(Ill) A 280-kg flatcar 25 m long is moving with a speed

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

Two blocks of mass m\ and m2 rest on a frictionless table and are connected by a spring. The blocks are pulled apart, stretching the spring, and then released. Describe the subsequent motion of the two blocks.

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

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

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

Two children float motionlessly in a space station. The 20-kg girl pushes on the 40-kg boy and he sails away at 1.0 m/s. The girl (a) remains motionless; (b) moves in the same direction at 1.0 m/s; (c) moves in the opposite direction at 1.0 m/s; (d) moves in the opposite direction at 2.0 m/s; (1e) none of these.

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.

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

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

It is said that in ancient times a rich man with a bag of gold coins was stranded on the surface of a frozen lake. Because the ice was frictionless, he could not push himself to shore and froze to death. What could he have done to save himself had he not been so miserly?

The speed of a tennis ball on the return of a serve can be just as fast as the serve, even though the racket isnt swung very fast. How can this be?

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

How could a force give zero impulse over a nonzero time interval even though the force is not zero for at least a part of that time interval?

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.

A 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.

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?

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?

A squash ball hits a wall at a 45 angle as shown in Fig. 9-36. What is the direction (a) of the change in momentum of the ball, (b) of the force on the wall?

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

Describe a collision in which all kinetic energy is lost.

Inelastic and elastic collisions are similar in that (a) momentum and kinetic energy are conserved in both; (b) momentum is conserved in both; (c) momentum and potential energy are conserved in both; (d) kinetic energy is conserved in both.

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?

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

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

Show on a diagram how your cm shifts when you move from a lying position to a sitting position.

Describe an analytic way of determining the cm of any thin, triangular-shaped, uniform plate.

Place yourself facing the edge of an open door. Position your feet astride the door with your nose and abdomen touching the doors edge. Try to rise on your tiptoes. Why cant this be done?

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?

A rocket following a parabolic path through the air suddenly explodes into many pieces. What can you say about the motion of this system of pieces?

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

In observations of nuclear /3-decay, the electron and recoil nucleus 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 in the disintegration.

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

At a carnival game you try to knock over a heavy cylinder by throwing a small ball at it. You have a choice of throwing either a ball that will stick to the cylinder, or a second ball of equal mass and speed that will bounce backward off the cylinder. Which ball is more likely to make the cylinder move?

(II) A 0.060-kg tennis ball, moving with a speed of 4.50 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.

(II) A 0.450-kg hockey puck, moving east with a speed of 4.80 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 object 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 (AK /K ) gets transferred to the second ball?

(II) A ball of mass 0.220 kg that is moving with a speed of 7.5 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) A ball of mass m makes a head-on elastic collision with a second ball (at rest) and rebounds with a speed equal to 0.350 its original speed. What is the mass of the second ball?

(II) Determine the fraction of kinetic energy lost by a neutron (mi = 1.01 u) when it collides head-on and elastically with a target particle at rest which is (a) }H (m = 1.01 u); (b) 2H (heavy hydrogen, m = 2.01 u); (c) x\C (m = 12.00 u); (d) 2jgPb (lead, m = 208 u).

(II) Show that, in general, for any head-on one-dimensional elastic collision, the speeds after collision are where vA and vB are the initial speeds of the two objects of mass mA and mB

(Ill) A 3.0-kg block slides along a frictionless tabletop at 8.0 m/s toward a second block (at rest) of mass 4.5 kg. A coil spring, which obeys Hookes law and has spring constant k = 850 N/m, is attached to the second block in such a way that it will be compressed when struck by the moving block, Fig. 9-40. (a) What will be the maximum compression of the spring? (b) What will be the final velocities of the blocks after the collision? (c) Is the collision elastic? Ignore the mass of the spring.

(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 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, A K /K, in terms of m and M for the ballistic pendulum collision of Example 9-11. (b) Evaluate for m = 16.0 g and M = 380 g.

(II) A 28-g rifle bullet traveling 210 m/s buries itself in a 3.6-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.

(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 7500 J is released in the explosion, how much kinetic energy does each piece acquire?

(II) A 920-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 2.8 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?

(II) You drop a 12-g ball from a height of 1.5 m and it only bounces back to a height of 0.75 m. What was the total impulse on the ball when it hit the floor? (Ignore air resistance).

(II) Car A hits car B (initially at rest and of equal mass) from behind while going 35 m/s. Immediately after the collision, car B moves forward at 25 m /s and car A is at rest. What fraction of the initial kinetic energy is lost in the collision?

