At the center of a 50-m-diameter circular ice rink, a 75

What is momentum?

What is impulse?

How are impulse and momentum related?

Is momentum conserved?

How does momentum apply to collisions?

Where else is momentum used?

The carts change of momentum is a. -30 kgm/s b. -20 kgm/s c. 0 kgm/s d. 10 kgm/s e. 20 kgm/s f. 30 kgm/s

A 150 g baseball is thrown with a speed of 20 m/s. It is hit straight back toward the pitcher at a speed of 40 m/s. The interaction force between the ball and the bat is shown in FIGURE 11.7. What maximum force Fmax does the bat exert on the ball? What is the average force of the bat on the ball?

A 10 g rubber ball and a 10 g clay ball are thrown at a wall with equal speeds. The rubber ball bounces, the clay ball sticks. Which ball delivers a larger impulse to the wall? a. The clay ball delivers a larger impulse because it sticks. b. The rubber ball delivers a larger impulse because it bounces. c. They deliver equal impulses because they have equal momenta. d. Neither delivers an impulse to the wall because the wall doesnt move.

A 250 g air-track glider is pushed across a level track toward a 500 g glider that is at rest. FIGURE 11.12 shows a position-versus-time graph of the 250 g glider as recorded by a motion detector. Best-fit lines have been found. What is the speed of the 500 g glider after the collision?

Bob sees a stationary cart 8.0 m in front of him. He decides to run to the cart as fast as he can, jump on, and roll down the street. Bob has a mass of 75 kg and the carts mass is 25 kg. If Bob accelerates at a steady 1.0 m/s2 , what is the carts speed just after Bob jumps on?

Objects A and C are made of different materials, with different springiness, but they have the same mass and are initially at rest. When ball B collides with object A, the ball ends up at rest. When ball B is thrown with the same speed and collides with object C, the ball rebounds to the left. Compare the velocities of A and C after the collisions. Is vA greater than, equal to, or less than vC?

In a laboratory experiment, a 200 g air-track glider and a 400 g air-track glider are pushed toward each other from opposite ends of the track. The gliders have Velcro tabs on the front and will stick together when they collide. The 200 g glider is pushed with an initial speed of 3.0 m/s. The collision causes it to reverse direction at 0.40 m/s. What was the initial speed of the 400 g glider?

The two particles are both moving to the right. Particle 1 catches up with particle 2 and collides with it. The particles stick together and continue on with velocity vf. Which of these statements is true? a. vf is greater than v1. b. vf = v1 c. vf is greater than v2 but less than v1. d. vf = v2 e. vf is less than v2. f. Cant tell without knowing the masses.

A 10 g bullet is fired into a 1200 g wood block hanging from a 150-cm-long string. The bullet embeds itself into the block, and the block then swings out to an angle of 40. What was the speed of the bullet? (This is called a ballistic pendulum.)

An explosion in a rigid pipe shoots out three pieces. A 6 g piece comes out the right end. A 4 g piece comes out the left end with twice the speed of the 6 g piece. From which end, left or right, does the third piece emerge?

A 10 g bullet is fired from a 3.0 kg rifle with a speed of 500 m/s. What is the recoil speed of the rifle?

An object traveling to the right with p u = 2 ni kgm/s suddenly explodes into two pieces. Piece 1 has the momentum p u 1 shown in the figure. What is the momentum p u 2 of the second piece?

A 238 U uranium nucleus is radioactive. It spontaneously disintegrates into a small fragment that is ejected with a measured speed of 1.50 * 107 m/s and a daughter nucleus that recoils with a measured speed of 2.56 * 105 m/s. What are the atomic masses of the ejected fragment and the daughter nucleus?

Peregrine falcons often grab their prey from above while both falcon and prey are in flight. A 0.80 kg falcon, flying at 18 m/s, swoops down at a 45 angle from behind a 0.36 kg pigeon flying horizontally at 9.0 m/s. What are the speed and direction of the falcon (now holding the pigeon) immediately after impact?

