rate of and accumulates in a pan. If the raindrops hit at estimate the force on the bottom of a pan due to the impacting rain which we assume does not rebound. Water has a mass of 1.00 * 103 kg per m3

A 95-kg fullback is running at to the east and is stopped in 0.85 s by a head-on tackle by a tackler running due west. Calculate (a) the original momentum of the fullback, (b) the impulse exerted on the fullback, (c) the impulse exerted on the tackler, and (d) the average force exerted on the tackler

With what impulse does a 0.50-kg newspaper have to be thrown to give it a velocity of 3.0 ms?

Suppose the force acting on a tennis ball (mass 0.060 kg) points in the direction and is given by the graph of Fig. 733 as a function of time. (a) Use graphical methods (count squares) to estimate the total impulse given the ball. (b) Estimate the velocity of the ball after being struck, assuming the ball is being served so it is nearly at rest initially. [Hint: See Section 62.]

(a) Calculate the impulse experienced when a 55-kg person lands on firm ground after jumping from a height of 2.8 m. (b) Estimate the average force exerted on the persons feet by the ground if the landing is stiff-legged, and again (c) with bent legs. With stiff legs, assume the body moves 1.0 cm during impact, and when the legs are bent, about 50 cm. [Hint: The average net force on him, which is related to impulse, is the vector sum of gravity and the force exerted by the ground. See Fig. 734.] We will see in Chapter 9 that the force in (b) exceeds the ultimate strength of bone (Table 92

A ball of mass 0.440 kg moving east ( direction) with a speed of collides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed and direction of each ball after the collision?

A 0.450-kg hockey puck, moving east with a speed of has a head-on collision with a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision, what will be the speed and direction of each puck after the collision?

A 0.060-kg tennis ball, moving with a speed of has a head-on collision with a 0.090-kg ball initially moving in the same direction at a speed of Assuming a perfectly elastic collision, determine the speed and direction of each ball after the collision

(II) Two billiard balls of equal mass undergo a perfectly elastic head-on collision. If one ball’s initial speed was 2.00 m/s, and the other’s was 3.60 m/s in the opposite direction, what will be their speeds and directions after the collision?

A 0.280-kg croquet ball makes an elastic head-on collision with a second ball initially at rest. The second ball moves off with half the original speed of the first ball. (a) What is the mass of the second ball? (b) What fraction of the original kinetic energy gets transferred to the second ball?

A ball of mass m makes a head-on elastic collision with a second ball (at rest) and rebounds with a speed equal to 0.450 its original speed. What is the mass of the second ball?

(II) A ball of mass 0.220 kg that is moving with a speed of 5.5 m/s collides head-on and elastically with another ball initially at rest. Immediately after the collision, the incoming ball bounces backward with a speed of 3.8 m/s. Calculate \((a)\) the velocity of the target ball after the collision, and \((b)\) the mass of the target ball.

(II) Determine the fraction of kinetic energy lost by a neutron \((m_1=1.01~ u)\) when it collides head-on and elastically with a target particle at rest which is \((a)~ _1^1 \mathrm H~ (m=1.01~ u)\); \((b)~ _1^2\mathrm H\) (heavy hydrogen, \(m=2.01~ \mathrm u\)); \((c)~_6^{12}\mathrm C~ (m=12.00~ \mathrm u)\); \((d)~_{82}^{208} \mathrm {Pb}\) (lead, \(m=208~ \mathrm u\)). Equation Transcription: Text Transcription: (m_1=1.01 u) (a) _1^1H (m=1.01 u) (b) _1^2H m=2.01 u (c)_6^{12}C (m=12.00 u) (d)_{82}^{208}Pb m=208 u

In a ballistic pendulum experiment, projectile 1 results in a maximum height h of the pendulum equal to 2.6 cm. A second projectile (of the same mass) causes the pendulum to swing twice as high, The second projectile was how many times faster than the first?

(II) \((a)\) Derive a formula for the fraction of kinetic energy lost, \(\Delta \mathrm {KE/KE}\), in terms of \(m\) and \(M\) for the ballistic pendulum collision of Example 7–9. \((b)\) Evaluate for \(m=18.0\) g and \(M=380\) g. Equation Transcription: Text Transcription: Delta KE/KE m=18.0 M=380

A 28-g rifle bullet traveling embeds itself in a 3.1-kg pendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine the vertical and horizontal components of the pendulums maximum displacement

An internal explosion breaks an object, initially at rest, into two pieces, one of which has 1.5 times the mass of the other. If 5500 J is released in the explosion, how much kinetic energy does each piece acquire?

A 980-kg sports car collides into the rear end of a 2300-kg SUV stopped at a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.6 m before stopping. The police officer, estimating the coefficient of kinetic friction between tires and road to be 0.80, calculates the speed of the sports car at impact. What was that speed?

You drop a 14-g ball from a height of 1.5 m and it only bounces back to a height of 0.85 m. What was the total impulse on the ball when it hit the floor? (Ignore air resistance.)

Car A hits car B (initially at rest and of equal mass) from behind while going Immediately after the collision, car B moves forward at and car A is at rest. What fraction of the initial kinetic energy is lost in the collision?

A wooden block is cut into two pieces, one with three times the mass of the other. A depression is made in both faces of the cut, so that a firecracker can be placed in it with the block reassembled. The reassembled block is set on a rough-surfaced table, and the fuse is lit. When the firecracker explodes inside, the two blocks separate and slide apart. What is the ratio of distances each block travels?

A 144-g baseball moving strikes a stationary 5.25-kg brick resting on small rollers so it moves without significant friction. After hitting the brick, the baseball bounces straight back, and the brick moves forward at (a) What is the baseballs speed after the collision? (b) Find the total kinetic energy before and after the collision

A pendulum consists of a mass M hanging at the bottom end of a massless rod of length which has a frictionless pivot at its top end. A mass m, moving as shown in Fig. 735 with velocity v, impacts M and becomes embedded. What is the smallest value of v sufficient to cause the pendulum (with embedded mass m) to swing clear over the top of its arc?

(III) A bullet of mass \(m=0.0010\) kg embeds itself in a wooden block with mass \(M=0.999\) kg which then compresses a spring \((k=140~ \mathrm{N/m})\) by a distance \(x=0.050~ \mathrm m\) before coming to rest. The coefficient of kinetic friction between the block and table is \(\mu=0.50\). \((a)\) What is the initial velocity (assumed horizontal) of the bullet? \((b)\) What fraction of the bullet’s initial kinetic energy is dissipated (in damage to the wooden block, rising temperature, etc.) in the collision between the bullet and the block? Equation Transcription: Text Transcription: m=0.0010 kg M=0.999 kg (k=140 N/m) x=0.050 m mu=0.50

Billiard ball A of mass moving with speed strikes ball B, initially at rest, of mass As a result of the collision, ball A is deflected off at an angle of 30.0 with a speed (a) Taking the x axis to be the original direction of motion of ball A, write down the equations expressing the conservation of momentum for the components in the x and y directions separately. (b) Solve these equations for the speed, and angle, of ball B after the collision. Do not assume the collision is elastic

A radioactive nucleus at rest decays into a second nucleus, an electron, and a neutrino. The electron and neutrino are emitted at right angles and have momenta of and respectively. Determine the magnitude and the direction of the momentum of the second (recoiling) nucleus.

(III) Billiard balls A and B, of equal mass, move at right angles and meet at the origin of an \(xy\) coordinate system as shown in Fig. 7–36. Initially ball A is moving along the y axis at +2.0 m/s, and ball B is moving to the right along the \(x\) axis with speed +3.7 m/s. After the collision (assumed elastic), ball B is moving along the positive \(y\) axis (Fig. 7–36) with velocity \(v^\prime_\mathrm B\). What is the final direction of ball A, and what are the speeds of the two balls? Equation Transcription: Text Transcription: v'_B v'_B v_B=3.7 m/s v_A=2.0 m/s

(III) An atomic nucleus of mass m traveling with speed v collides elastically with a target particle of mass 2m (initially at rest) and is scattered at \(90^{\circ}\). (a) At what angle does the target particle move after the collision? (b) What are the final speeds of the two particles? (c) What fraction of the initial kinetic energy is transferred to the target particle?

A neon atom makes a perfectly elastic collision with another atom at rest. After the impact, the neon atom travels away at a 55.6 angle from its original direction and the unknown atom travels away at a angle. What is the mass (in u) of the unknown atom? [Hint: You could use the law of sines.]

The distance between a carbon atom and an oxygen atom in the CO molecule is How far from the carbon atom is the center of mass of the molecule?

Find the center of mass of the three-mass system shown in Fig. 737 relative to the 1.00-kg mass.

The CM of an empty 1250-kg car is 2.40 m behind the front of the car. How far from the front of the car will the CM be when two people sit in the front seat 2.80 m from the front of the car, and three people sit in the back seat 3.90 m from the front? Assume that each person has a mass of 65.0 kg.

Three cubes, of side and are placed next to one another (in contact) with their centers along a straight line as shown in Fig. 738. What is the position, along this line, of the CM of this system? Assume the cubes are made of the same uniform material

(II) A (lightweight) pallet has a load of ten identical cases of tomato paste (see Fig. 7–39), each of which is a cube of length \(\ell\). Find the center of gravity in the horizontal plane, so that the crane operator can pick up the load without tipping it.

Determine the CM of the uniform thin L-shaped construction brace shown in Fig. 740.

A uniform circular plate of radius 2R has a circular hole of radius R cut out of it. The center of the smaller circle is a distance 0.80R from the center C of the larger circle, Fig. 741. What is the position of the center of mass of the plate? [Hint: Try subtraction.]

