Center of mass and momentum Questions and Answers

A pitcher claims he can throw a 0.143-kg baseball with as much momentum as a 2.26-g bullet moving with a speed of 1.50 x 103 m/s. (a) What must the baseball's speed be if the pitcher's claim is valid? m/s (b) Which has greater kinetic energy, the ball or the bullet? The bullet has greater kinetic energy. The ball has greater kinetic energy. Both have the same kinetic energy.

An unstable atomic nucleus of mass 1.84 x 10^-26 kg initially at rest disintegrates into three particles. One of the particles, of mass 5.04 x 10^-27 kg, moves in the y direction with a speed of 6.00 x 10^6 m/s. Another particle, of mass 8.44 x 10^-27 kg, moves in the x direction with a speed of 4.00 x 10^6 m/s. (a) Find the velocity of the third particle. __ î+ __) j) m/s (b) Find the total kinetic energy increase in the process. J

An athlete at the gym holds a 3.0 kg steel ball in his hand. His arm is 70 cm long and has a mass of 4.0 kg. For the steps and strategies involved in solving a similar problem, you may view a Video Tutor Solution. Part A What is the magnitude of the torque about his shoulder if he holds his arm straight out to his side, parallel to the floor? Express your answer with the appropriate units. T= Part B What is the magnitude of the torque about his shoulder if he holds his arm straight, but 60° below horizontal? Express your answer with the appropriate units. T=

You shoot a ball with mass of 0.107 kg into a ballistic pendulum. The pendulum has a mass of 0.442 kg. After the pendulum catches the ball, it swings up, rising by a height of 0.2 meters. What is the speed of the pendulum after the ball is caught in the pendulum? What is the speed of the ball after the pendulum caught the ball? How fast was the ball shot before hitting the pendulum?

Solve the following problem. Write your answer on the space provided. Show your complete solution. 1. A bowling ball which mass is 4.0 kg is rolling at a rate of 2.5 m/s. What is its momentum? 2. A skateboard is rolling at a velocity of 3.0 m/s with a momentum of 6.0 kg-m/s. What is its mass? 3. A baseball was thrown with a mass of 0.5 kg and a

Imagine that you are standing in a boat. If you catch a ball, you exert an impulse on that ball. If you throw the ball at the same speed, the impulse exerted is impulse exerted when catching the ball.

A bumper car with a mass of 225 kg is moving with a velocity of 18.0 km/h [W] hits a bumper car of the same mass travelling with a velocity of 9.00 km/h [E]. The two cars stick together in an inelastic collision and an instant after impact move in the same direction. Calculate the final velocity of the two (stuck together) bumper cars.

A cheetah, weighing 150 kg, chases a deer, weighing 30 kg, in a straight path. The speed of the cheetah is 20 m s-¹ and that of the deer is 25 m s-¹. The approximate speed (in m s¹) of the centre of mass of the pair is

A cannon consists of a 200-kg cannon and a 5-kg cannonball. The cannonball begins at rest Inside the resting cannon prior to launch. After the explosion of powder, the cannonball moves with a velocity of +40 m/s. What is the velocity of the cannon? * a.-200 m/s b.-40 m/s c. - 8 m/s d. - 1 m/s

A 0.057 kg tennis ball and a tennis racket collide. The racket has an initial momentum of -2.80 kg-m/s and a final momentum of -1.97 kg-m/s. The ball has an initial momentum of 0.02565 kg-m/s. If you assume the collision is elastic, what is the final velocity of the ball? A. -0.80 m/s B. -14.11 m/s C. -4.75 m/s D. -83.26 m/s

As an example, consider the case of a board of length L and negligible mass. Take the x axis to be the horizontal axis along the board and the y axis to be the vertical axis perpendicular to the board. A mass of weight W is strapped to the board a distance x from the left-hand end. (Figure 1) This is a static equilibrium problem, and a good first step is to write down the equation for the sum of all the forces in the y direction since the only nonzero forces of ΣF = 0 that exist are in the y direction. What is ΣFy? Your equation for the net force in the y direction on the board should contain all the forces acting vertically on the board. Express your answer in terms of the weight W and the tensions in the two vertical ropes at the left and right ends Tl and TR . Recall that positive forces point upward. ΣFy=0=

A 45.00-kg girl jumps from the side of a pool into a raft (m = 0.08 kg) floating on the surface of the water. She leaves the side at a speed of 1.10 m/s and lands on the raft. At what speed will the girl and the raft begin to travel across the pool?

