Chapter 6

Two motorcycles of equal mass collide at a \(90^{\circ}\) intersection. If the momentum of motorcycle \(\mathrm{A}\) is \(450 \mathrm{~kg} \mathrm{~km} / \mathrm{h}\) west and the momentum of motorcycle \(\mathrm{B}\) is \(725 \mathrm{~kg}\) \(\mathrm{km} / \mathrm{h}\) south, what is the magnitude of the resulting momentum of the final mass?

One ball of mass \(0.500 \mathrm{~kg}\) traveling \(6.00 \mathrm{~m} / \mathrm{s}\) to the right collides with a ball of mass \(0.200 \mathrm{~kg}\) initially at rest. After the collision, the heavier ball is traveling \(2.57 \mathrm{~m} / \mathrm{s}\) to the right. What is the velocity of the lighter ball after the collision?

Find the momentum of each object. \(\quad m=2.00 \mathrm{~kg}, v=40.0 \mathrm{~m} / \mathrm{s}\)

Two pickup trucks crash at a \(90^{\circ}\) intersection. If the momentum of pickup \(\mathrm{A}\) is \(4.60 \times 10^{4} \mathrm{~kg} \mathrm{~km} / \mathrm{h}\) north and the momentum of pickup \(\mathrm{B}\) is \(6.25 \times 10^{4} \mathrm{~kg} \mathrm{~km} / \mathrm{h}\) east, what is the magnitude of the resulting momentum of the final mass?

Find the momentum of each object. \(\quad m=5.00 \mathrm{~kg}, v=90.0 \mathrm{~m} / \mathrm{s}\)

Two vehicles collide at a \(90^{\circ}\) intersection. If the momentum of vehicle \(\mathrm{A}\) is \(6.10 \times 10^{5} \mathrm{~kg} \mathrm{~km} / \mathrm{h}\) south and the momentum of vehicle \(\mathrm{B}\) is \(7.20 \times 10^{5} \mathrm{~kg} \mathrm{~km} / \mathrm{h}\) east, what is the magnitude of the resulting momentum of the final mass?

A \(0.600-\mathrm{kg}\) ball traveling \(4.00 \mathrm{~m} / \mathrm{s}\) to the right collides with a \(1.00-\mathrm{kg}\) ball traveling \(5.00 \mathrm{~m} / \mathrm{s}\) to the left. After the collision, the lighter ball is traveling \(7.25 \mathrm{~m} / \mathrm{s}\) to the left. What is the velocity of the heavier ball after the collision?

Find the momentum of each object. \(m=17.0\) slugs, \(v=45.0 \mathrm{ft} / \mathrm{s}\)

Two vehicles of equal mass collide at a \(90^{\circ}\) intersection. If the momentum of vehicle \(A\) is \(1.20 \times 10^{5} \mathrm{~kg} \mathrm{~km} / \mathrm{h}\) east and the momentum of vehicle \(\mathrm{B}\) is \(8.50 \times 10^{4} \mathrm{~kg} \mathrm{~km} / \mathrm{h}\) north, what is the resulting momentum of the final mass?

A \(90.0\) -g disk traveling \(3.00 \mathrm{~m} / \mathrm{s}\) to the right collides with a \(75.0\) -g disk traveling \(8.00 \mathrm{~m} / \mathrm{s}\) to the left. After the collision, the heavier disk is traveling \(7.00 \mathrm{~m} / \mathrm{s}\) to the left. What is the velocity of the lighter disk after the collision?

Find the momentum of each object. \(\quad m=38.0 \mathrm{~kg}, v=97.0 \mathrm{~m} / \mathrm{s}\)

A vehicle with a mass of \(1000 \mathrm{~kg}\) is going east at a velocity of \(30.0 \mathrm{~m} / \mathrm{s}\). It collides with a stationary vehicle of the same mass and is deflected \(35.0^{\circ}\) north of its original course. The second vehicle's final path is \(90^{\circ}\) to the right of the final path of the first vehicle. (a) What is the momentum of the first vehicle after the collision? (b) What is the momentum of the second vehicle after the collision? (c) What is the velocity of the first vehicle after the collision? (d) What is the velocity of the second vehicle after the collision?

A \(98.0\) -kg parts cart with rubber bumpers rolling \(1.20 \mathrm{~m} / \mathrm{s}\) to the right crashes into a similar cart of mass \(125 \mathrm{~kg}\) moving left at \(0.750 \mathrm{~m} / \mathrm{s}\). After the collision, the lighter cart is traveling \(0.986 \mathrm{~m} / \mathrm{s}\) to the left. What is the velocity of the heavier cart after the collision?