Assume that your proportions are the same as those in Table 71, and calculate the mass of one of your legs

Determine the CM of an outstretched arm using Table 71.

Use Table 71 to calculate the position of the CM of an arm bent at a right angle. Assume that the person is 155 cm tal

When a high jumper is in a position such that his arms and lower legs are hanging vertically, and his thighs, trunk, and head are horizontal just above the bar, estimate how far below the torsos median line the CM will be. Will this CM be outside the body? Use Table 71.

Repeat Problem 59 assuming the body bends at the hip joint by about 15. Estimate, using Fig. 727 as a model.

The masses of the Earth and Moon are and respectively, and their centers are separated by (a) Where is the CM of the EarthMoon system located? (b) What can you say about the motion of the EarthMoon system about the Sun, and of the Earth and Moon separately about the Sun?

A mallet consists of a uniform cylindrical head of mass 2.30 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 742. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory

A 52-kg woman and a 72-kg man stand 10.0 m apart on nearly frictionless ice. (a) How far from the woman is their CM? (b) If each holds one end of a rope, and the man pulls on the rope so that he moves 2.5 m, how far from the woman will he be now? (c) How far will the man have moved when he collides with the woman?

Suppose that in Example 714 (Fig. 728), (a) Where then would land?

Two people, one of mass 85 kg and the other of mass 55 kg, sit in a rowboat of mass 58 kg. With the boat initially at rest, the two people, who have been sitting at opposite ends of the boat, 3.0 m apart from each other, now exchange seats. How far and in what direction will the boat move?

A huge balloon and its gondola, of mass M, are in the air and stationary with respect to the ground. A passenger, of mass m, then climbs out and slides down a rope with speed v, measured with respect to the balloon. With what speed and direction (relative to Earth) does the balloon then move? What happens if the passenger stops?

Two astronauts, one of mass 55 kg and the other 85 kg, are initially at rest together in outer space. They then push each other apart. How far apart are they when the lighter astronaut has moved 12 m?

Two asteroids strike head-on: before the collision, asteroid A has velocity and asteroid B has velocity in the opposite direction. If the asteroids stick together, what is the velocity (magnitude and direction) of the new asteroid after the collision

A ball is dropped from a height of 1.60 m and rebounds to a height of 1.20 m. Approximately how many rebounds will the ball make before losing 90% of its energy?

A 4800-kg open railroad car coasts at a constant speed of on a level track. Snow begins to fall vertically and fills the car at a rate of Ignoring friction with the tracks, what is the cars speed after 60.0 min? (See Section 72.)

Two bumper cars in an amusement park ride collide elastically as one approaches the other directly from the rear (Fig. 743). Car A has a mass of 435 kg and car B 495 kg, owing to differences in passenger mass. If car A approaches at and car B is moving at calculate (a) their velocities after the collision, and (b) the change in momentum of each.

A gun fires a bullet vertically into a 1.40-kg block of wood at rest on a thin horizontal sheet, Fig. 744. If the bullet has a mass of 25.0 g and a speed of how high will the block rise into the air after the bullet becomes embedded in it?

You have been hired as an expert witness in a court case involving an automobile accident. The accident involved car A of mass 1500 kg which crashed into stationary car B of mass 1100 kg. The driver of car A applied his brakes 15 m before he skidded and crashed into car B. After the collision, car A slid 18 m while car B slid 30 m. The coefficient of kinetic friction between the locked wheels and the road was measured to be 0.60. Show that the driver of car A was exceeding the speed limit before applying the brakes.

A meteor whose mass was about struck the Earth with a speed of about and came to rest in the Earth. (a) What was the Earths recoil speed (relative to Earth at rest before the collision)? (b) What fraction of the meteors kinetic energy was transformed to kinetic energy of the Earth? (c) By how much did the Earths kinetic energy change as a result of this collision?

A 28-g bullet strikes and becomes embedded in a 1.35-kg block of wood placed on a horizontal surface just in front of the gun. If the coefficient of kinetic friction between the block and the surface is 0.28, and the impact drives the block a distance of 8.5 m before it comes to rest, what was the muzzle speed of the bullet?

You are the design engineer in charge of the crashworthiness of new automobile models. Cars are tested by smashing them into fixed, massive barriers at A new model of mass 1500 kg takes 0.15 s from the time of impact until it is brought to rest. (a) Calculate the average force exerted on the car by the barrier. (b) Calculate the average deceleration of the car in gs

A 0.25-kg skeet (clay target) is fired at an angle of 28 to the horizontal with a speed of (Fig. 745). When it reaches the maximum height, h, it is hit from below by a 15-g pellet traveling vertically upward at a speed of The pellet is embedded in the skeet. (a) How much higher, does the skeet go up? (b) How much extra distance, does the skeet travel because of the collision?

Two balls, of masses and are suspended as shown in Fig. 746. The lighter ball is pulled away to a 66 angle with the vertical and released. (a) What is the velocity of the lighter ball before impact? (b) What is the velocity of each ball after the elastic collision? (c) What will be the maximum height of each ball after the elastic collision?

A block of mass slides down a 30.0 incline which is 3.60 m high. At the bottom, it strikes a block of mass which is at rest on a horizontal surface, Fig. 747. (Assume a smooth transition at the bottom of the incline.) If the collision is elastic, and friction can be ignored, determine (a) the speeds of the two blocks after the collision, and (b) how far back up the incline the smaller mass will go

The space shuttle launches an 850-kg satellite by ejecting it from the cargo bay. The ejection mechanism is activated and is in contact with the satellite for 4.8 s to give it a velocity of in the x direction relative to the shuttle. The mass of the shuttle is 92,000 kg. (a) Determine the component of velocity of the shuttle in the minus x direction resulting from the ejection. (b) Find the average force that the shuttle exerts on the satellite during the ejection.

Astronomers estimate that a 2.0-km-diameter asteroid collides with the Earth once every million years. The collision could pose a threat to life on Earth. (a) Assume a spherical asteroid has a mass of 3200 kg for each cubic meter of volume and moves toward the Earth at How much destructive energy could be released when it embeds itself in the Earth? (b) For comparison, a nuclear bomb could release about How many such bombs would have to explode simultaneously to release the destructive energy of the asteroid collision with the Earth?

An astronaut of mass 210 kg including his suit and jet pack wants to acquire a velocity of to move back toward his space shuttle. Assuming the jet pack can eject gas with a velocity of what mass of gas will need to be ejected?

Two blocks of mass and resting on a frictionless table, are connected by a stretched spring and then released (Fig. 748). (a) Is there a net external force on the system before release? (b) Determine the ratio of their speeds, (c) What is the ratio of their kinetic energies? (d) Describe the motion of the CM of this system. Ignore mass of spring

A golf ball rolls off the top of a flight of concrete steps of total vertical height 4.00 m. The ball hits four times on the way down, each time striking the horizontal part of a different step 1.00 m lower. If all collisions are perfectly elastic, what is the bounce height on the fourth bounce when the ball reaches the bottom of the stairs

A massless spring with spring constant k is placed between a block of mass m and a block of mass 3m. Initially the blocks are at rest on a frictionless surface and they are held together so that the spring between them is compressed by an amount D from its equilibrium length. The blocks are then released and the spring pushes them off in opposite directions. Find the speeds of the two blocks when they detach from the spring

A novice pool player is faced with the corner pocket shot shown in Fig. 749. Relative dimensions are also shown. Should the player worry that this might be a scratch shot, in which the cue ball will also fall into a pocket? Give details. Assume equal-mass balls and an elastic collision.Ignore spin

Problem 1COQ 1. A railroad car loaded with rocks coasts on a level track without friction. A worker at the back of the car starts throwing the rocks horizontally backward from the car. Then what happens? (a) The car slows down. (b) The car speeds up. (c) First the car speeds up and then it slows down. (d) The car’s speed remains constant. (e) None of these.

Problem 1MCQ A truck going 15 km/h has a head-on collision with a small car going 30 km/h. Which statement best describes the situation? (a) The truck has the greater change of momentum because it has the greater mass. (b) The car has the greater change of momentum because it has the greater speed. (c) Neither the car nor the truck changes its momentum in the collision because momentum is conserved. (d) They both have the same change in magnitude of momentum because momentum is conserved. (e) None of the above is necessarily true.

Problem 1P (I) What is the magnitude of the momentum of a 28-g sparrow flying with a speed of 8.4 m/s?

Problem 1Q We claim that momentum is conserved. Yet most moving objects eventually slow down and stop. Explain.

Problem 2COQ Which answer would you choose if the rocks fall out through a hole in the floor of the car, one at a time?

Problem 2MCQ A small boat coasts at constant speed under a bridge. A heavy sack of sand is dropped from the bridge onto the boat. The speed of the boat (a) increases. (b) decreases. (c) does not change. (d)Without knowing the mass of the boat and the sand, we can’t tell.

Problem 2P (I) A constant friction force of 25 N acts on a 65-kg skier for 15 s on level snow. What is the skier’s change in velocity?

Problem 2Q A light object and a heavy object have the same kinetic energy. Which has the greater momentum? Explain.

Problem 3MCQ Two identical billiard balls traveling at the same speed have a head-on collision and rebound. If the balls had twice the mass, but maintained the same size and speed, how would the rebound be different? (a) At a higher speed. (b) At slower speed. (c) No difference.

Problem 3P (I) A 7150-kg railroad car travels alone on a level frictionless track with a constant speed of 15.0 m/s. A 3350-kg load, initially at rest, is dropped onto the car. What will be the car’s new speed?

Problem 3Q When a person jumps from a tree to the ground, what happens to the momentum of the person upon striking the ground?