A 10-g block slides with a velocity of 21 cm/s on a smooth level surface and makes a head-on collision with a 25 g block moving in the opposite direction with a velocity of 8 cm/s. If the collision is perfectly elastic, what is the velocity of the 25-g block after the collision?

A mortar fires a shell of mass m at speed v₀. The shell explodes at the top of its trajectory (shown by a star in (Figure 1)) as designed. However, rather than creating a shower of colored flares, it breaks into just two pieces, a smaller piece of mass 1/5m and a larger piece of mass 4/5m. Both pieces land at exactly the same time. The smaller piece lands perilously close to the mortar (at a distance of zero from the mortar). The larger piece lands a distance d from the mortar. If there had been no explosion, the shell would have landed a distance r from the mortar. Assume that air resistance and the mass of the shell's explosive charge are negligible. Find the distance d from the mortar at which the larger piece of the shell lands. Express d in terms of r.

A 13-g bullet being fired at 250 m/s passes through a 4.0 cm thick foam plastic sheet. The bullet emerges with a speed of 90 m/s after a time interval of 2.4 x 10-⁵ s. What is the average force that impeded the bullet's motion through the plastic? 8.7 x 10⁴N 7.4 x 10⁴ N 10.2 x10³ N 5.2x10⁴ N

A 2.5 kg firework moving with a velocity of 5.6 m/s to the right explodes in mid-air into two pieces. One of the exploded pieces has a mass of 1.4 kg and a velocity of 16.4 m/s to the right. What is the speed of the other piece?

A bullet with a mass of 0.0098 kg and a speed of 639.4 m/s is fired so that it hits a block of wood with a mass of 0.074 kg that is initially at rest on a frictionless surface. The bullet flies into the block and through the other side with a speed of 331.2m/s. What is the speed of the wood block after the bullet has passed through it?

A 757 kg train car moving with a speed of 12.6 m/s to the right, crashes into a 2nd 1269 kg train car moving with a speed of 3.8 m/s to the right. The trains lock up and move together. What is the speed of the combined train cars?

A bullet with a mass of 0.0063 kg and a speed of 748.0 m/s is fired so that it hits a block of wood with a mass of 0.233 kg that is initially at rest on a frictionless surface. The bullet flies into the block and through the other side with a speed of 349.1 m/s. What is the speed of the wood block after the bullet has passed through it?

A locomotive of mass m is sitting on a track. A train car of mass m/2 with velocity v hits the locomotive in a totally inelastic collision. What is the resulting velocity of the locomotive + car? a. v b. 2v c. v/2 d. v/3

Two bowling balls, each with a mass of 5 kg, collide head-on. Before the collision, they are both travelling at the same speed (but with opposite velocities). a. Which of the following scenarios is consistent with momentum conservation? i. After the collision, both balls come to a rest. ii. After the collision, both balls bounce off each other with the same speed they had before the collision. iii. After the collision, both balls bounce off each other with equal speeds, but the speed is less than the speed they had before the collision. Suppose the initial speed of both balls is 5 m/s. b. If the collision is perfectly inelastic, what will the final speed of the balls be? c. Alice makes the claim that after the collision, both balls can travel at 6 m/s (in opposite directions). i. In this scenario, is momentum conserved? ii. Is energy conserved?iii. Is this a physically realistic scenario? Why or why not?