A 10.0 g projectile is traveling east at 2.0 m/s when it suddenly explodes into three pieces. A 3.0 g fragment is shot due west at 10 m/s while another 3.0 g fragment travels 40 north of east at 12 m/s. What are the speed and direction of the third fragment?

Sounding rockets are small rockets used to gather weather data and do atmospheric research. One of the most popular sounding rockets has been the fairly small (10-in-diameter, 16-ft-long) Black Brant III. It is loaded with 210 kg of fuel, has a launch mass of 290 kg, and generates 49 kN of thrust for 9.0 s. What would be the maximum speed of a Black Brant III if launched from rest in deep space?

A 200 g steel ball hangs on a 1.0-m-long string. The ball is pulled sideways so that the string is at a 45 angle, then released. At the very bottom of its swing the ball strikes a 500 g steel paperweight that is resting on a frictionless table. To what angle does the ball rebound?

Rank in order, from largest to smallest, the momenta 1px2a to 1px2e of the objects in FIGURE Q11.1.

A 2 kg object is moving to the right with a speed of 1 m/s when it experiences an impulse of 4 Ns. What are the objects speed and direction after the impulse?

A 2 kg object is moving to the right with a speed of 1 m/s when it experiences an impulse of -4 Ns. What are the objects speed and direction after the impulse?

A 0.2 kg plastic cart and a 20 kg lead cart can both roll without friction on a horizontal surface. Equal forces are used to push both carts forward for a time of 1 s, starting from rest. After the force is removed at t = 1 s, is the momentum of the plastic cart greater than, less than, or equal to the momentum of the lead cart? Explain

A 0.2 kg plastic cart and a 20 kg lead cart can both roll without friction on a horizontal surface. Equal forces are used to push both carts forward for a distance of 1 m, starting from rest. After traveling 1 m, is the momentum of the plastic cart greater than, less than, or equal to the momentum of the lead cart? Explain.

Angie, Brad, and Carlos are discussing a physics problem in which two identical bullets are fired with equal speeds at equalmass wood and steel blocks resting on a frictionless table. One bullet bounces off the steel block while the second becomes embedded in the wood block. All the masses and speeds are the same, says Angie, so I think the blocks will have equal speeds after the collisions. But what about momentum? asks Brad. The bullet hitting the wood block transfers all its momentum and energy to the block, so the wood block should end up going faster than the steel block. I think the bounce is an important factor, replies Carlos. The steel block will be faster because the bullet bounces off it and goes back the other direction. Which of these three do you agree with, and why?

It feels better to catch a hard ball while wearing a padded glove than to catch it bare handed. Use the ideas of this chapter to explain why

Automobiles are designed with crumple zones intended to collapse in a collision. Use the ideas of this chapter to explain why.

A golf club continues forward after hitting the golf ball. Is momentum conserved in the collision? Explain, making sure you are careful to identify the system.

Suppose a rubber ball collides head-on with a more massive steel ball traveling in the opposite direction with equal speed. Which ball, if either, receives the larger impulse? Explain.

Two particles collide, one of which was initially moving and the other initially at rest. a. Is it possible for both particles to be at rest after the collision? Give an example in which this happens, or explain why it cant happen. b. Is it possible for one particle to be at rest after the collision? Give an example in which this happens, or explain why it cant happen

Two ice skaters, Paula and Ricardo, push off from each other. Ricardo weighs more than Paula. a. Which skater, if either, has the greater momentum after the push-off? Explain. b. Which skater, if either, has the greater speed after the pushoff? Explain.

Two balls of clay of known masses hang from the ceiling on massless strings of equal length. They barely touch when both hang at rest. One ball is pulled back until its string is at 45, then released. It swings down, collides with the second ball, and they stick together. To determine the angle to which the balls swing on the opposite side, would you invoke (a) conservation of momentum, (b) conservation of mechanical energy, (c) both, (d) either but not both, or (e) these laws alone are not sufficient to find the angle? Explain.