(II) A measure of inelasticity in a head-on collision of two objects is the coefficient o f restitution, e, defined as where vA vB is the relative velocity of the two objects after the collision and vA is their relative velocity before it. (a) Show that e = 1 for a perfectly elastic collision, and e = 0 for a completely inelastic collision, (b) A simple method for measuring the coefficient of restitution for an object colliding with a very hard surface like steel is to drop the object onto a heavy steel plate, as shown in Fig. 9-41. Determine a formula for e in terms of the original height h and the maximum height h' reached after collision.

(II) 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. 9-42 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?

(II) 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 = 120 N/m) by a distance x = 0.050 m before coming to rest. The coefficient of kinetic friction between the block and table is fi = 0.50. (a) What is the initial speed 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) 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 baseballs speed after the collision? (b) Find the total kinetic energy before and after the collision.

(II) A 6.0-kg object moving in the +x direction at 5.5 m/s collides head-on with an 8.0-kg object moving in the x direction at 4.0 m/s. Find the final velocity of each mass if: (a) the objects stick together; (b) the collision is elastic; (c) the 6.0-kg object is at rest after the collision; (d) the 8.0-kg object is at rest after the collision; (e) the 6.0-kg object has a velocity of 4.0 m/s in the x direction after the collision. Are the results in (c), (d), and (e) reasonable? Explain.

(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 me = 0.140 kg. As a result of the collision, ball A is deflected off at an angle of 30.0 with a speed vA = 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, vB, and angle, 0B, of ball B. Do not assume the collision is elastic.

(II) 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 9.6 X 10_23kg-m/s and 6.2 X 10_23kg-m/s, respectively. Determine the magnitude and the direction of the momentum of the second (recoiling) nucleus.

(II) Two billiard balls of equal mass move at right angles and meet at the origin of an xy coordinate system. Initially ball A is moving upward 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), the second ball is moving along the positive y axis (Fig. 9-43). What is the final direction of ball A, and what are the speeds of the two balls?

(II) 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?

(II) A neutron collides elastically with a helium nucleus (at rest initially) whose mass is four times that of the neutron. The helium nucleus is observed to move off at an angle #He = 45. Determine the angle of the neutron, 0'n , and the speeds of the two particles, v n and ^He > after the collision. The neutrons initial speed is 6.2 X 105 m/s.

(Ill) 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.]

(Ill) For an elastic collision between a projectile particle of mass mA and a target particle (at rest) of mass mB, show that the scattering angle, 0A , of the projectile (a) can take any value, 0 to 180, for mA < mB, but (b) has a maximum angle (f) given by cos2(f> = 1 (mB/mA)2 for mA > mB.

(Ill) Prove that in the elastic collision of two objects of identical mass, with one being a target initially at rest, the angle between their final velocity vectors is always 90.

(I) The cm of an empty 1250-kg car is 2.50 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 70.0 kg.

(I) The distance between a carbon atom (m = 12 u) and an oxygen atom (m = 16 u) in the CO molecule is 1.13 X 10- 10m. How far from the carbon atom is the center of mass of the molecule?

(II) Three cubes, of side 0, 20, and 30, are placed next to one another (in contact) with their centers along a straight line as shown in Fig. 9-44. What is the position, along this line, of the cm of this r _ q system? Assume the cubes are made of the same uniform material.

(II) A square uniform raft, 18 m by 18 m, of mass 6200 kg, is used as a ferryboat. If three cars, each of mass 1350 kg, occupy the NE, SE, and SW corners, determine the cm of the loaded ferryboat relative to the center of the raft.

(II) 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 0.80i? from the center C of the larger circle, Fig. 9-45. What is the position of the center of mass of the plate? [Hint: Try subtraction.]

(II) A uniform thin wire is bent into a semicircle of radius r. Determine the coordinates of its center of mass with respect to an origin of coordinates at the center of the full circle.

(II) Find the center of mass of the ammonia molecule. The chemical formula is NH3. The hydrogens are at the corners of an equilateral triangle (with sides 0.16 nm) that forms the base of a pyramid, with nitrogen at the apex (0.037 nm vertically above the plane of the triangle).

(Ill) Determine the cm of a machine part that is a uniform cone of height h and radius R, Fig. 9-46. [Hint: Divide the cone into an infinite number of disks of thickness dz, one of which is shown.}

(Ill) Determine the cm of a uniform pyramid that has four triangular faces and a square base with equal sides all of length s. [Hint: See Problem 69.]

(Ill) Determine the cm of a thin, uniform, semicircular plate.

(II) Mass Ma = 35 kg and mass AfB = 25 kg. They have velocities (in m/s) vA = 12i - 16j and vB = -2 0 i + 14j. Determine the velocity of the center of mass of the system.