A 1000 kg truck is moving at 30 m/s and hits a 500 kg car that's moving at 15 m/s from behind. If the two cars stick together, what is their final speed?

A 5 kg toy truck is moving at 5 m/s and hits another 3 kg toy car that is moving at 2 m/s from behind. If the car gets a final speed of 4 m/s, what is the final speed of the toy truck?

A cannon (m=275 kg) fires a cannonball (m= 8.00 kg), and the cannon recoils. If the cannon recoils with a speed of 1.25 m s', what is the speed of the cannonball when it leaves the cannon?

Two astronauts, each with a mass of 57 kg, are connected by a 6.3 m massless rope. Initially they are rotating around their center of mass with an angular velocity of 0.9 rad/s. One of the astronauts then pulls on the rope shortening the distance between the two astronauts to 4.9 m. What is the change in the rotational kinetic energy (in J) of this system? You may model each astronaut as a point particle.

A 3.0-kg object moves to the right at 4.0 m/s. It collides head-on with a 6.0-kg object moving to the left at 2.0 m/s. Which statement is correct? a. The total momentum both before and after the collision is 24 kg. m/s. b. The total momentum before the collision is 24 kg-m/s, and after the collision is 0 kg-m/s. c. The total momentum both before and after the collision is zero. d. None of the above is true.

A damselfly is circling about a poplar tree. At some moment in time, its linear momentum is given by p = (2i - 2j) g m/s and its distance from the poplar is r = (3j + 4k) m. The angular momentum of the damselfly about the poplar, in g m²/s, is -6i + -4j+ 12k 2i+j+ 4k 8i +8j-6k -2k

A 4.0kg model train going right at 6.0m/s bumps into a toy wagon moving in the same direction at 2.0m/s. The model train has a final speed of 4.8m/s, and the wagon has a final speed of 5.2m/s, both to the right. What is the mass of the wagon?

A thin rectangular plate of mass 0.60 kg has a face of width 0.20 m and length 0.45 m. Determine the moment of inertia for the plate when it is rotated about its center of mass on an axis perpendicular to its face. 0.010 kg m² 0.012 kg m² 0.033 kg m² 0.049 kg m²

Can a small, light ball have the same momentum as a large, heavy ball? A. yes, because the small ball may be able to gain as much inertia as the large ball B. no, because there is a difference in the inertia of the two balls c. no, because there is a difference in the masses of the two balls D. yes, because the velocity of the small ball may be much greater than that of the large ball

A 60-kg swimmer suddenly dives horizontally from a 150-kg raft with a speed of 1.5 m/s. The raft is initially at rest. What is the speed of the raft immediately after the diver jumps if the water has negligible effect on the raft?

12. A very light ping-pong ball moving east at a speed of 4 m/s collides with a very heavy stationary bowling ball. The Ping-Pong ball bounces back to the west, and the bowling ball moves very slowly to the east. Which object experiences the greater magnitude impulse during the collision? It is impossible to tell since the velocities after the collision are unknown. the bowling ball Neither; both experienced the same magnitude impulse. the Ping-Pong ball It is impossible to tell since the actual mass values are not given.

(hrw8c9p40) A space vehicle is traveling at 4200 km/h relative to the Earth when the exhausted rocket motor is disengaged and sent backward with a speed of 72 km/h relative to the command module. The mass of the motor is four times the mass of the module. What is the speed (km/h) of the command module relative to Earth after the separation? (Note: this answer requires slightly higher precision than normal.)

A tennis ball of mass 0.0591 kg is served. It strikes the ground with a velocity of 52.6 m/s (118 mi/h) at an angle of 22.8° below the horizontal, Just after the bounce it is moving at 50.6 m/s at an angle of 19.0° above the horizontal. If the interaction with the ground lasts 0.0701 s, what average force did the ground exert on the ball?

Which statement must necessarily be true for the momentum of a system to be conserved? The net external force on the system is zero. The net external force on the system is non-zero. The internal forces sum to zero. There are no external forces acting on the system.