In a physics lab, a cube slides down a frictionless incline as shown in Fig. 7-50 and elastically strikes another cube at the bottom that is only one-half its mass. If the incline is 35 cm high and the table is 95 cm off the floor, where does each cube land? [Hint: Both leave the incline moving horizontally.] FIGURE 7-50 Search and Learn 3.

Problem 4MCQ An astronaut is a short distance away from her space station without a tether rope. She has a large wrench. What should she do with the wrench to move toward the space station? (a) Throw it directly away from the space station. (b) Throw it directly toward the space station. (c) Throw it toward the station without letting go of it. (d) Throw it parallel to the direction of the station’s orbit. (e) Throw it opposite to the direction of the station’s orbit.

Problem 4P (I) A 110-kg tackler moving at 2.5 m/s meets head-on (and holds on to) an 82-kg halfback moving at 5.0 m/s. What will be their mutual speed immediately after the collision?

Problem 4Q When you release an inflated but untied balloon, why does it fly across the room?

The gravitational slingshot effect. Figure 7–51 shows the planet Saturn moving in the negative x direction at its orbital speed (with respect to the Sun) of 9.6 km/s. The mass of Saturn is \(5.69 \times 10^{26}\ kg\). A spacecraft with mass 825 kg approaches Saturn. When far from Saturn, it moves in the +x direction at 10.4 km/s. The gravitational attraction of Saturn (a conservative force) acting on the spacecraft causes it to swing around the planet (orbit shown as dashed line) and head off in the opposite direction. Estimate the final speed of the spacecraft after it is far enough away to be considered free of Saturn’s gravitational pull.

Problem 5MCQ A space vehicle, in circular orbit around the Earth, collides with a small asteroid which ends up in the vehicle’s storage bay. For this collision, (a) only momentum is conserved. (b) only kinetic energy is conserved. (c) both momentum and kinetic energy are conserved. (d) neither momentum nor kinetic energy is conserved.

Problem 5P (II) Calculate the force exerted on a rocket when the propelling gases are being expelled at a rate of 1300 kg/s with a speed of 4.5 X 104 m/s.

Problem 5Q Explain, on the basis of conservation of momentum, how a fish propels itself forward by swishing its tail back and forth.

Take the general case of an object of mass \(m_{A}\) and velocity \(v_{A}\) elastically striking a stationary \(\left(v_{B}=0\right)\) object of mass \(m_{B}\) head-on. (a) Show that the final velocities \(v_{A}^{\prime}\) and \(v_{B}^{\prime}\) are given by \(v_{A}^{\prime}=\left(\frac{m_{A}-m_{B}}{m_{A}+m_{B}}\right) v_{A}\), \(v_{B}^{\prime}=\left(\frac{2 m_{A}}{m_{A}+m_{B}}\right) v_{A}\). (b) What happens in the extreme case when \(m_{A}\) is much smaller than \(m_{B}\)? Cite a common example of this (c) What happens in the extreme case when \(m_{A}\) is much larger than \(m_{B}\)? Cite a common example of this. What happens in the case when \(m_{A}=m_{B}\)? Cite a common example. ________________ Equation Transcription: Text Transcription: m_A v_A (v_B=0) m_B v'_A v'_B v'_A=({m_A-m_B} over {m_A+m_B})v_A v'_B=({2m_A} over {m_A+m_B})v_A m_A m_B m_A m_B m_A=m_B

Problem 6MCQ A golf ball and an equal-mass bean bag are dropped from the same height and hit the ground. The bean bag stays on the ground while the golf ball rebounds. Which experiences the greater impulse from the ground? (a) The golf ball. (b) The bean bag. (c) Both the same. (d) Not enough information.

Problem 6P (II) A 7700-kg boxcar traveling 14 m/s strikes a second car at rest. The two stick together and move off with a speed of 5.0 m/s. What is the mass of the second car?

Problem 7EA Can a small sports car ever have the same momentum as a large sport-utility vehicle with three times the sports car’s mass? Explain.

EXERCISE B If the water splashes back from the car in Example 7-2, would the force on the car be larger or smaller?

EXERCISE C In Example 7-3, \(m_{A}=m_{B}\), so in the last equation, \(m_{A} /\left(m_{A}+m_{B}\right)=\frac{1}{2}\). Hence \(v^{\prime}=\frac{1}{2} v_{A}\). What result do you get if (a) \(m_{B}=3 m_{A}\), (b) \(m_{B}\) is much larger than \(m_{A}\left(m_{B} \gg m_{A}\right)\), and (c) \(m_{B} \ll m_{A}\)? ________________ Equation Transcription: Text Transcription: m_{A}=m_{B} m_{A}/(m_{A}+m_{B})={1}over{2} v’={1}over{2} v_{A} m_{B}=3 m_{A} m_{B} m_{A}(m_{B} >> m_{A}) m_{B} << m_{A}

Problem 7ED A 50-kg child runs off a dock at 2.0m/s (horizontally) and lands in a waiting rowboat of mass 150 kg. At what speed does the rowboat move away from the dock?

Problem 7EE Return to the Chapter-Opening Questions, page 170, and answer them again now. Try to explain why you may have answered differently the first time. CHAPTER-OPENING QUESTIONS 1. A railroad car loaded with rocks coasts on a level track without friction. A worker at the back of the car starts throwing the rocks horizontally backward from the car. Then what happens? (a) The car slows down. (b) The car speeds up. (c) First the car speeds up and then it slows down. (d) The car’s speed remains constant. (e) None of these. 2. Which answer would you choose if the rocks fall out through a hole in the floor of the car, one at a time?

EXERCISE F Suppose Fig. 7-9 shows the force on a golf ball vs. time during the time interval when the ball hits a wall. How would the shape of this curve change if a softer rubber ball with the same mass and speed hit the same wall?

EXERCISE G Calculate the CM of the three people in Example , taking the origin at the driver (\(x_{C}=0\)) on the right. Is the physical location of the the same? Note that the coordinates of the CM depend on the reference frame or coordinate system chosen. But the physical location of the is independent of that choice. If the particles are spread out in two or three dimensions, then we must specify not only the coordinate of the CM \(\left(x_{C M}\right)\), but also the and coordinates, which will be given by formulas like Eq. . For example, the coordinate of the will be \(y_{C M}=\frac{m_{A} y_{A}+m_{B} y_{B}+\cdots}{m_{A}+m_{B}+\cdots}=\frac{m_{A} y_{A}+m_{B} y_{B}+\cdots}{M}\) (7-9b) where is the total mass of all the particles. A concept similar to center of mass is center of gravity (CG). An object’s CG is that point at which the force of gravity can be considered to act. The force of gravity actually acts on all the different parts or particles of an object, but for purposes of determining the translational motion of an object as a whole, we can assume that the entire weight of the object (which is the sum of the weights of all its parts) acts at the CG. There is a conceptual difference between the center of gravity and the center of mass, but for nearly all practical purposes, they are at the same point.† It is often easier to determine the CM or CG of an extended object experimentally rather than analytically. If an object is suspended from any point, it will swing (Fig. 7–24) due to the force of gravity on it, unless it is placed so its CG lies on a vertical line directly below the point from which it is suspended. If the object is two dimensional, or has a plane of symmetry, it need only be hung from two different pivot points and the respective vertical (plumb) lines drawn. Then the center of gravity will be at the intersection of the two lines, as in Fig. 7–25. If the object doesn’t have a plane of symmetry, the CG with respect to the third dimension is found by suspending the object from at least three points whose plumb lines do not lie in the same plane. For symmetrically shaped objects such as uniform cylinders (wheels), spheres, and rectangular solids, the CM is located at the geometric center of the object. To locate the center of mass of a group of extended objects, we can use Eqs. 7–9, where the m’s are the masses of these objects and the x’s, y’s, and z’s are the coordinates of the CM of each of the objects. FIGURE 7-24 The force of gravity, considered to act at the CG, causes this object to rotate about the pivot point; if the CG were on a vertical line directly below the pivot, the object would remain at rest. FIGURE 7-25 Finding the CG ________________ Equation Transcription: Text Transcription: x_{C}=0 (x_{C M}) y_{C M}={m_{A} y_{A}+m_{B} y_{B}+cdots} over {m_{A}+m_{B}+\cdots}= {m_{A} y_{A}+m_{B} y_{B}+\cdots} over {M} m vector{g}

Problem 7EH A woman stands up in a rowboat and walks from one end of the boat to the other. How does the boat move, as seen from the shore?

Problem 7MCQ You are lying in bed and want to shut your bedroom door. You have a bouncy ball and a blob of clay, both with the same mass. Which one would be more effective to throw at your door to close it? (a) The superball. (b) The blob of clay. (c) Both the same. (d) Neither will work.

(II) A child in a boat throws a 5.30-kg package out horizontally with a speed of \(\text {10.0 m/s}\), Fig. 7-31. Calculate the velocity of the boat immediately after, assuming it was initially at rest. The mass of the child is 24.0 kg and the mass of the boat is 35.0 kg. ________________ Equation Transcription: Text Transcription: 10.0 m/s v=10.0 m/s

According to Eq. 7-4, the longer the impact time of an impulse, the smaller the force can be for the same momentum change, and hence the smaller the deformation of the object on which the force acts. On this basis, explain the value of air bags, which are intended to inflate during an automobile collision and reduce the possibility of fracture or death.

Problem 8MCQ A baseball is pitched horizontally toward home plate with a velocity of 110 km h. In which of the following scenarios does the change in momentum of the baseball have the largest magnitude? (a) The catcher catches the ball. (b) The ball is popped straight up at a speed of 110 km h. (c) The baseball is hit straight back to the pitcher at a speed of 110 km h. (d) Scenarios (a) and (b) have the same change in momentum. (e) Scenarios (a), (b), and (c) have the same change in momentum.