At what speed do a bicycle and its rider, with a combined mass of 100 kg, have the same momentum as a 1500 kg car traveling at 5.0 m/s?

What is the magnitude of the momentum of a. A 3000 kg truck traveling at 15 m/s? b. A 200 g baseball thrown at 40 m/s?

What impulse does the force shown in FIGURE EX11.3 exert on a 250 g particle?

What is the impulse on a 3.0 kg particle that experiences the force shown in FIGURE EX11.4?

In FIGURE EX11.5, what value of Fmax gives an impulse of 6.0 Ns?

FIGURE EX11.6 is an incomplete momentum bar chart for a collision that lasts 10 ms. What are the magnitude and direction of the average collision force exerted on the object?

FIGURE EX11.7 is an incomplete momentum bar chart for a 50 g particle that experiences an impulse lasting 10 ms. What were the speed and direction of the particle before the impulse?

A 2.0 kg object is moving to the right with a speed of 1.0 m/s when it experiences the force shown in FIGURE EX11.8. What are the objects speed and direction after the force ends?

A 2.0 kg object is moving to the right with a speed of 1.0 m/s when it experiences the force shown in FIGURE EX11.9. What are the objects speed and direction after the force ends?

A sled slides along a horizontal surface on which the coefficient of kinetic friction is 0.25. Its velocity at point A is 8.0 m/s and at point B is 5.0 m/s. Use the momentum principle to find how long the sled takes to travel from A to B

Far in space, where gravity is negligible, a 425 kg rocket traveling at 75 m/s fires its engines. FIGURE EX11.11 shows the thrust force as a function of time. The mass lost by the rocket during these 30 s is negligible. a. What impulse does the engine impart to the rocket? b. At what time does the rocket reach its maximum speed? What is the maximum speed?

A 600 g air-track glider collides with a spring at one end of the track. FIGURE EX11.12 shows the gliders velocity and the force exerted on the glider by the spring. How long is the glider in contact with the spring?

A 250 g ball collides with a wall. FIGURE EX11.13 shows the balls velocity and the force exerted on the ball by the wall. What is vfx, the balls rebound velocity?

A 5000 kg open train car is rolling on frictionless rails at 22 m/s when it starts pouring rain. A few minutes later, the cars speed is 20 m/s. What mass of water has collected in the car?

A 10,000 kg railroad car is rolling at 2.0 m/s when a 4000 kg load of gravel is suddenly dropped in. What is the cars speed just after the gravel is loaded?

A 10-m-long glider with a mass of 680 kg (including the passengers) is gliding horizontally through the air at 30 m/s when a 60 kg skydiver drops out by releasing his grip on the glider. What is the gliders velocity just after the skydiver lets go?

Three identical train cars, coupled together, are rolling east at speed v0. A fourth car traveling east at 2v0 catches up with the three and couples to make a four-car train. A moment later, the train cars hit a fifth car that was at rest on the tracks, and it couples to make a five-car train. What is the speed of the five-car train?

A 300 g bird flying along at 6.0 m/s sees a 10 g insect heading straight toward it at a speed of 30 m/s. The bird opens its mouth wide and enjoys a nice lunch. What is the birds speed immediately after swallowing?

The parking brake on a 2000 kg Cadillac has failed, and it is rolling slowly, at 1.0 mph, toward a group of small children. Seeing the situation, you realize you have just enough time to drive your 1000 kg Volkswagen head-on into the Cadillac and save the children. With what speed should you impact the Cadillac to bring it to a halt?

A 1500 kg car is rolling at 2.0 m/s. You would like to stop the car by firing a 10 kg blob of sticky clay at it. How fast should you fire the clay?

Fred (mass 60 kg) is running with the football at a speed of 6.0 m/s when he is met head-on by Brutus (mass 120 kg), who is moving at 4.0 m/s. Brutus grabs Fred in a tight grip, and they fall to the ground. Which way do they slide, and how far? The coefficient of kinetic friction between football uniforms and Astroturf is 0.30.