Find the momentum of each object. \(m=3.8 \times 10^{5} \mathrm{~kg}, v=2.5 \times 10^{3} \mathrm{~m} / \mathrm{s}\)

Ball A with a mass of \(0.500 \mathrm{~kg}\) is moving east at a velocity of \(0.800 \mathrm{~m} / \mathrm{s}\). It strikes ball \(\mathrm{B}\), also of mass \(0.500 \mathrm{~kg}\), which is stationary. Ball A glances off \(\mathrm{B}\) at an angle of \(40.0^{\circ}\) north of its original path. Ball \(\mathrm{B}\) is pushed along a path perpendicular to the final path of ball A. (a) What is the momentum of ball A after the collision? (b) What is the momentum of ball B after the collision? (c) What is the velocity of ball A after the collision? (d) What is the velocity of ball B after the collision?

A \(75.0\) -kg paint cart with rubber bumpers is rolling \(0.965 \mathrm{~m} / \mathrm{s}\) to the right and strikes a second cart of mass \(85.0 \mathrm{~kg}\) moving \(1.30 \mathrm{~m} / \mathrm{s}\) to the left. After the collision, the heavier cart is traveling \(0.823 \mathrm{~m} / \mathrm{s}\) to the right. What is the velocity of the lighter cart after the collision?

Find the momentum of each object. \(\quad m=3.84 \mathrm{~kg}, v=1.6 \times 10^{5} \mathrm{~m} / \mathrm{s}\)

A vehicle with mass of \(95 \overline{0} \mathrm{~kg}\) is driving east with velocity \(12.0 \mathrm{~m} / \mathrm{s}\). It crashes into a stationary vehicle of the same mass. Assume an elastic collision. The first vehicle is deflected at an angle of \(40.0^{\circ}\) north of its original path. The second vehicle's path is \(90^{\circ}\) to the right of the first vehicle's final path. (a) What is the momentum of the first vehicle after the crash? (b) What is the momentum of the second vehicle after the crash? (c) What is the velocity of the first vehicle after the crash? (d) What is the velocity of the second vehicle after the crash?

A railroad car of mass \(2.00 \times 10^{4} \mathrm{~kg}\) is traveling north \(6.00 \mathrm{~m} / \mathrm{s}\) and collides with a railroad car of mass \(1.50 \times 10^{4}\) kg traveling south \(4.00 \mathrm{~m} / \mathrm{s}\). Find the velocity of the railroad cars that become coupled after the collision.

A vehicle with a mass of \(800 \mathrm{~kg}\) is traveling west with a velocity of \(20.0 \mathrm{~m} / \mathrm{s}\). It collides with a vehicle of the same mass that is not moving. Assume an elastic collision. the first vehicle is deflected at \(30.0^{\circ}\) north from its original path. The second vehicle's path is \(90^{\circ}\) to the left of the first vehicle's final path. (a) What is the momentum of the first vehicle after the crash? (b) What is momentum of the second vehicle after the crash? (c) What is the velocity of the first vehicle after the crash? (d) What is the velocity of the second vehicle after the crash?

One cart of mass \(12.0 \mathrm{~kg}\) is moving \(6.00 \mathrm{~m} / \mathrm{s}\) to the right on a frictionless track and collides with a cart of mass \(4.00 \mathrm{~kg}\) moving in the opposite direction \(3.00 \mathrm{~m} / \mathrm{s}\). Find the final velocity of the carts that become stuck together after the collision.

(a) Find the momentum of a heavy automobile weighing 5850 lb traveling \(70.0 \mathrm{ft} / \mathrm{s}\). (b) Find the velocity of a light automobile weighing \(2580 \mathrm{lb}\) so that it has the same momentum as the heavy automobile.

One cart of mass \(15.0 \mathrm{~kg}\) is moving \(5.00 \mathrm{~m} / \mathrm{s}\) to the right on a frictionless track and collides with a cart of mass \(3.00 \mathrm{~kg}\). The final velocity of the carts that become stuck together after the collision is \(1.50 \mathrm{~m} / \mathrm{s}\) to the right. Find the velocity of the second cart before the collision.

(a) Find the momentum of a bullet of mass \(1.00 \times 10^{-3}\) slug traveling \(70 \overline{0} \mathrm{ft} / \mathrm{s}\). (b) Find the velocity of a bullet of mass \(5.00 \times 10^{-4}\) slug so that it has the same momentum as the bullet in part (a).