Problem 8P (II) An atomic nucleus at rest decays radioactively into an alpha particle and a different nucleus. What will be the speed of this recoiling nucleus if the speed of the alpha particle is 2.8 X 105Assume the recoiling nucleus has a mass 57 times greater than that of the alpha particle.

Problem 8Q If a falling ball were to make a perfectly elastic collision with the floor, would it rebound to its original height? Explain.

Problem 9MCQ A small car and a heavy pickup truck are both out of gas. The truck has twice the mass of the car. After you push first the car and then the truck for the same amount of time with the same force, what can you say about the momentum and kinetic energy (KE) of the car and the truck? Ignore friction. (a) They have the same momentum and the same KE. (b) The car has more momentum and more KE than the truck. (c) The truck has more momentum and more KE than the car. (d) They have the same momentum, but the car has more kinetic energy than the truck. (e) They have the same kinetic energy, but the truck has more momentum than the car.

Problem 9P (II) An atomic nucleus initially moving at 320 m/s emits an alpha particle in the direction of its velocity, and the remaining nucleus slows to 280 m/s. If the alpha particle has a mass of 4.0 u and the original nucleus has a mass of 222 u, what speed does the alpha particle have when it is emitted?

Problem 9Q A boy stands on the back of a rowboat and dives into the water. What happens to the boat as he leaves it? Explain.

Choose the best answer in the previous Question (# 9) but now assume that you push both the car and the truck for the \(same~distance\) with the same force. [\(Hint\): See also Chapter 6.] A small car and a heavy pickup truck are both out of gas. The truck has twice the mass of the car. After you push first the car and then the truck for the \(same~ amount~ of~ time\) with the same force, what can you say about the momentum and kinetic energy (KE) of the car and the truck? Ignore friction. \((a)\) They have the same momentum and the same KE. \((b)\) The car has more momentum and more KE than the truck. \((c)\) The truck has more momentum and more KE than the car. \((d)\) They have the same momentum, but the car has more kinetic energy than the truck. \((e)\) They have the same kinetic energy, but the truck has more momentum than the car.

Problem 12P (III) A 0.145-kg baseball pitched horizontally at 27.0 m/s strikes a bat and pops straight up to a height of 31.5 m. If the contact time between bat and ball is 2.5 ms, calculate the average force between the ball and bat during contact.

Problem 12Q Is it possible for an object to receive a larger impulse from a small force than from a large force? Explain.

Problem 11MCQ A railroad tank car contains milk and rolls at a constant speed along a level track. The milk begins to leak out the bottom. The car then (a) slows down. (b) speeds up. (c) maintains a constant speed. (d) Need more information about the rate of the leak.

Problem 11P (II) A 22-g bullet traveling 240 m/s penetrates a 2.0-kg block of wood and emerges going 150 m/s. If the block is stationary on a frictionless surface when hit, how fast does it move after the bullet emerges?

Problem 11Q The speed of a tennis ball on the return of a serve can be just as fast as the serve, even though the racket isn’t swung very fast. How can this be?

A bowling ball hangs from a 1.0-m-long cord, Fig. 7-30: (i) A 200-gram putty ball moving \(\text {5.0 m/s}\) hits the bowling ball and sticks to it, causing the bowling ball to swing up; (ii) a 200-gram rubber ball moving \(\text {5.0 m/s}\) hits the bowling ball and bounces straight back at nearly \(\text {5.0 m/s}\) causing the bowling ball to swing up. Describe what happens. (a) The bowling ball swings up by the same amount in both (i) and (ii). (b) The ball swings up farther in (i) than in (ii). (c) The ball swings up farther in (ii) than in (i). (d) Not enough information is given; we need the contact time between the rubber ball and the bowling ball. ________________ Equation Transcription: Text Transcription: 5.0 m/s 5.0 m/s 5.0 m/s

Problem 13P (III) Air in a 120-km/h wind strikes head-on the face of a building 45 m wide by 75 m high and is brought to rest. If air has a mass of 1.3 kg per cubic meter, determine the average force of the wind on the building.

Problem 13Q In a collision between two cars, which would you expect to be more damaging to the occupants: if the cars collide and remain together, or if the two cars collide and rebound backward? Explain.

Problem 14P (III) A 725-kg two-stage rocket is traveling at a speed of 6.60 X 103 m/s away from Earth when a predesigned explosion separates the rocket into two sections of equal mass that then move with a speed of 2.80 X 103 m/s relative to each other along the original line of motion. (a) What is the speed and direction of each section (relative to Earth) after the explosion? (b) How much energy was supplied by the explosion? [Hint:What is the change in kinetic energy as a result of the explosion?]

Problem 14Q A very elastic “superball” is dropped from a height h onto a hard steel plate (fixed to the Earth), from which it rebounds at very nearly its original speed. (a) Is the momentum of the ball conserved during any part of this process? (b) If we consider the ball and the Earth as our system, during what parts of the process is momentum conserved? (c) Answer part (b) for a piece of putty that falls and sticks to the steel plate.

Problem 15P (I) A 0.145-kg baseball pitched at 31.0 m/s is hit on a horizontal line drive straight back at the pitcher at 46.0 m/s If the contact time between bat and ball is 5.00 X 20-3 s. calculate the force (assumed to be constant) between the ball and bat.

Problem 15Q 15. Cars used to be built as rigid as possible to withstand collisions. Today, though, cars are designed to have “crumple zones” that collapse upon impact. What is the advantage of this new design?

Problem 16P (II) A golf ball of mass 0.045 kg is hit off the tee at a speed Of 38 m/s. The golf club was in contact with the ball for 3.5 X 10-3 s. Find (a) the impulse imparted to the golf ball, and (b) the average force exerted on the ball by the golf club.

Problem 16Q At a hydroelectric power plant, water is directed at high speed against turbine blades on an axle that turns an electric generator. For maximum power generation, should the turbine blades be designed so that the water is brought to a dead stop, or so that the water rebounds?

Problem 17P (II) A 12-kg hammer strikes a nail at a velocity of 7.5 m/s and comes to rest in a time interval of 8.0 ms. (a) What is the impulse given to the nail? (b) What is the average force acting on the nail?

A squash ball hits a wall at a \(45^\circ\) angle as shown in Fig. 7-29. What is the direction (a) of the change in momentum of the ball, (b) of the force on the wall? ________________ Equation Transcription: Text Transcription: 45^o

(II) A tennis ball of mass \(m=0.060 \mathrm{\ kg}\) and speed \(v=28 \mathrm{\ m} / \mathrm{s}\) strikes a wall at a \(45^{\circ}\) angle and rebounds with the same speed at \(45^{\circ}\) (Fig. 7-32). What is the impulse (magnitude and direction) given to the ball? FIGURE 7-32 Problem 18. ________________ Equation Transcription: Text Transcription: m=0.060 kg v=28 m/s 45^o 45^o 45^o 45^o

Why can a batter hit a pitched baseball farther than a ball he himself has tossed up in the air?

Problem 19P (II) A 125-kg astronaut (including space suit) acquires a speed of 2.50 m/s by pushing off with her legs from a 1900-kg space capsule. (a) What is the change in speed of the space capsule? (b) If the push lasts 0.600 s, what is the average force exerted by each on the other? As the reference frame, use the position of the capsule before the push. (c) What is the kinetic energy of each after the push?

Describe a collision in which all kinetic energy is lost.

Problem 20P (II) Rain is falling at the rate of 2.5 cm/h and accumulates in a pan. If the raindrops hit at estimate the force on the bottom of a 1.0 m2 pan due to the impacting rain which we assume does not rebound. Water has a mass of 1.00 X 103 kg per m3

Problem 20Q If a 20-passenger plane is not full, sometimes passengers are told they must sit in certain seats and may not move to empty seats. Why might this be?

Problem 21P (II) A 95-kg fullback is running at 3.0 m/s to the east and is stopped in 0.85 s by a head-on tackle by a tackler running due west. Calculate (a) the original momentum of the fullback, (b) the impulse exerted on the fullback, (c) the impulse exerted on the tackler, and (d) the average force exerted on the tackler.

Problem 21Q Why do you tend to lean backward when carrying a heavy load in your arms?

(II) With what impulse does a 0.50-kg newspaper have to be thrown to give it a velocity of 3.0 m/s?

Problem 22Q Why is the CM of a 1-m length of pipe at its midpoint, whereas this is not true for your arm or leg?

(III) Suppose the force acting on a tennis ball (mass 0.060 kg) points in the \(+x\) direction and is given by the graph of Fig. 7–33 as a function of time. (a) Use graphical methods (count squares) to estimate the total impulse given the ball. (b) Estimate the velocity of the ball after being struck, assuming the ball is being served so it is nearly at rest initially. [Hint: See Section 6–2.] FIGURE 7-33 Problem 23. ________________ Equation Transcription: Text Transcription: +x F(N)t(s)

How can a rocket change direction when it is far out in space and essentially in a vacuum?

(III) (a) Calculate the impulse experienced when a 55-kg person lands on firm ground after jumping from a height of 2.8 m. (b) Estimate the average force exerted on the person’s feet by the ground if the landing is stiff-legged, and again (c) with bent legs. With stiff legs, assume the body moves 1.0 cm during impact, and when the legs are bent, about 50 cm. [Hint: The average net force on him, which is related to impulse, is the vector sum of gravity and the force exerted by the ground. See Fig. 7–34.] We will see in Chapter 9 that the force in (b) exceeds the ultimate strength of bone (Table 9–2). FIGURE 7-34 Problem 24. ________________ Equation Transcription: Text Transcription: m vector{g} vector{F}_grd

Problem 24Q Bob and Jim decide to play tug-of-war on a frictionless (icy) surface. Jim is considerably stronger than Bob, but Bob weighs 160 lb whereas Jim weighs 145 lb. Who loses by crossing over the midline first? Explain.