A 50 g marble moving at 2.0 m/s strikes a 20 g marble at rest. What is the speed of each marble immediately after the collision?

A proton is traveling to the right at 2.0 * 107 m/s. It has a headon perfectly elastic collision with a carbon atom. The mass of the carbon atom is 12 times the mass of the proton. What are the speed and direction of each after the collision?

A 50 g ball of clay traveling at speed v0 hits and sticks to a 1.0 kg brick sitting at rest on a frictionless surface. a. What is the speed of the brick after the collision? b. What percentage of the mechanical energy is lost in this collision?

A package of mass m is released from rest at a warehouse loading dock and slides down the 3.0-m-high, frictionless chute of FIGURE EX11.25 to a waiting truck. Unfortunately, the truck driver went on a break without having removed the previous package, of mass 2m, from the bottom of the chute. a. Suppose the packages stick together. What is their common speed after the collision? b. Suppose the collision between the packages is perfectly elastic. To what height does the package of mass m rebound?

A 50 kg archer, standing on frictionless ice, shoots a 100 g arrow at a speed of 100 m/s. What is the recoil speed of the archer?

A 70.0 kg football player is gliding across very smooth ice at 2.00 m/s. He throws a 0.450 kg football straight forward. What is the players speed afterward if the ball is thrown at a. 15.0 m/s relative to the ground? b. 15.0 m/s relative to the player?

Dan is gliding on his skateboard at 4.0 m/s. He suddenly jumps backward off the skateboard, kicking the skateboard forward at 8.0 m/s. How fast is Dan going as his feet hit the ground? Dans mass is 50 kg and the skateboards mass is 5.0 kg.

Two ice skaters, with masses of 50 kg and 75 kg, are at the center of a 60-m-diameter circular rink. The skaters push off against each other and glide to opposite edges of the rink. If the heavier skater reaches the edge in 20 s, how long does the lighter skater take to reach the edge?

A ball of mass m and another ball of mass 3m are placed inside a smooth metal tube with a massless spring compressed between them. When the spring is released, the heavier ball flies out of one end of the tube with speed v0. With what speed does the lighter ball emerge from the other end?

Two particles collide and bounce apart. FIGURE EX11.31 shows the initial momenta of both and the final momentum of particle 2. What is the final momentum of particle 1? Write your answer using unit vectors.

An object at rest explodes into three fragments. FIGURE EX11.32 shows the momentum vectors of two of the fragments. What is the momentum of the third fragment? Write your answer using unit vectors.

A 20 g ball of clay traveling east at 3.0 m/s collides with a 30 g ball of clay traveling north at 2.0 m/s. What are the speed and the direction of the resulting 50 g ball of clay? Give your answer as an angle north of east.

At the center of a 50-m-diameter circular ice rink, a 75 kg skater traveling north at 2.5 m/s collides with and holds on to a 60 kg skater who had been heading west at 3.5 m/s. a. How long will it take them to glide to the edge of the rink? b. Where will they reach it? Give your answer as an angle north of west.

A small rocket with 15 kN thrust burns 250 kg of fuel in 30 s. What is the exhaust speed of the hot gases?

A rocket in deep space has an empty mass of 150 kg and exhausts the hot gases of burned fuel at 2500 m/s. What mass of fuel is needed to reach a top speed of 4000 m/s?

A rocket in deep space has an exhaust-gas speed of 2000 m/s. When the rocket is fully loaded, the mass of the fuel is five times the mass of the empty rocket. What is the rockets speed when half the fuel has been burned?

A tennis player swings her 1000 g racket with a speed of 10 m/s. She hits a 60 g tennis ball that was approaching her at a speed of 20 m/s. The ball rebounds at 40 m/s. a. How fast is her racket moving immediately after the impact? You can ignore the interaction of the racket with her hand for the brief duration of the collision. b. If the tennis ball and racket are in contact for 10 ms, what is the average force that the racket exerts on the ball? How does this compare to the gravitational force on the ball?

