Example Problems 7.2 Conservation of E1. A monkey fires a 10 kg rifle. The bullet of mass 0.02 kg, leaves with a muzzle of the rifle with a velocity of 310 m/s to the right. What is the recoil velocity of the rifle? v 1,2o = E2. A 60-kg gorilla and a 40-kg monkey face each other on skateboards and touch hands. The gorilla and the monkey start at rest. The monkey pushes the gorilla and the gorilla moves away at a speed of 2 m/s. Calculate the speed of the monkey. v 1,2o = 1
E3. A railroad car with a mass of 11,000 kg is moving at 4.5 m/s to the right when it collides and couples with a second car of mass 19,000 kg that is initially at rest. Calculate the final velocity of the coupled rail cars after the collision. v 1,2 f = E4. A 0.105-kg hockey puck is moving at 24 m/s when it is caught by a 75 kg goalie who is at rest. With what speed do the goalie and the puck slide together after the goalie catches the puck? v 1,2 f = 2
E5. A 0.035-kg bullet strikes a 5.0-kg stationary wooden block and embeds itself in the block. The block and bullet slide off together at 8.6 m/s. What was the original speed of the bullet? v 1,2 f = E6. A 0.035-kg bullet moving at 475 m/s strikes a 2.5-kg wooden block that is at rest. The bullet passes through the block and exists on the opposite side at a speed of 275 m/s. Calculate how fast the block is moving after the bullet passes through. 3
E7. Ball A is traveling at 6.0 m/s when it has a head-on collision with ball B moving in the opposite direction at a speed of 12.0 m/s. Ball A bounces backward at 14 m/s after the collision. If ball A has a mass of 0.50 kg and ball B a mass of 1.0 kg, find the speed of ball B after the collision. E8. A monkey throws a 0.05-kg foam ball in the living room and knocks over his mother s 0.60-kg antique vase. After the collision, the foam ball bounces straight back with a speed of 7.0 m/s, while the vase is moving at 1.3 m/s in the opposite direction. How fast did the monkey throw the football? 4
Student Problems 7.2 Conservation of 1. A 2.8 kilogram block and a 1.7 kilogram block are initially at rest on a frictionless, horizontal surface. A compressed spring pushes the two blocks apart. The 2.8-kilogram block moves to the right at 1.5 meters per second, as shown.? 1.5 m/s 1.7 kg 2.8 kg Frictionless horizontal surface What is the speed of the 1.7-kilogram block after the spring is released? v 1,2o = 5
2. A monkey fires a 5 kg rifle. The bullet of mass 0.01 kg, leaves with a muzzle with a velocity of 420 m/s to the right. What is the recoil velocity of the rifle? v 1,2o = 3. A 36.3 kg monkey is standing at rest on 2.5 kg skateboard when he decides to jumps off the skateboard sending him in one direction and the skateboard flies off in the opposite direction. The monkey s final velocity is 0.5 m/s to the north, what is the magnitude and the direction of the skateboard s velocity? v 1,2o = 6
4. An 82 kg gorilla and a 48 kg monkey pair figure skating team are gliding across the ice at 7.4 m/s to the north, preparing for a throw maneuver. The gorilla tosses the monkey forward with a speed of 8.6 m/s to the north. Determine the magnitude and the direction of the gorilla s velocity immediately after the throw. v 1,2o = 7
5. A 5.0-kilogram block is at rest on a friction- less horizontal surface. A 1.5-kilogram lump of clay is propelled horizontally at 4.0 meters per second toward the block as shown in the diagram below Steel block Clay 1.5 kg 4.0 m/s 5.0 kg Frictionless surface Upon the collision, the clay and block stick together and move to the right. What is the combined velocity of the clay and block together? v 1,2 f = 8
6. A1000.-kilogram empty cart moving with a speed of 6.0 meters per second is about to collide with a stationary loaded cart having a total mass of 5000. kilograms, as shown. After the collision, the carts lock and move together. Calculate the speed of the combined carts after the collision. v = 6.0 m/s v = 0.0 m/s 1000. kg 5000. kg v 1,2 f = 9
7. A 20,000-kg truck driven by a gorilla has a head on collision with a 1,500-kg car driven by a monkey. Just before impact the truck s speed is 5.00 m/s to the west and the car s was 8.00 m/s in the opposite direction towards the east. If the truck and the car stick together after the collision, calculate is the velocity of the wreckage immediately after the collision. v 1,2 f = 8. A bullet (0.068 kg) is shot from a gun and embeds itself into a 2-kg block of wood originally sitting at rest on a table. After the collision, the bullet and the block are moving at 4.93 m/s. What was the original speed of the bullet before the collision? v 1,2 f = 10