Problem 25P (II) A ball of mass 0.440 kg moving east (+ X direction) with a speed 3.80 m/s of collides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed and direction of each ball after the collision?

In one type of nuclear radioactive decay, an electron and a recoil nucleus are emitted but often do not separate along the same line. Use conservation of momentum in two dimensions to explain why this implies the emission of at least one other particle (it came to be called a “neutrino”).

Problem 26P (II) A 0.450-kg hockey puck, moving east with a speed of 5.80 m/s has a head-on collision with a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision, what will be the speed and direction of each puck after the collision?

Problem 26Q Show on a diagram how your CM shifts when you move from a lying position to a sitting position.

Problem 27P (II) A 0.060-kg tennis ball, moving with a speed of 5.50 m/s, has a head-on collision with a 0.090-kg ball initially moving in the same direction at a speed of 3.00 m/s. Assuming a perfectly elastic collision, determine the speed and direction of each ball after the collision.

Problem 27Q If only an external force can change the momentum of the center of mass of an object, how can the internal force of the engine accelerate a car?

Problem 28P (II) Two billiard balls of equal mass undergo a perfectly elastic head-on collision. If one ball’s initial speed was 2.00 m/s, and the other’s was 3.60 m/s in the opposite direction, what will be their speeds and directions after the collision?

Problem 29P (II) A 0.280-kg croquet ball makes an elastic head-on collision with a second ball initially at rest. The second ball moves off with half the original speed of the first ball. (a) What is the mass of the second ball? (b) What fraction of the original kinetic energy (? KE/KE) gets transferred to the second ball?

Problem 30P (II) A ball of mass m makes a head-on elastic collision with a second ball (at rest) and rebounds with a speed equal to 0.450 its original speed. What is the mass of the second ball?

Problem 31P (II) A ball of mass 0.220 kg that is moving with a speed Of 5.5 m/s collides head-on and elastically with another ball initially at rest. Immediately after the collision, the incoming ball bounces backward with a speed of 3.8 m/s. Calculate (a) the velocity of the target ball after the collision, and (b) the mass of the target ball.

(II) Determine the fraction of kinetic energy lost by a neutron \(\left(m_{1}=1.01 u\right)\) when it collides head-on and elastically with a target particle at rest which is () \({ }_{1}^{1} H\) \((m=1.01\mathrm{\ u})\); (b) \({ }_{1}^{2} H\) (heavy hydrogen, \(m=2.01\mathrm{\ u}\)); (c) \({ }_{6}^{12} C\) \((m=12.00\ \mathrm u)\); (d) \({ }_{82}^{208} \mathrm{~Pb}\) (lead, \(m=208\ \mathrm u\)). ________________ Equation Transcription: Text Transcription: (m_{1}=1.01 u) _1 ^1H (m=1.01 u) _1 ^2H m=2.01 u _6 ^12C (m=12.00 u) _82 ^208Pb m=208 u

Problem 33P (I) In a ballistic pendulum experiment, projectile 1 results in a maximum height h of the pendulum equal to 2.6 cm. A second projectile (of the same mass) causes the pendulum to swing twice as high, h2 =5.2 cm. The second projectile was how many times faster than the first?

(II) (a) Derive a formula for the fraction of kinetic energy lost, \(\mathrm {\Delta K E / K E}\), in terms of and for the ballistic pendulum collision of Example Evaluate for \(m=18.0 \mathrm{\ g}\) and \(M=380 \mathrm{\ g}\). ________________ Equation Transcription: Text Transcription: Delta KE/KE m=18.0 g M=380 g

Problem 36P (II) An internal explosion breaks an object, initially at rest, into two pieces, one of which has 1.5 times the mass of the other. If 5500 J is released in the explosion, how much kinetic energy does each piece acquire?

(II) A 28-g rifle bullet traveling 190 m/s embeds itself in a 3.1-kg pendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine the vertical and horizontal components of the pendulum’s maximum displacement.

Problem 37P (II) A 980-kg sports car collides into the rear end of a 2300-kg SUV stopped at a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.6 m before stopping. The police officer, estimating the coefficient of kinetic friction between tires and road to be 0.80, calculates the speed of the sports car at impact. What was that speed?

Problem 38P (II) You drop a 14-g ball from a height of 1.5 m and it only bounces back to a height of 0.85 m. What was the total impulse on the ball when it hit the floor? (Ignore air resistance.)

Problem 39P Croquet ball A moving at 8.3 m/s makes a head on collision with ball B of equal mass and initially at rest. Immediately after the collision ball B moves forward at 7.1 m/s. What fraction of the initial kinetic energy is lost in the collision?

Problem 40P (II) A wooden block is cut into two pieces, one with three times the mass of the other. A depression is made in both faces of the cut, so that a firecracker can be placed in it with the block reassembled. The reassembled block is set on a rough-surfaced table, and the fuse is lit .When the firecracker explodes inside, the two blocks separate and slide apart. What is the ratio of distances each block travels?

Problem 41P (II) A 144-g baseball moving 28.0 m/s strikes a stationary 5.25-kg brick resting on small rollers so it moves without significant friction. After hitting the brick, the baseball bounces straight back, and the brick moves forward at 1.10 m/s. (a) What is the baseball’s speed after the collision? (b) Find the total kinetic energy before and after the collision.

(III) A pendulum consists of a mass hanging at the bottom end of a massless rod of length \(\ell\), which has a frictionless pivot at its top end. A mass , moving as shown in Fig. with velocity , impacts and becomes embedded. What is the smallest value of sufficient to cause the pendulum (with embedded mass ) to swing clear over the top of its arc? FIGURE 7-35 Problem 42. ________________ Equation Transcription: ? ? Text Transcription: ell ell vector{v}

Problem 44P (II) Billiard ball A of mass mA =0.120 kg moving with Speed vA =2.80 m/s strikes ball B, initially at rest, of Mass mB =0.140 kg. As a result of the collision, ball A is deflected off at an angle of 30.0° with a speed v’A =2.10 m/s. (a) Taking the x axis to be the original direction of motion of ball A, write down the equations expressing the conservation of momentum for the components in the x and y directions separately. (b) Solve these equations for the speed, v’B, and angle, ?’B, of ball B after the collision. Do not assume the collision is elastic.

(III) Billiard balls A and B, of equal mass, move at r angles and mect at the origin of an \(x y \) coordinate system as shown in Fig. 7-36. Initially ball is moving along the axis at \(+2.0 \mathrm{\ m} / \mathrm{s}\), and ball is moving to the right along the axis with speed \(+3.7 \mathrm{\ m} / \mathrm{s}\). After the collision (assumed clastic), ball is moving along the positive axis (Fig. 7-36) with velocity \(v_{B}^{\prime}\). What is the final direction of ball , and what are the speeds of the two balls? FIGURE 7-36 Problem 46. (Ball A after the collision is not shown.) ________________ Equation Transcription: Text Transcription: xy +2.0 m/s +3.7 m/s v'_B +y v'_B v_B=3.7 m/s +x v_A=2.0 m/s

Problem 48P (III) A neon atom (m =20.0 u) makes a perfectly elastic collision with another atom at rest. After the impact, the neon atom travels away at a 55.6° angle from its original direction and the unknown atom travels away at a -50.0° angle. What is the mass (in u) of the unknown atom? [Hint: You could use the law of sines.]

Problem 49P (I) The distance between a carbon atom (m =12 u) and an oxygen atom (m =16 u) in the CO molecule is 1.3 X 10-10 m How far from the carbon atom is the center of mass of the molecule?

(I) Find the center of mass of the three-mass system shown in Fig. 7-37 relative to the 1.00-kg mass.

(II) The CM of an empty 1250-kg car is 2.40 m behind the front of the car. How far from the front of the car will the CM be when two people sit in the front seat 2.80 m from the front of the car, and three people sit in the back seat 3.90 m from the front? Assume that each person has a mass of 65.0 kg.

(II) Three cubes, of side \(\ell_0,\ 2\ell_0\), and \(3 \ell_{0}\), are placed next to one another (in contact) with their centers along a straight line as shown in Fig. What is the position, along this line, of the of this system? Assume the cubes are made of the same uniform material. FIGURE 7-38 Problem 52. ________________ Equation Transcription: ?0, 2?0 3?0 ?0 2?0 3?0 Text Transcription: ell_0, 2 ell_0 3 ell_0 x=0 ell_0 2 ell_0 3 ell_0

(II) A (lightweight) pallet has a load of ten identical cases of tomato paste (see Fig. ), each of which is a cube of length \(\ell\). Find the center of gravity in the horizontal plane, so that the crane operator can pick up the load without tipping it. FIGURE 7-39 Problem 53 ________________ Equation Transcription: ? ? Text Transcription: ell ell

(III) Determine the CM of the uniform thin L-shaped construction brace shown in Fig. 7–40. FIGURE 7-40 Problem 54. This L-shaped object has uniform thickness d (not shown). ________________ Equation Transcription: Text Transcription: CM_A CM_B

(III) A uniform circular plate of radius 2R has a circular hole of radius R cut out of it. The center C’ of the smaller circle is a distance 0.80 R from the center C of the larger circle, Fig. 7-41. What is the position of the center of mass of the plate? [Hint: Try subtraction.]