(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 108m. (a) Where is the cm of this 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 2.80 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. 9-47. 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?

(II) A 55-kg woman and a 72-kg man stand 10.0 m apart on 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 9-18 (Fig. 9-32), ran = 3m i. (a) Where then would ran land? (b) What if mi = 3mn?

(II) Two people, one of mass 85 kg and the other of mass 55 kg, sit in a rowboat of mass 78 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?

(Ill) A 280-kg flatcar 25 m long is moving with a speed of 6.0 m/s along horizontal frictionless rails. A 95-kg worker starts walking from one end of the car to the other in the direction of motion, with speed 2.0 m/s with respect to the car. In the time it takes for him to reach the other end, how far has the flatcar moved?

(Ill) 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?

(II) A 3500-kg rocket is to be accelerated at 3.0 g at take-off from the Earth. If the gases can be ejected at a rate of 27 kg/s, what must be their exhaust speed?

(II) Suppose the conveyor belt of Example 9-19 is retarded by a friction force of 150 N. Determine the required output power (hp) of the motor as a function of time from the moment gravel first starts falling (t = 0) until 3.0 s after the gravel begins to be dumped off the end of the 22-m-long conveyor belt.

(II) The jet engine of an airplane takes in 120 kg of air per second, which is burned with 4.2 kg of fuel per second. The burned gases leave the plane at a speed of 550 m/s (relative to the plane). If the plane is traveling 270 m/s (600mi/h), determine: (a) the thrust due to ejected fuel; (b) the thrust due to accelerated air passing through the engine; and (c) the power (hp) delivered.

(II) A rocket traveling 1850 m/s away from the Earth at an altitude of 6400 km fires its rockets, which eject gas at a speed of 1300 m/s (relative to the rocket). If the mass of the rocket at this moment is 25,000 kg and an acceleration of 1.5 m/s2 is desired, at what rate must the gases be ejected?

(II) A rocket traveling 1850 m/s away from the Earth at an altitude of 6400 km fires its rockets, which eject gas at a speed of 1300 m/s (relative to the rocket). If the mass of the rocket at this moment is 25,000 kg and an acceleration of 1.5 m/s2 is desired, at what rate must the gases be ejected?

A novice pool player is faced with the corner pocket shot shown in Fig. 9-48. 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.

During a Chicago storm, winds can whip horizontally at speeds of 120 km/h. If the air strikes a person at the rate of 45 kg/s per square meter and is brought to rest, calculate the force of the wind on a person. Assume the person is 1.60 m high and 0.50 m wide. Compare to the typical maximum force of friction (/x ~ 1 .0) between the person and the ground, if the person has a mass of 75 kg.

A ball is dropped from a height of 1.50 m and rebounds to a height of 1.20 m. Approximately how many rebounds will the ball make before losing 90% of its energy?

In order to convert a tough split in bowling, it is necessary to strike the pin a glancing blow as shown in Fig. 9-49. Assume that the bowling ball, initially traveling at 13.0 m/s, has five times the mass of a pin and that the pin goes off at 75 from the original direction of the ball. Calculate the speed (a) of the pin and (b) of the ball just after collision, and (c) calculate the angle through which the ball was deflected. Assume the collision is elastic and ignore any spin of the ball.

A gun fires a bullet vertically into a 1.40-kg block of wood at rest on a thin horizontal sheet, Fig. 9-50. If the bullet has a mass of 24.0 g and a speed of 310 m/s, how high will the block rise into the air after the bullet becomes embedded in it?

A hockey puck of mass 4 m has been rigged to explode, as part of a practical joke. Initially the puck is at rest on a frictionless ice rink. Then it bursts into three pieces. One chunk, of mass m, slides across the ice at velocity vi. Another chunk, of mass 2m, slides across the ice at velocity 2vj. Determine the velocity of the third chunk.

For the completely inelastic collision of two railroad cars that we considered in Example 9-3, calculate how much of the initial kinetic energy is transformed to thermal or other forms of energy.

A 4800-kg open railroad car coasts along with a constant speed of 8.60 m/s on a level track. Snow begins to fall vertically and fills the car at a rate of 3.80 kg/min. Ignoring friction with the tracks, what is the speed of the car after 60.0 min? (See Section 9-2.)

Consider the railroad car of Problem 92, which is slowly filling with snow, (a) Determine the speed of the car as a function of time using Eqs. 9-19. (b ) What is the speed of the car after 60.0 min? Does this agree with the simpler calculation (Problem 92)?