9. A 1100 kg car traveling north collides head-on with a 2500 kg van traveling south at 8.0 m/s. After the collision the vehicles lock together and travel south at 1.73 m/s. What was the original velocity of the 1100 kg car before the collision? v 1,2 f = 10. A 7-kg bowling ball strikes a 1.5-kg bowling-pin head on. The pin flies off with a speed of 4-m/s and the bowling ball continues at 2-m/s. What was the original speed of the bowling ball before it hit the pin? 11
11. A monkey throws his 0.20-kg football in the living room and it knocks over his mother s 0.80-kg antique vase. After the collision, the football bounces straight back with a speed of 3.9 m/s, while the vase is moving at 2.6 m/s in the opposite direction. How fast did the monkey throw the football? 12. A 10-g (0.01 kg) bullet is fired at a speed of 520 m/s into a 0.4-kg wooden block that is initially at rest. The bullet passes through the block and leaves with a speed of 200- m/s. Calculate the final speed of the block after the collision. 12
Monkey Busters 7.2 Conservation of 13. A loaded freight car whose mass is 16,000 kg rolls along a level track at a speed of 1.5 m/s toward an empty stationary freight car. The two couple and proceed at a speed of 1.0 m/s. Determine the mass of the empty freight car. Calculate the initial and final kinetic energies. b) 14. A 10-g bullet is fired into a 0.5-kg wooden block which is initially at rest on a horizontal surface. The bullet passes through the block, leaving with a speed of 250 m/s. The block acquires a speed of 8 m/s in the event. Calculate the impact speed of the bullet and the energy dissipated as heat within the block of wood. b) 13
15. A 60-kg man, standing on smooth ice, pushes a 10-kg curling stone toward a companion. The companion, whose mass is 70 kg, is sliding on the ice toward the approaching curling stone at a speed of 3 m/s. After the companion catches hold of the curling stone, his forward speed is reduced to 2 m/s. What was the speed of the curling stone on the ice, and what is the velocity of the 60-kg man after he has released the stone? b) 16. A mass of 3 kg moving to the right at a speed of 4 m/s collides with and sticks to a mass of 5 kg that is initially at rest What are the momentum and KE of the system after the collision? b) 14
17. A bullet of mass 0.008 kg is fired into a ballistic pendulum of mass 0.60 kg. If the speed of the bullet at impact is 400 m/s, what is the maximum height of the pendulum s swing? 18. A bullet is fired horizontally into the 1.8-kg block of a ballistic pendulum. The mass of the bullet is 20 g, and the pendulum swings to a height of 1.2 m. What was the speed of the bullet just before it entered the block of wood? 15
19. A 34-g bullet is fired up into a block of wood of mass 1.25 kg. The bullet lodges in the wood, which rises to a height of 6 meter. Find the speed of the bullet on impact with the wood. 20. A wooden puck slides due east on an air table with a speed of 1.5 m/s. At the center of the table it collides with an identical puck, which is at rest. The collision is elastic, and following the impact, the two pucks move with equal speeds. Determine the velocity of each puck. b) 16
21. A 75-kg man stands on a rectangular raft of mass 45 kg. The man then walks from one end of the 4-m-long raft to the other. How far has the raft moved in the process? 22. A mass of 0.6 kg makes a perfectly elastic head on collision with a mass of 0.4 kg that is initially at rest. Following the collision, the 0.6-kg mass moves at a speed of 2 m/s. Find the initial speed of the 0.6-kg mass and the final speed of the 0.4-kg mass. b) 17
23. A mass of 1.2 kg, moving at a speed of 10 m/s, collides head-on with a mass of 0.8 kg, which is at rest. What are the velocities of the two masses following the collision if the collision is ( elastic? (b) perfectly inelastic? b) 24. A 7-kg bowling ball strikes a 1.5-kg bowling pin head-on. Following the collision, the bowling ball continues its forward motion at 2 m/s. Assuming the collision is elastic, find the speed of the bowling pin just after the collision and that of the bowling ball just before it struck the pin. b) 18