A 60 g tennis ball with an initial speed of 32 m/s hits a wall and rebounds with the same speed. FIGURE P11.39 shows the force of the wall on the ball during the collision. What is the value of Fmax, the maximum value of the contact force during the collisi

A 500 g cart is released from rest 1.00 m from the bottom of a frictionless, 30.0 ramp. The cart rolls down the ramp and bounces off a rubber block at the bottom. FIGURE P11.40 shows the force during the collision. After the cart bounces, how far does it roll back up the ramp?

A 200 g ball is dropped from a height of 2.0 m, bounces on a hard floor, and rebounds to a height of 1.5 m. FIGURE P11.41 shows the impulse received from the floor. What maximum force does the floor exert on the ball?

The flowers of the bunchberry plant open with astonishing force and speed, causing the pollen grains to be ejected out of the flower in a mere 0.30 ms at an acceleration of 2.5 * 104 m/s2 . If the acceleration is constant, what impulse is delivered to a pollen grain with a mass of 1.0 * 10-7 g?

A particle of mass m is at rest at t = 0. Its momentum for t 7 0 is given by px = 6t 2 kg m/s, where t is in s. Find an expression for Fx1t2, the force exerted on the particle as a function of time

Air-track gliders with masses 300 g, 400 g, and 200 g are lined up and held in place with lightweight springs compressed between them. All three are released at once. The 200 g glider flies off to the right while the 300 g glider goes left. Their position-versus-time graphs, as measured by motion detectors, are shown in FIGURE P11.44. What are the direction (right or left) and speed of the 400 g glider that was in the middle?

Most geologists believe that the dinosaurs became extinct 65 million years ago when a large comet or asteroid struck the earth, throwing up so much dust that the sun was blocked out for a period of many months. Suppose an asteroid with a diameter of 2.0 km and a mass of 1.0 * 1013 kg hits the earth 16.0 * 1024 kg2 with an impact speed of 4.0 * 104 m/s. a. What is the earths recoil speed after such a collision? (Use a reference frame in which the earth was initially at rest.) b. What percentage is this of the earths speed around the sun? The earth orbits the sun at a distance of 1.5 * 101

Squids rely on jet propulsion to move around. A 1.50 kg squid (including the mass of water inside the squid) drifting at 0.40 m/s suddenly ejects 0.10 kg of water to get itself moving at 2.50 m/s. If drag is ignored over the small interval of time needed to expel the water (the impulse approximation), what is the waters ejection speed relative to the squid?

A firecracker in a coconut blows the coconut into three pieces. Two pieces of equal mass fly off south and west, perpendicular to each other, at speed v0. The third piece has twice the mass as the other two. What are the speed and direction of the third piece? Give the direction as an angle east of north

One billiard ball is shot east at 2.0 m/s. A second, identical billiard ball is shot west at 1.0 m/s. The balls have a glancing collision, not a head-on collision, deflecting the second ball by 90 and sending it north at 1.41 m/s. What are the speed and direction of the first ball after the collision? Give the direction as an angle south of east.

a. A bullet of mass m is fired into a block of mass M that is at rest. The block, with the bullet embedded, slides distance d across a horizontal surface. The coefficient of kinetic friction is mk. Find an expression for the bullets speed vbullet. b. What is the speed of a 10 g bullet that, when fired into a 10 kg stationary wood block, causes the block to slide 5.0 cm across a wood table?

You are part of a search-andrescue mission that has been called out to look for a lost explorer. Youve found the missing explorer, but, as FIGURE P11.50 shows, youre separated from him by a 200-m-high cliff and a 30-m-wide raging river. To save his life, you need to get a 5.0 kg package of emergency supplies across the river. Unfortunately, you cant throw the package hard enough to make it across. Fortunately, you happen to have a 1.0 kg rocket intended for launching flares. Improvising quickly, you attach a sharpened stick to the front of the rocket, so that it will impale itself into the package of supplies, then fire the rocket at ground level toward the supplies. What minimum speed must the rocket have just before impact in order to save the explorers life?