Two blocks of mass raA and mB, resting on a frictionless table, are connected by a stretched spring and then released (Fig. 9-51). (a) Is there a net external force on the system? (b ) Determine the ratio of their speeds, v a / vq . (c) What is the ratio of their kinetic energies? (d) Describe the motion of the cm of this system. (e) How would the presence of friction alter the above results?

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.

A meteor whose mass was about 2.0 X 108kg struck the Earth (raE = 6.0 X 1024kg) with a speed of about 25km/s 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?

Two astronauts, one of mass 65 kg and the other 85 kg, are initially at rest in outer space. They then push each other apart. How far apart are they when the lighter astronaut has moved 12 m?

A 22-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?

Two balls, of masses mA = 45 g and mB = 65 g, are suspended as shown in Fig. 9-52. 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 A collision?

A block of mass ra = 2.20 kg slides down a 30.0 incline which is 3.60 m high. At the bottom, it strikes a block of mass M = 7.00 kg which is at rest on a horizontal surface, Fig. 9-53. (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.

In Problem 100 (Fig. 9-53), what is the upper limit on mass ra if it is to rebound from M, slide up the incline, stop, slide down the incline, and collide with M again?

After a completely inelastic collision between two objects of equal mass, each having initial speed, v, the two move off together with speed v/3. What was the angle between their initial directions?

A 0.25-kg skeet (clay target) is fired at an angle of 28 to the horizon with a speed of 25 m/s (Fig. 9-54). When it reaches the maximum height, h, it is hit from below by a 15-g pellet traveling vertically upward at a speed of 230 m/s. The pellet is embedded in the skeet. (a) How much higher, h', did the skeet go up? (b) How much extra distance, Ax, does the skeet travel because of the collision?

A massless spring with spring constant k is placed between a block of mass ra and a block of mass 3 ra. 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.

The gravitational slingshot effect. Figure 9-55 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 X 1026 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 Saturns gravitational pull.

Two bumper cars in an amusement park ride collide elastically as one approaches the other directly from the rear (Fig. 9-56). Car A has a mass of 450 kg and car B 490 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 mA = in momentum of 450 kg each.

In a physics lab, a cube slides down shown in Fig. 9-57 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.] frictionless incline as

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 4.0 s to give it a velocity of 0.30 m/s in the z-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 z-direction resulting from the ejection, (b) Find the average force that the shuttle exerts on the satellite during the ejection.

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.

Astronomers estimate that a 2.0-km-wide 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 15km/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 1016J. 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 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?

An extrasolar planet can be detected by observing the wobble it produces on the star around which it revolves. Suppose an extrasolar planet of mass raB revolves around its star of mass mA. If no external force acts on this simple two-object system, then its cm is stationary. Assume mA and raB are in circular orbits with radii rA and rB about the systems cm. (a) Show that raB rA mA rB- (b) Now consider a Sun-like star and a single planet with the same characteristics as Jupiter. That is, mB = 1.0 X 10_3mA and the planet has an orbital radius of 8.0 X 1011 m. Determine the radius rA of the stars orbit about the systems cm. (c) When viewed from Earth, the distant system appears to wobble over a distance of 2 rA . If astronomers are able to detect angular displacements 6 of about 1 milliarcsec (1 arcsec = ^ of a degree), from what distance d (in light-years) can the stars wobble be detected (l ly = 9.46 X 1015 m)? (d) The star nearest to our Sun is about 4 ly away. Assuming stars are uniformly distributed throughout our region of the Milky Way Galaxy, about how many stars can this technique be applied to in the search for extrasolar planetary systems?

Suppose two asteroids strike head on. Asteroid A (mA = 7.5 X 1012kg) has velocity 3.3km/s before the collision, and asteroid B (mB = 1.45 X 1013kg) has velocity 1.4 km/s before the collision in the opposite direction. If the asteroids stick together, what is the velocity (magnitude and direction) of the new asteroid after the collision?

(Ill) A particle of mass raA traveling with speed v A collides elastically head-on with a stationary particle of smaller mass mB. (a) Show that the speed of mB after the collision is , _ 2va Vb 1 + mB/m A (b) Consider now a third particle of mass mc at rest between mA and mB so that mA first collides head on with mc and then mc collides head on with mB. Both collisions are elastic. Show that in this case, , _ _______mc mA_______ VB VA(mC + + mc) (c) From the result of part (b), show that for maximum v'B , mc = \Jm AmB. (d) Assume mB = 2.0 kg, mA = 18.0 kg and vA = 2.0 m/s. Use a spreadsheet to calculate and graph the values of v'B from rac = 0.0 kg to mc = 50.0 kg in steps of 1.0 kg. For what value of mc is the value of v B maximum? Does your numerical result agree with your result in part (c)?