A \(1650-\mathrm{kg}\) automobile moving south \(12.0 \mathrm{~m} / \mathrm{s}\) collides with a \(2450-\mathrm{kg}\) automobile moving north on an icy road. The automobiles stick together and move \(3.00 \mathrm{~m} / \mathrm{s}\) to the north after the collision. What is the speed of the heavier automobile before the collision?

(a) Find the momentum of an automobile of mass \(2630 \mathrm{~kg}\) traveling \(21.0 \mathrm{~m} / \mathrm{s}\). (b) Find the velocity (in \(\mathrm{km} / \mathrm{h}\) ) of a light auto of mass \(1170 \mathrm{~kg}\) so that it has the same momentum as the auto in part (a).

A \(16.0\) -g bullet is shot into a wooden block at rest with mass \(4550 \mathrm{~g}\) on a frictionless surface. The block moves \(1.20 \mathrm{~m} / \mathrm{s}\) after the bullet strikes and becomes lodged in the block. Find the speed of the bullet before striking the block.

A ball of mass \(0.50 \mathrm{~kg}\) is thrown straight up at \(6.0 \mathrm{~m} / \mathrm{s}\). (a) What is the initial momentum of the ball? (b) What is the momentum of the ball at its peak? (c) What is the momentum of the ball as it hits the ground?

A \(2450-\mathrm{kg}\) automobile moving north \(12.0 \mathrm{~m} / \mathrm{s}\) collides with a \(1650-\mathrm{kg}\) automobile moving \(8.00 \mathrm{~m} / \mathrm{s}\) on an icy road. The automobiles stick together and move after the collision. Find the velocity of the automobiles after the collision if the automobiles were traveling in (a) opposite directions and (b) the same direction before the collision.

A bullet with mass \(60.0 \mathrm{~g}\) is fired with an initial velocity of \(575 \mathrm{~m} / \mathrm{s}\) from a gun with mass \(4.50 \mathrm{~kg}\). What is the speed of the recoil of the gun?

A cannon is mounted on a railroad car. The cannon shoots a \(1.75-\mathrm{kg}\) ball with a muzzle velocity of \(30 \overline{0} \mathrm{~m} / \mathrm{s}\). The cannon and the railroad car together have a mass of \(45 \overline{0} \mathrm{~kg}\). If the ball, cannon, and railroad car are initially at rest, what is the recoil velocity of the car and cannon?

A \(125-\mathrm{kg}\) pile driver falls from a height of \(10.0 \mathrm{~m}\) to hit a piling. (a) What is its speed as it hits the piling? (b) With what momentum does it hit the piling?

A person is traveling \(75.0 \mathrm{~km} / \mathrm{h}\) in an automobile and throws a bottle of mass \(0.500 \mathrm{~kg}\) out the window. (a) With what momentum does the bottle hit a roadway sign? (b) With what momentum does the bottle hit an oncoming automobile traveling \(85.0 \mathrm{~km} / \mathrm{h}\) in the opposite direction? (c) With what momentum does the bottle hit an automobile passing and traveling \(85.0 \mathrm{~km} / \mathrm{h}\) in the same direction?

(a) What force is required to stop a \(1250-\mathrm{kg}\) car traveling \(95.0 \mathrm{~km} / \mathrm{h}\) within \(4.00 \mathrm{~s}\) ? (b) How far does the car travel during its deceleration?

(a) What force is required to slow a \(1350-\mathrm{kg}\) car traveling \(90.0 \mathrm{~km} / \mathrm{h}\) to \(25.0 \mathrm{~km} / \mathrm{h}\) within \(4.00 \mathrm{~s}\) ? (b) How far does the car travel during its deceleration? (c) How long does it take for the car to come to a complete stop at this same rate of deceleration?

What force is needed to stop a piece of heavy equipment moving \(10.0 \mathrm{~km} / \mathrm{h}\) in \(6.00 \mathrm{~s}\) if its mass is \(50 \overline{0} 0 \mathrm{~kg}\) ?

A standard \(5.0\) -oz baseball is thrown and reaches a batter with a velocity of \(85 \mathrm{mi} / \mathrm{h}\) when it is struck with a bat that causes it to reverse direction with a velocity of \(95 \mathrm{mi} / \mathrm{h}\). Find (a) the impulse and (b) the force exerted on the baseball if the bat is in contact with the ball for \(7.0 \mathrm{~ms}\).