10. A 0.050-kilogram bullet is fired from a 4.0- tien kilogram rifle that is initially at rest. If the bullet leaves the rifle with momentum having a magnitude of 20. kilogram meters per second, the rifle will recoil with a momentum having a magnitude of (1) 80. kg m/s (2) 1,600 kg m/s (3) 0.25 kg m/s (4) 20. kg m/s

Two identical ice hockey pucks, labeled A and B, are sliding toward each other at speed v. Which one of the following statements is true concerning their momenta and kinetic energies? HINT -PB and KEA = -KEB OPA = P and KEA PB -KEB O PA = -PB and KEA = KEB O PA O PA =- PB and KEA = = KEB

An 825-kg cannon rests on a frictionless surface and fires a 1.12-kg projectile at 124 meters per second to the right. What is the velocity of the cannon immediately after the projectile is fired? (a) 0.124 to the left (b) 0.152 (c) 0.168 (d) 0.174 S m --- S S to the left to the left to the left

A barefoot field-goal kicker imparts a speed of 19 m/s to a football initially at rest. If the football has a mass of 0.43 kg and the time of contact with the ball is 0.023 s, what is the magnitude of the force exerted by the ball on the kicker's foot? Answer in units of N.

4. A 2kg object initially moving with a constant velocity is subjected to a force of magnitude F in the direction of motion. A graph of F as a function of time t is shown above. What is the change in momentum of the object during the first four seconds shown in the graph? (A) 1.0 kg-m/s (B) 4.0 kg-m/s (C) 5.0 kg-m/s (D) 6.0 kg-m/s

A ball with a mass of 7.8 kg moving at 8 m/ s collides elastically with a second ball that is initially stationary. If the second ball moves away at 3 after the collision, find the mass of the second ball.

After being struck by a bowling ball, a 1.7 kg bowling pin sliding to the right at 3.2 m/s collides head-on with another 1.7 kg bowling pin initially at rest. Find the final velocity of the second pin in the following situations: a) The first pin moves to the right after the collision at 0.7 m/s. b) The first pin stops moving when it hits the second pin.

An impulse of 149 Ns is required to stop a person's head in a car collision. If the face is in contact with the steering wheel for 0.0263 s, what is the average force on the cheekbone? If an average force of 899 N fractures the cheekbone, how long must it be in contact with the steering wheel in order to fracture?

What is the momentum of a two-particle system composed of a 1000 kg car moving east at 100 m/s and a second 1400 kg car moving west at 45 m/s? Let east be the positive direction.

A 0.200 kg air-track glider moving at 1.20 m/s bumps into a 0.600 kg glider at rest. (a) Find the total kinetic energy after collision if the collision is elastic. (b) Find the total kinetic energy after collision if the collision is completely inelastic.

Explain why a rapidly spinning gyroscope, mounted in a frame that allows it to rotate in any direction independently of the frame's rotation, tends to maintain its axis pointed in the same direction in space.

A 14 kg rock starting from rest free falls through a distance of 5.0 m with no air resistance. Find the momentum change of the rock caused by its fall and the resulting change in the magnitude of earth's velocity. Earth's mass is 6.0x1024 kg Show all your work, assuming the rock-earth system is closed.

A round body kept on a smooth horizontal surface is pulled by a constant horizontal force applied at the topmost point of the body. Which of the following shapes can the body have if it rolls purely without slipping? A hollow cylinder A solid cylinder A uniform sphere A thin ring

A thread holds two carts together on a frictionless surface. A compressed spring acts on the carts. After the thread is burned, the 1.5-kg cart moves with a velocity of 27 cm/s to the left. What is the velocity of the 4.5-kg cart, in cm/s?

A particle strikes a smooth wall, moving on a smooth horizontal plane, obliquely. The speed just after the collision becomes 1/√3 times the speed just before collision. If coefficient of restitution is then find the 1/3 angle of deviation of a particle in degrees.