An object at rest on a flat, horizontal surface explodes into two fragments, one seven times as massive as the other. The heavier fragment slides 8.2 m before stopping. How far does the lighter fragment slide? Assume that both fragments have the same coefficient of kinetic friction.

A 1500 kg weather rocket accelerates upward at 10 m/s2 . It explodes 2.0 s after liftoff and breaks into two fragments, one twice as massive as the other. Photos reveal that the lighter fragment traveled straight up and reached a maximum height of 530 m. What were the speed and direction of the heavier fragment just after the explosion?

In a ballistics test, a 25 g bullet traveling horizontally at 1200 m/s goes through a 30-cm-thick 350 kg stationary target and emerges with a speed of 900 m/s. The target is free to slide on a smooth horizontal surface. What is the targets speed just after the bullet emerges?

Two 500 g blocks of wood are 2.0 m apart on a frictionless table. A 10 g bullet is fired at 400 m/s toward the blocks. It passes all the way through the first block, then embeds itself in the second block. The speed of the first block immediately afterward is 6.0 m/s. What is the speed of the second block after the bullet stops in it?

A 100 g granite cube slides down a 40 frictionless ramp. At the bottom, just as it exits onto a horizontal table, it collides with a 200 g steel cube at rest. How high above the table should the granite cube be released to give the steel cube a speed of 150 cm/s?

You have been asked to design a ballistic spring system to measure the speed of bullets. A spring whose spring constant is k is suspended from the ceiling. A block of mass M hangs from the spring. A bullet of mass m is fired vertically upward into the bottom of the block and stops in the block. The springs maximum compression d is measured. a. Find an expression for the bullets speed vB in terms of m, M, k, and d. b. What was the speed of a 10 g bullet if the blocks mass is 2.0 kg and if the spring, with k = 50 N/m, was compressed by 45 cm?

In FIGURE P11.57, a block of mass m slides along a frictionless track with speed vm. It collides with a stationary block of mass M. Find an expression for the minimum value of vm that will allow the second block to circle the loop-the-loop without falling off if the collision is (a) perfectly inelastic or (b) perfectly elastic

The stoplight had just changed and a 2000 kg Cadillac had entered the intersection, heading north at 3.0 m/s, when it was struck by a 1000 kg eastbound Volkswagen. The cars stuck together and slid to a halt, leaving skid marks angled 35 north of east. How fast was the Volkswagen going just before the impact?

Ann (mass 50 kg) is standing at the left end of a 15-m-long, 500 kg cart that has frictionless wheels and rolls on a frictionless track. Initially both Ann and the cart are at rest. Suddenly, Ann starts running along the cart at a speed of 5.0 m/s relative to the cart. How far will Ann have run relative to the ground when she reaches the right end of the cart?

Force Fx = 110 N2 sin12pt/4.0 s2 is exerted on a 250 g particle during the interval 0 s t 2.0 s. If the particle starts from rest, what is its speed at t = 2.0 s?

A 500 g particle has velocity vx = -5.0 m/s at t = -2 s. Force Fx = 14 - t 2 2 N, where t is in s, is exerted on the particle between t = -2 s and t = 2 s. This force increases from 0 N at t = -2 s to 4 N at t = 0 s and then back to 0 N at t = 2 s. What is the particles velocity at t = 2 s?

A 30 ton rail car and a 90 ton rail car, initially at rest, are connected together with a giant but massless compressed spring between them. When released, the 30 ton car is pushed away at a speed of 4.0 m/s relative to the 90 ton car. What is the speed of the 30 ton car relative to the ground?