(I) Determine the CM of an outstretched arm using Table 7-1

(II) Use Table 7-1to calculate the position of the CM of an arm bent at a right angle. Assume that the person is 155 cm tall.

(III) Repeat Problem 59 assuming the body bends at the hip joint by about \(15^{\circ}\). Estimate, using Fig. 7–27 as a model. ________________ Equation Transcription: Text Transcription: 15^o

Problem 61P (II) The masses of the Earth and Moon are 5.98 X 1024 kg And 7.35 X 1022 kg, respectively, and their centers are separated by 3.84 X 108 m. (a) Where is the CMof the Earth–Moon system located? (b) What can you say about the motion of the Earth–Moon system about the Sun, and of the Earth and Moon separately about the Sun?

(II) A mallet consists of a uniform cylindrical head of mass 2.30 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory? FIGURE 7-42 Problem 62.

Problem 63P (II) A 52-kg woman and a 72-kg man stand 10.0 m apart on nearly frictionless ice. (a) How far from the woman is their CM? (b) If each holds one end of a rope, and the man pulls on the rope so that he moves 2.5 m, how far from the woman will he be now? (c) How far will the man have moved when he collides with the woman?

(II) Suppose that in Example 7-14 (Fig. 7-28), \(m_\mathrm{I I}=3 m_\mathrm{I}\). (a) Where then would \(m_\mathrm{I I}\) land? (b) What if \(m_{I}=3 m_\mathrm {I I}\)?

Problem 65P (II) Two people, one of mass 85 kg and the other of mass 55 kg, sit in a rowboat of mass 58 kg. With the boat initially at rest, the two people, who have been sitting at opposite ends of the boat, 3.0 m apart from each other, now exchange seats. How far and in what direction will the boat move?

Problem 66P (III) A huge balloon and its gondola, of mass M, are in the air and stationary with respect to the ground. A passenger, of mass m, then climbs out and slides down a rope with speed v, measured with respect to the balloon. With what speed and direction (relative to Earth) does the balloon then move? What happens if the passenger stops?

Problem 67GP Two astronauts, one of mass 55 kg and the other 85 kg, are initially at rest together in outer space. They then push each other apart. How far apart are they when the lighter astronaut has moved 12 m?

Problem 68GP Two asteroids strike head-on: before the collision, asteroid A (mA = 7.5 x 1012 kg) has velocity 3.3 km/s and asteroid B (mB = 1.45 x 1013 kg) has velocity in the opposite direction. If the asteroids stick together, what is the velocity (magnitude and direction) of the new asteroid after the collision?

Problem 69GP A ball is dropped from a height of 1.60 m and rebounds to a height of 1.20 m. Approximately how many rebounds will the ball make before losing 90% of its energy?

Problem 70GP A 4800-kg open railroad car coasts at a constant speed of 7.60 m/s on a level track. Snow begins to fall vertically and fills the car at a rate of 3.80kg/min. Ignoring friction with the tracks, what is the car’s speed after 60.0 min? (See Section 7–2.)

Problem 71GP Two bumper cars in an amusement park ride collide elastically as one approaches the other directly from the rear (Fig. 7–43). Car A has a mass of 435 kg and car B 495 kg, owing to differences in passenger mass. If car A approaches at 4.50 m/s and car B is moving at 3.70 m/s, calculate (a) their velocities after the collision, and (b) the change in momentum of each.

A gun fires a bullet vertically into a 1.40-kg block of wood at rest on a thin horizontal sheet, Fig. 7–44. If the bullet has a mass of 25.0 g and a speed of \(\text {230 m/s}\), show high will the block rise into the air after the bullet becomes embedded in it? FIGURE 7-44 Problem 72. ________________ Equation Transcription: Text Transcription: 230 m/s v=230 m/s

Problem 73GP You have been hired as an expert witness in a court case involving an automobile accident. The accident involved car A of mass 1500 kg which crashed into stationary car B of mass 1100 kg. The driver of car A applied his brakes 15 m before he skidded and crashed into car B. After the collision, car A slid 18 m while car B slid 30 m. The coefficient of kinetic friction between the locked wheels and the road was measured to be 0.60. Show that the driver of car A was exceeding the 55-mi/h (90-km/h) speed limit before applying the brakes.

Problem 74GP A meteor whose mass was about 1.5 x 108 kg struck the Earth (mE = 6.0 x 1024 kg) with a speed of about 25km/s and came to rest in the Earth. (a) What was the Earth’s recoil speed (relative to Earth at rest before the collision)? (b) What fraction of the meteor’s kinetic energy was transformed to kinetic energy of the Earth? (c) By how much did the Earth’s kinetic energy change as a result of this collision?

Problem 75GP A 28-g bullet strikes and becomes embedded in a 1.35-kg block of wood placed on a horizontal surface just in front of the gun. If the coefficient of kinetic friction between the block and the surface is 0.28, and the impact drives the block a distance of 8.5 m before it comes to rest, what was the muzzle speed of the bullet?

Problem 76GP You are the design engineer in charge of the crashworthiness of new automobile models. Cars are tested by smashing them into fixed, massive barriers at 45 km/h. A new model of mass 1500 kg takes 0.15 s from the time of impact until it is brought to rest. (a) Calculate the average force exerted on the car by the barrier. (b) Calculate the average deceleration of the car in g’s.

A skeet (clay target) is fired at an angle of \(28^{\circ}\) to the horizontal with a speed of \(25 \mathrm{\ m} / \mathrm{s}\) (Fig. ). When it reaches the maximum height, , it is hit from below by a 15 -g pellet traveling vertically upward at a speed of \(230 \mathrm{\ m} / \mathrm{s}\). The pellet is embedded in the skeet. (a) How much higher, \(h^{\prime}\), does the skeet go up? (b) How much extra distance, \(\Delta x\), does the skeet travel because of the collision? FIGURE 7-45 Problem 77. ________________ Equation Transcription: Text Transcription: 28^o 25 m/s 230 m/s h' x 28^o v_0=25 m/s v=230 m/s h' Delta x

Two balls, of masses \(m_A=45\mathrm{\ g}\) and \(m_B=65\mathrm{\ g}\), are suspended as shown in Fig. 7-46. The lighter ball is pulled away to a \(66^{\circ}\) angle with the vertical and released. ( ) What is the velocity of the lighter ball before impact? ( ) What is the velocity of each ball after the elastic collision? ( ) What will be the maximum height of each ball after the elastic collision? FIGURE 7-46 Problem 78. ________________ Equation Transcription: Text Transcription: m_A=45 g m_B=65 g 66^o 66^o m_A m_A m_B

Problem 80GP The space shuttle launches an 850-kg satellite by ejecting it from the cargo bay. The ejection mechanism is activated and is in contact with the satellite for 4.8 s to give it a velocity of 0.30 m/s in the x direction relative to the shuttle. The mass of the shuttle is 92,000 kg. (a) Determine the component of velocity vf of the shuttle in the minus x direction resulting from the ejection. (b) Find the average force that the shuttle exerts on the satellite during the ejection.

Problem 81GP Astronomers estimate that a 2.0-km-diameter asteroid collides with the Earth once every million years. The collision could pose a threat to life on Earth. (a) Assume a spherical asteroid has a mass of 3200 kg for each cubic meter of volume and moves toward the Earth at 15 km/s. How much destructive energy could be released when it embeds itself in the Earth? (b) For comparison, a nuclear bomb could release about 4.0 x 1016 J. How many such bombs would have to explode simultaneously to release the destructive energy of the asteroid collision with the Earth?

Problem 82GP An astronaut of mass 210 kg including his suit and jet pack wants to acquire a velocity of 2.0 m/s to move back toward his space shuttle. Assuming the jet pack can eject gas with a velocity of 35 m/s, what mass of gas will need to be ejected?

Two blocks of mass \(m_{A}\) and \(m_{B}\), resting on a frictionless table, are connected by a stretched spring and then released (Fig. ). () Is there a net external force on the system before release? (b) Determine the ratio of their speeds, \(v_{A} / v_{B}\). (c) What is the ratio of their kinetic energies? (d) Describe the motion of the of this system. Ignore mass of spring. ________________ Equation Transcription: Text Transcription: m_A m_B v_A/v_B m_A vector{V}_A vector{V}_B m_B

Problem 84GP A golf ball rolls off the top of a flight of concrete steps of total vertical height 4.00 m. The ball hits four times on the way down, each time striking the horizontal part of a different step 1.00 m lower. If all collisions are perfectly elastic, what is the bounce height on the fourth bounce when the ball reaches the bottom of the stairs?

Probelm 85GP A massless spring with spring constant k is placed between a block of mass m and a block of mass 3m. Initially the blocks are at rest on a frictionless surface and they are held together so that the spring between them is compressed by an amount D from its equilibrium length. The blocks are then released and the spring pushes them off in opposite directions. Find the speeds of the two blocks when they detach from the spring.

A novice pool player is faced with the corner pocket shot shown in Fig. 7–49. Relative dimensions are also shown. Should the player worry that this might be a “scratch shot,” in which the cue ball will also fall into a pocket? Give details. Assume equal-mass balls and an elastic collision.Ignore spin. FIGURE 7-49 Problem 86. ________________ Equation Transcription: Text Transcription: sqrt{3.0}

What is the magnitude of the momentum of a 28-g sparrow flying with a speed of 8.4 m/s?

A constant friction force of 25 N acts on a 65-kg skier for 15 s on level snow. What is the skiers change in velocity?

A 7150-kg railroad car travels alone on a level frictionless track with a constant speed of A 3350-kg load, initially at rest, is dropped onto the car. What will be the cars new speed?

