Example Problems 8.2 Conservation of Momentum Brake Apart: p i p f ( )v 1,2i v 1f v 2 f Stick Together: p i p f v 1i v 2i ( )v 1,2 f Bouncing/Pass Through: p i p f v 1i v 2i v 1f v 2 f Example 1: - A monkey fires a 10-kg rifle. The bullet of mass 0.02-kg, leaves with a muzzle with a velocity of 310 m/s to the right. What is the recoil velocity of the rifle? m 2 v 1,2i v 1f v 2 f Example 2: - Barry, a 65.0-kg skin diver, shoots a 2.0-kg spear with a speed of 15 m/s at a fish who darts quickly away without getting hit. How fast does Barry move backwards when the spear is shot? m 2 v 1,2i v 1f v 2 f Doc Fizzix Example Problems Conservation of Momentum 27
Example 3: - Two freight cars, each with a mass of 300,000kg, collide. One was initially moving at 2.2 m/s; the other was at rest. They stick together. What is their final speed? v 1,2 f Example 4: -A 0.105-kg hockey puck moving at 24 m/s is caught and held by a 75-kg goalie at rest. With what speed does the goalie slide on the ice? v 1,2 f Doc Fizzix Example Problems Conservation of Momentum 28
Example 5: - A 0.035-kg bullet strikes a 5.0-kg stationary wooden block and embeds itself in the block. The block and bullet fly off together at 8.6 m/s. What was the original speed of the bullet? v 1,2 f Example 6: - A 35.0-g bullet moving at 475 m/s strikes a 2.5-kg wooden block that is at rest. The bullet passes through the block, leaving at 275 m/s. How fast is the block moving when the bullet leaves? v 1f v 2 f Doc Fizzix Example Problems Conservation of Momentum 29
Example 7: - A 0.50-kg ball traveling at 6.0 m/s collides head-on with a 1.00-kg ball moving in the opposite direction at a speed of 12.0 m/s. The 0.50-kg ball bounces backward at 14 m/s after the collision. Find the speed of the second ball after the collision. v 1f v 2 f Example 8: - Macy throws a 0.05-kg foam ball in the living room and knocks over her 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 Macy throw the football? v 1f v 2 f Doc Fizzix Example Problems Conservation of Momentum 30
Student Problems 8.2 Conservation of Momentum - Break Apart Conservation of momentum tells us that what ever momentum a system starts with will also be the momentum the system ends with after some event like braking apart of colliding. p i p f ( )v 1,2i v 1 f v 2 f 1. 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? m 2 v 1,2i v 1f v 2 f 31
2. A 1.2-kilogram block and a 1.8-kilogram block are initially at rest on a frictionless, horizontal surface. When a compressed spring between the blocks is released, the 1.8-kilogram block moves to the right at 2.0 meters per second, as shown.? 2.0 m/s 1.2 kg 1.8 kg Frictionless horizontal surface What is the speed of the 1.2-kilogram block after the spring is released? m 2 v 1,2i v 1f v 2 f 32
3. A 3.63-kg monkey is standing at rest on 2-kg skateboard when he decides to jumps off the skateboard sending him in one direction and the skateboard in the opposite direction. The monkey s final velocity is 3.05 m/s to the north, what is the magnitude and the direction of the skateboard s velocity? m 2 v 1,2i v 1f v 2 f 4. An 82-kg gorilla and a 48-kg monkey pair figure skating team are gliding across the ice at 7.4 m/s, 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. m 2 v 1,2i v 1f v 2 f 33
8.3 Conservation of Momentum - Inelastic Collisions Inelastic collisions occur when objects collide and stick together becoming one mass traveling with one velocity. All collisions including inelastic collisions follow the law of conservation of momentum. p i p f v 1i v 2i ( )v 1,2 f 5. A 3.0-kilogram block is at rest on a friction- less horizontal surface. A 1.0-kilogram lump of clay is propelled horizontally at 6.0 meters per second toward the block as shown in the diagram below. Steel block Clay 1.0 kg 6.0 m/s 3.0 kg Frictionless surface Upon the collision, the clay and block stick together and move to the right. What is the combined velocity? v 1,2 f 34
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 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, what is the magnitude and the direction of the velocity of the wreckage immediately after the collision? v 1,2 f 35
8. A bullet (0.068 kg) is shot from a gun and collides with, and embeds itself in a 2-kg block of wood 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 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 36
8.4 Conservation of Momentum - Elastic Collisions Elastic collisions occur when objects collide but do not stick together, they may bounce off one another or even pass through each other. All collisions including elastic collisions follow the law of conservation of momentum. p i p f v 1i v 2i v 1f v 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? v 1f v 2 f 37
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? v 1f v 2 f 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? v 1f v 2 f 38