A 20 g ball is fired horizontally with speed v0 toward a 100 g ball hanging motionless from a 1.0-m-long string. The balls undergo a head-on, perfectly elastic collision, after which the 100 g ball swings out to a maximum angle umax = 50. What was v0?

A 100 g ball moving to the right at 4.0 m/s catches up and collides with a 400 g ball that is moving to the right at 1.0 m/s. If the collision is perfectly elastic, what are the speed and direction of each ball after the collision?

A 100 g ball moving to the right at 4.0 m/s collides head-on with a 200 g ball that is moving to the left at 3.0 m/s. a. If the collision is perfectly elastic, what are the speed and direction of each ball after the collision? b. If the collision is perfectly inelastic, what are the speed and direction of the combined balls after the collision?

Old naval ships fired 10 kg cannon balls from a 200 kg cannon. It was very important to stop the recoil of the cannon, since otherwise the heavy cannon would go careening across the deck of the ship. In one design, a large spring with spring constant 20,000 N/m was placed behind the cannon. The other end of the spring braced against a post that was firmly anchored to the ships frame. What was the speed of the cannon ball if the spring compressed 50 cm when the cannon was fired?

A proton (mass 1 u) is shot toward an unknown target nucleus at a speed of 2.50 * 106 m/s. The proton rebounds with its speed reduced by 25% while the target nucleus acquires a speed of 3.12 * 105 m/s. What is the mass, in atomic mass units, of the target nucleus?

The nucleus of the polonium isotope 214Po (mass 214 u) is radioactive and decays by emitting an alpha particle (a helium nucleus with mass 4 u). Laboratory experiments measure the speed of the alpha particle to be 1.92 * 107 m/s. Assuming the polonium nucleus was initially at rest, what is the recoil speed of the nucleus that remains after the decay?

A neutron is an electrically neutral subatomic particle with a mass just slightly greater than that of a proton. A free neutron is radioactive and decays after a few minutes into other subatomic particles. In one experiment, a neutron at rest was observed to decay into a proton 1mass 1.67 * 10-27 kg2 and an electron 1mass 9.11 * 10-31 kg2. The proton and electron were shot out back-to-back. The proton speed was measured to be 1.0 *105 m/s and the electron speed was 3.0 * 107 m/s. No other decay products were detected. a. Did momentum seem to be conserved in the decay of this neutron?

A 20 g ball of clay traveling east at 2.0 m/s collides with a 30 g ball of clay traveling 30 south of west at 1.0 m/s. What are the speed and direction of the resulting 50 g blob of clay?

FIGURE P11.71 shows a collision between three balls of clay. The three hit simultaneously and stick together. What are the speed and direction of the resulting blob of clay?

A 2100 kg truck is traveling east through an intersection at 2.0 m/s when it is hit simultaneously from the side and the rear. (Some people have all the luck!) One car is a 1200 kg compact traveling north at 5.0 m/s. The other is a 1500 kg midsize traveling east at 10 m/s. The three vehicles become entangled and slide as one body. What are their speed and direction just after the collision?

A rocket in deep space has an empty mass of 150 kg and exhausts the hot gases of burned fuel at 2500 m/s. It is loaded with 600 kg of fuel, which it burns in 30 s. What is the rockets speed 10 s, 20 s, and 30 s after launch?

a. To understand why rockets often have multiple stages, first consider a single-stage rocket with an empty mass of 200 kg, 800 kg of fuel, and a 2000 m/s exhaust speed. If fired in deep space, what is the rockets maximum speed? b. Now divide the rocket into two stages, each with an empty mass of 100 kg, 400 kg of fuel, and a 2000 m/s exhaust speed. The first stage is released after it runs out of fuel. What is the top speed of the second stage? Youll need to consider how the equation for vmax should be altered when a rocket is not starting from rest.