A 110-kg tackler moving at meets head-on (and holds on to) an 82-kg halfback moving at What will be their mutual speed immediately after the collision?

Calculate the force exerted on a rocket when the propelling gases are being expelled at a rate of with a speed of 4.5 x 10 m/s?

A 7700-kg boxcar traveling strikes a second car at rest. The two stick together and move off with a speed of What is the mass of the second car?

A child in a boat throws a 5.30-kg package out horizontally with a speed of Fig. 731. Calculate the velocity of the boat immediately after, assuming it was initially at rest. The mass of the child is 24.0 kg and the mass of the boat is 35.0 kg

An atomic nucleus at rest decays radioactively into an alpha particle and a different nucleus. What will be the speed of this recoiling nucleus if the speed of the alpha particle is Assume the recoiling nucleus has a mass 57 times greater than that of the alpha particle

An atomic nucleus initially moving at emits an alpha particle in the direction of its velocity, and the remaining nucleus slows to If the alpha particle has a mass of 4.0 u and the original nucleus has a mass of 222 u, what speed does the alpha particle have when it is emitted?

An object at rest is suddenly broken apart into two fragments by an explosion. One fragment acquires twice the kinetic energy of the other. What is the ratio of their masses?

(II) A 22-g bullet traveling 240 m/s penetrates a 2.0-kg block of wood and emerges going 150 m/s. If the block is stationary on a frictionless surface when hit, how fast does it move after the bullet emerges?

A 0.145-kg baseball pitched horizontally at strikes a bat and pops straight up to a height of 31.5 m. If the contact time between bat and ball is 2.5 ms, calculate the average force between the ball and bat during contact

Air in a 120-km/h wind strikes head-on the face of a building 45 m wide by 75 m high and is brought to rest. If air has a mass of 1.3 kg per cubic meter, determine the average force of the wind on the building.

(III) A 725-kg two-stage rocket is traveling at a speed of \(6.60 \times 10^3 \ \mathrm {m/s}\) away from Earth when a predesigned explosion separates the rocket into two sections of equal mass that then move with a speed of \(2.80 \times 10^3 \ \mathrm {m/s}\) relative to each other along the original line of motion. (a) What is the speed and direction of each section (relative to Earth) after the explosion? (b) How much energy was supplied by the explosion? [Hint: What is the change in kinetic energy as a result of the explosion?]

A 0.145-kg baseball pitched at is hit on a horizontal line drive straight back at the pitcher at If the contact time between bat and ball is calculate the force (assumed to be constant) between the ball and bat

A golf ball of mass 0.045 kg is hit off the tee at a speed of The golf club was in contact with the ball for Find (a) the impulse imparted to the golf ball, and (b) the average force exerted on the ball by the golf club.

A 12-kg hammer strikes a nail at a velocity of and comes to rest in a time interval of 8.0 ms. (a) What is the impulse given to the nail? (b) What is the average force acting on the nail?

A tennis ball of mass and speed strikes a wall at a 45 angle and rebounds with the same speed at 45 (Fig. 732). What is the impulse (magnitude and direction) given to the ball

A 125-kg astronaut (including space suit) acquires a speed of by pushing off with her legs from a 1900-kg space capsule. (a) What is the change in speed of the space capsule? (b) If the push lasts 0.600 s, what is the average force exerted by each on the other? As the reference frame, use the position of the capsule before the push. (c) What is the kinetic energy of each after the push?

Rain is falling at the rate of and accumulates in a pan. If the raindrops hit at estimate the force on the bottom of a pan due to the impacting rain which we assume does not rebound. Water has a mass of 1.00 * 103 kg per m3

A 95-kg fullback is running at to the east and is stopped in 0.85 s by a head-on tackle by a tackler running due west. Calculate (a) the original momentum of the fullback, (b) the impulse exerted on the fullback, (c) the impulse exerted on the tackler, and (d) the average force exerted on the tackler

With what impulse does a 0.50-kg newspaper have to be thrown to give it a velocity of 3.0 ms?

Suppose the force acting on a tennis ball (mass 0.060 kg) points in the direction and is given by the graph of Fig. 733 as a function of time. (a) Use graphical methods (count squares) to estimate the total impulse given the ball. (b) Estimate the velocity of the ball after being struck, assuming the ball is being served so it is nearly at rest initially. [Hint: See Section 62.]

(a) Calculate the impulse experienced when a 55-kg person lands on firm ground after jumping from a height of 2.8 m. (b) Estimate the average force exerted on the persons feet by the ground if the landing is stiff-legged, and again (c) with bent legs. With stiff legs, assume the body moves 1.0 cm during impact, and when the legs are bent, about 50 cm. [Hint: The average net force on him, which is related to impulse, is the vector sum of gravity and the force exerted by the ground. See Fig. 734.] We will see in Chapter 9 that the force in (b) exceeds the ultimate strength of bone (Table 92

A ball of mass 0.440 kg moving east ( direction) with a speed of collides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed and direction of each ball after the collision?

A 0.450-kg hockey puck, moving east with a speed of has a head-on collision with a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision, what will be the speed and direction of each puck after the collision?

A 0.060-kg tennis ball, moving with a speed of has a head-on collision with a 0.090-kg ball initially moving in the same direction at a speed of Assuming a perfectly elastic collision, determine the speed and direction of each ball after the collision

Two billiard balls of equal mass undergo a perfectly elastic head-on collision. If one balls initial speed was and the others was in the opposite direction, what will be their speeds and directions after the collision

(II) A 0.280-kg croquet ball makes an elastic head-on collision with a second ball initially at rest. The second ball moves off with half the original speed of the first ball. (a) What is the mass of the second ball? (b) What fraction of the original kinetic energy \((\Delta KE/KE)\) gets transferred to the second ball?

A ball of mass m makes a head-on elastic collision with a second ball (at rest) and rebounds with a speed equal to 0.450 its original speed. What is the mass of the second ball?

A ball of mass 0.220 kg that is moving with a speed of collides head-on and elastically with another ball initially at rest. Immediately after the collision, the incoming ball bounces backward with a speed of Calculate (a) the velocity of the target ball after the collision, and (b) the mass of the target ball.

Determine the fraction of kinetic energy lost by a neutron when it collides head-on and elastically with a target particle at rest which is (a) (b) (heavy hydrogen, ); (c) (d) (lead, ).

(I) In a ballistic pendulum experiment, projectile 1 results in a maximum height h of the pendulum equal to 2.6 cm. A second projectile (of the same mass) causes the pendulum to swing twice as high, \(h_2 = 5.2\ cm\). The second projectile was how many times faster than the first?

(a) Derive a formula for the fraction of kinetic energy lost, in terms of m and M for the ballistic pendulum collision of Example 79. (b) Evaluate for

A 28-g rifle bullet traveling embeds itself in a 3.1-kg pendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine the vertical and horizontal components of the pendulums maximum displacement

An internal explosion breaks an object, initially at rest, into two pieces, one of which has 1.5 times the mass of the other. If 5500 J is released in the explosion, how much kinetic energy does each piece acquire?

A 980-kg sports car collides into the rear end of a 2300-kg SUV stopped at a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.6 m before stopping. The police officer, estimating the coefficient of kinetic friction between tires and road to be 0.80, calculates the speed of the sports car at impact. What was that speed?

You drop a 14-g ball from a height of 1.5 m and it only bounces back to a height of 0.85 m. What was the total impulse on the ball when it hit the floor? (Ignore air resistance.)

Car A hits car B (initially at rest and of equal mass) from behind while going Immediately after the collision, car B moves forward at and car A is at rest. What fraction of the initial kinetic energy is lost in the collision?

(II) A wooden block is cut into two pieces, one with three times the mass of the other. A depression is made in both faces of the cut, so that a firecracker can be placed in it with the block reassembled. The reassembled block is set on a rough-surfaced table, and the fuse is lit.When the firecracker explodes inside, the two blocks separate and slide apart. What is the ratio of distances each block travels?

A 144-g baseball moving strikes a stationary 5.25-kg brick resting on small rollers so it moves without significant friction. After hitting the brick, the baseball bounces straight back, and the brick moves forward at (a) What is the baseballs speed after the collision? (b) Find the total kinetic energy before and after the collision

A pendulum consists of a mass M hanging at the bottom end of a massless rod of length which has a frictionless pivot at its top end. A mass m, moving as shown in Fig. 735 with velocity v, impacts M and becomes embedded. What is the smallest value of v sufficient to cause the pendulum (with embedded mass m) to swing clear over the top of its arc?

A bullet of mass embeds itself in a wooden block with mass which then compresses a spring by a distance before coming to rest. The coefficient of kinetic friction between the block and table is (a) What is the initial velocity (assumed horizontal) of the bullet? (b) What fraction of the bullets initial kinetic energy is dissipated (in damage to the wooden block, rising temperature, etc.) in the collision between the bullet and the block?

(II) Billiard ball A of mass \(m_A = 0.120\ kg\) moving with speed \(v_A = 2.80\ m/s\) strikes ball B, initially at rest, of mass \(m_B = 0.140\ kg\). As a result of the collision, ball A is deflected off at an angle of \(30.0^{\circ}\) with a speed \(v’_A = 2.10\ m/s\). (a) Taking the x axis to be the original direction of motion of ball A, write down the equations expressing the conservation of momentum for the components in the x and y directions separately. (b) Solve these equations for the speed, \(v’_B\), and angle, \(\theta’_B\), of ball B after the collision. Do not assume the collision is elastic.

A radioactive nucleus at rest decays into a second nucleus, an electron, and a neutrino. The electron and neutrino are emitted at right angles and have momenta of and respectively. Determine the magnitude and the direction of the momentum of the second (recoiling) nucleus.