In Problems 75 through 78 you are given the equation(s) used to solve a problem. For each of these, you are to a. Write a realistic problem for which this is the correct equation(s). b. Finish the solution of the problem, including a pictorial representation.10.10 kg2140 m/s2 - 10.10 kg21-30 m/s2 = 1 2 11400 N2t

In Problems 75 through 78 you are given the equation(s) used to solve a problem. For each of these, you are to a. Write a realistic problem for which this is the correct equation(s). b. Finish the solution of the problem, including a pictorial representation.600 g214.0 m/s2 = 1400 g213.0 m/s2 + 1200 g21vix22

In Problems 75 through 78 you are given the equation(s) used to solve a problem. For each of these, you are to a. Write a realistic problem for which this is the correct equation(s). b. Finish the solution of the problem, including a pictorial representation.13000 kg2vfx = 12000 kg215.0 m/s2 + 11000 kg21-4.0 m/s2

In Problems 75 through 78 you are given the equation(s) used to solve a problem. For each of these, you are to a. Write a realistic problem for which this is the correct equation(s). b. Finish the solution of the problem, including a pictorial representation.10.10 kg + 0.20 kg2v1x = 10.10 kg213.0 m/s2 1 2 10.30 kg210 m/s22 + 1 2 13.0 N/m21x222 = 1 2 10.30 kg21v1x22 + 1 2 13.0 N/m210 m2

A 1000 kg cart is rolling to the right at 5.0 m/s. A 70 kg man is standing on the right end of the cart. What is the speed of the cart if the man suddenly starts running to the left with a speed of 10 m/s relative to the cart?

A spaceship of mass 2.0 * 106 kg is cruising at a speed of 5.0 * 106 m/s when the antimatter reactor fails, blowing the ship into three pieces. One section, having a mass of 5.0 * 105 kg, is blown straight backward with a speed of 2.0 * 106 m/s. A second piece, with mass 8.0 * 105 kg, continues forward at 1.0 * 106 m/s. What are the direction and speed of the third piece?

A 20 kg wood ball hangs from a 2.0-m-long wire. The maximum tension the wire can withstand without breaking is 400 N. A 1.0 kg projectile traveling horizontally hits and embeds itself in the wood ball. What is the greatest speed this projectile can have without causing the wire to break?

A two-stage rocket is traveling at 1200 m/s with respect to the earth when the first stage runs out of fuel. Explosive bolts release the first stage and push it backward with a speed of 35 m/s relative to the second stage. The first stage is three times as massive as the second stage. What is the speed of the second stage after the separation?

The air-track carts in FIGURE CP11.83 are sliding to the right at 1.0 m/s. The spring between them has a spring constant of 120 N/m and is compressed 4.0 cm. The carts slide past a flame that burns through the string holding them together. Afterward, what are the speed and direction of each cart?

Section 11.6 found an equation for vmax of a rocket fired in deep space. What is vmax for a rocket fired vertically from the surface of an airless planet with free-fall acceleration g? Referring to Section 11.6, you can write an equation for Py, the change of momentum in the vertical direction, in terms of dm and dvy. Py is no longer zero because now gravity delivers an impulse. Rewrite the momentum equation by including the impulse due to gravity during the time dt during which the mass changes by dm. Pay attention to signs! Your equation will have three differentials, but two are related through the fuel burn rate R. Use this relationshipagain pay attention to signs; m is decreasingto write your equation in terms of dm and dvy. Then integrate to find a modified expression for vmax at the instant all the fuel has been burned. a. What is vmax for a vertical launch from an airless planet? Your answer will be in terms of mR, the empty rocket mass; mF0, the initial fuel mass; vex, the exhaust speed; R, the fuel burn rate; and g. b. A rocket with a total mass of 330,000 kg when fully loaded burns all 280,000 kg of fuel in 250 s. The engines generate 4.1 MN of thrust. What is this rockets speed at the instant all the fuel has been burned if it is launched in deep space? If it is launched vertically from the earth?

What are the overarching findings of Part II?

What laws of physics govern energy and momentum?

What are the most common models for using conservation laws?

What are the most important tools for using energy and momentum?