Billiard balls A and B, of equal mass, move at right angles and meet at the origin of an xy coordinate system as shown in Fig. 736. Initially ball A is moving along the y axis at and ball B is moving to the right along the x axis with speed After the collision (assumed elastic), ball B is moving along the positive y axis (Fig. 736) with velocity What is the final direction of ball A, and what are the speeds of the two balls?

An atomic nucleus of mass m traveling with speed v collides elastically with a target particle of mass 2m (initially at rest) and is scattered at 90. (a) At what angle does the target particle move after the collision? (b) What are the final speeds of the two particles? (c) What fraction of the initial kinetic energy is transferred to the target particle?

A neon atom makes a perfectly elastic collision with another atom at rest. After the impact, the neon atom travels away at a 55.6 angle from its original direction and the unknown atom travels away at a angle. What is the mass (in u) of the unknown atom? [Hint: You could use the law of sines.]

The distance between a carbon atom and an oxygen atom in the CO molecule is How far from the carbon atom is the center of mass of the molecule?

Find the center of mass of the three-mass system shown in Fig. 737 relative to the 1.00-kg mass.

The CM of an empty 1250-kg car is 2.40 m behind the front of the car. How far from the front of the car will the CM be when two people sit in the front seat 2.80 m from the front of the car, and three people sit in the back seat 3.90 m from the front? Assume that each person has a mass of 65.0 kg.

Three cubes, of side and are placed next to one another (in contact) with their centers along a straight line as shown in Fig. 738. What is the position, along this line, of the CM of this system? Assume the cubes are made of the same uniform material

A (lightweight) pallet has a load of ten identical cases of tomato paste (see Fig. 739), each of which is a cube of length Find the center of gravity in the horizontal plane, so that the crane operator can pick up the load without tipping it

Determine the CM of the uniform thin L-shaped construction brace shown in Fig. 740.

A uniform circular plate of radius 2R has a circular hole of radius R cut out of it. The center of the smaller circle is a distance 0.80R from the center C of the larger circle, Fig. 741. What is the position of the center of mass of the plate? [Hint: Try subtraction.]

Assume that your proportions are the same as those in Table 71, and calculate the mass of one of your legs

(I) Determine the CM of an outstretched arm using Table 7–1.

Use Table 71 to calculate the position of the CM of an arm bent at a right angle. Assume that the person is 155 cm tal

When a high jumper is in a position such that his arms and lower legs are hanging vertically, and his thighs, trunk, and head are horizontal just above the bar, estimate how far below the torsos median line the CM will be. Will this CM be outside the body? Use Table 71.

Repeat Problem 59 assuming the body bends at the hip joint by about 15. Estimate, using Fig. 727 as a model.

The masses of the Earth and Moon are and respectively, and their centers are separated by (a) Where is the CM of the EarthMoon system located? (b) What can you say about the motion of the EarthMoon system about the Sun, and of the Earth and Moon separately about the Sun?

A mallet consists of a uniform cylindrical head of mass 2.30 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 742. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory

A 52-kg woman and a 72-kg man stand 10.0 m apart on nearly frictionless ice. (a) How far from the woman is their CM? (b) If each holds one end of a rope, and the man pulls on the rope so that he moves 2.5 m, how far from the woman will he be now? (c) How far will the man have moved when he collides with the woman?

Suppose that in Example 714 (Fig. 728), (a) Where then would land?

Two people, one of mass 85 kg and the other of mass 55 kg, sit in a rowboat of mass 58 kg. With the boat initially at rest, the two people, who have been sitting at opposite ends of the boat, 3.0 m apart from each other, now exchange seats. How far and in what direction will the boat move?

(III) A huge balloon and its gondola, of mass M, are in the air and stationary with respect to the ground. A passenger, of mass m, then climbs out and slides down a rope with speed v, measured with respect to the balloon. With what speed and direction (relative to Earth) does the balloon then move? What happens if the passenger stops?

Two astronauts, one of mass 55 kg and the other 85 kg, are initially at rest together in outer space. They then push each other apart. How far apart are they when the lighter astronaut has moved 12 m?

Two asteroids strike head-on: before the collision, asteroid A has velocity and asteroid B has velocity in the opposite direction. If the asteroids stick together, what is the velocity (magnitude and direction) of the new asteroid after the collision

A ball is dropped from a height of 1.60 m and rebounds to a height of 1.20 m. Approximately how many rebounds will the ball make before losing 90% of its energy?

A 4800-kg open railroad car coasts at a constant speed of on a level track. Snow begins to fall vertically and fills the car at a rate of Ignoring friction with the tracks, what is the cars speed after 60.0 min? (See Section 72.)

Two bumper cars in an amusement park ride collide elastically as one approaches the other directly from the rear (Fig. 743). Car A has a mass of 435 kg and car B 495 kg, owing to differences in passenger mass. If car A approaches at and car B is moving at calculate (a) their velocities after the collision, and (b) the change in momentum of each.

A gun fires a bullet vertically into a 1.40-kg block of wood at rest on a thin horizontal sheet, Fig. 744. If the bullet has a mass of 25.0 g and a speed of how high will the block rise into the air after the bullet becomes embedded in it?

You have been hired as an expert witness in a court case involving an automobile accident. The accident involved car A of mass 1500 kg which crashed into stationary car B of mass 1100 kg. The driver of car A applied his brakes 15 m before he skidded and crashed into car B. After the collision, car A slid 18 m while car B slid 30 m. The coefficient of kinetic friction between the locked wheels and the road was measured to be 0.60. Show that the driver of car A was exceeding the speed limit before applying the brakes.

A meteor whose mass was about struck the Earth with a speed of about and came to rest in the Earth. (a) What was the Earths recoil speed (relative to Earth at rest before the collision)? (b) What fraction of the meteors kinetic energy was transformed to kinetic energy of the Earth? (c) By how much did the Earths kinetic energy change as a result of this collision?

A 28-g bullet strikes and becomes embedded in a 1.35-kg block of wood placed on a horizontal surface just in front of the gun. If the coefficient of kinetic friction between the block and the surface is 0.28, and the impact drives the block a distance of 8.5 m before it comes to rest, what was the muzzle speed of the bullet?

You are the design engineer in charge of the crashworthiness of new automobile models. Cars are tested by smashing them into fixed, massive barriers at A new model of mass 1500 kg takes 0.15 s from the time of impact until it is brought to rest. (a) Calculate the average force exerted on the car by the barrier. (b) Calculate the average deceleration of the car in gs

A 0.25-kg skeet (clay target) is fired at an angle of 28 to the horizontal with a speed of (Fig. 745). When it reaches the maximum height, h, it is hit from below by a 15-g pellet traveling vertically upward at a speed of The pellet is embedded in the skeet. (a) How much higher, does the skeet go up? (b) How much extra distance, does the skeet travel because of the collision?

Two balls, of masses and are suspended as shown in Fig. 746. The lighter ball is pulled away to a 66 angle with the vertical and released. (a) What is the velocity of the lighter ball before impact? (b) What is the velocity of each ball after the elastic collision? (c) What will be the maximum height of each ball after the elastic collision?

A block of mass slides down a 30.0 incline which is 3.60 m high. At the bottom, it strikes a block of mass which is at rest on a horizontal surface, Fig. 747. (Assume a smooth transition at the bottom of the incline.) If the collision is elastic, and friction can be ignored, determine (a) the speeds of the two blocks after the collision, and (b) how far back up the incline the smaller mass will go

The space shuttle launches an 850-kg satellite by ejecting it from the cargo bay. The ejection mechanism is activated and is in contact with the satellite for 4.8 s to give it a velocity of in the x direction relative to the shuttle. The mass of the shuttle is 92,000 kg. (a) Determine the component of velocity of the shuttle in the minus x direction resulting from the ejection. (b) Find the average force that the shuttle exerts on the satellite during the ejection.

Astronomers estimate that a 2.0-km-diameter asteroid collides with the Earth once every million years. The collision could pose a threat to life on Earth. (a) Assume a spherical asteroid has a mass of 3200 kg for each cubic meter of volume and moves toward the Earth at How much destructive energy could be released when it embeds itself in the Earth? (b) For comparison, a nuclear bomb could release about How many such bombs would have to explode simultaneously to release the destructive energy of the asteroid collision with the Earth?

An astronaut of mass 210 kg including his suit and jet pack wants to acquire a velocity of to move back toward his space shuttle. Assuming the jet pack can eject gas with a velocity of what mass of gas will need to be ejected?

Two blocks of mass and resting on a frictionless table, are connected by a stretched spring and then released (Fig. 748). (a) Is there a net external force on the system before release? (b) Determine the ratio of their speeds, (c) What is the ratio of their kinetic energies? (d) Describe the motion of the CM of this system. Ignore mass of spring

A golf ball rolls off the top of a flight of concrete steps of total vertical height 4.00 m. The ball hits four times on the way down, each time striking the horizontal part of a different step 1.00 m lower. If all collisions are perfectly elastic, what is the bounce height on the fourth bounce when the ball reaches the bottom of the stairs

A massless spring with spring constant k is placed between a block of mass m and a block of mass 3m. Initially the blocks are at rest on a frictionless surface and they are held together so that the spring between them is compressed by an amount D from its equilibrium length. The blocks are then released and the spring pushes them off in opposite directions. Find the speeds of the two blocks when they detach from the spring

A novice pool player is faced with the corner pocket shot shown in Fig. 749. Relative dimensions are also shown. Should the player worry that this might be a scratch shot, in which the cue ball will also fall into a pocket? Give details. Assume equal-mass balls and an elastic collision.Ignore spin