6-8 Conservation of Momentum

Transcription

1 Worksheet 6-8 Conservation of Momentum 1. Represent the momentum of each object with a velocity-mass bar graph. a. A 1000 kg car travels to the right at 22 m/s. b. A kg airplane has an instantaneous velocity of 2 m/s while accelerating to the left at 25 m/s 2. c. A tugboat exerts a N force on a huge barge with a mass of kg. Due to friction from the water, they both move to the left with a constant speed of 0.32 m/s.

2 2. Two girls are at rest on frictionless in-line skates. The younger one has a mass of 30 kg and the older one has a mass of 60 kg. The older girl pushes the younger girl so that the latter rolls to the right at a speed of 10 m/s. a. Draw a before and after velocity-mass bar graph for this situation, and determine any unknown variables. b. Which girl had the greater change in momentum? Explain why your answer makes sense by referring to laws of physics. c. Which girl had the greater change in velocity? Explain why your answer makes sense by referring to laws of physics. d. What ids the velocity of the older girl? 3. In a freight yard a train is being put together from freight cars. An empty freight car, coasting at 10 m/s, strikes a loaded car that is stationary, and the cars couple together. Each of the cars has a mass of kg when empty, and the loaded car contains kg of cargo. a. Draw a before and after velocity-mass bar graph for this situation, and determine any unknown variables. b. Which freight car had the greater change in momentum? Explain why your answer makes sense by referring to laws of physics. c. Which freight car had the greater change in velocity? Explain why your answer makes sense by referring to laws of physics. d. What is the velocity of the two cars after coupling?

3 4. A tennis player s 1 kg racket is moving with a velocity of 30 m/s when it impacts a tennis ball traveling at 30 m/s from the opponent s serve. The 0.20 kg ball is hit straight back at 25 m/s. a. Draw a before and after velocity-mass bar graph for this situation, and determine any unknown variables. b. Which object had the greater change in momentum, the racket or the ball? Explain why your answer makes sense by referring to laws of physics. c. Which object had the greater change in velocity, the racket or the ball? Explain why your answer makes sense by referring to laws of physics. d. What is the final velocity of the tennis racket? 5. Kim holds a 2 kg air rifle loosely and fires a bullet of mass 1 g. The muzzle velocity of the bullet is 150 m/s to the right. What is the recoil speed of the rifle? (The gun does not cause her to move.) 6. If the girl in the previous question holds the rifle tightly against her body, the recoil speed is less. Explain. Calculate the new recoil speed assuming the girl has a mass of 48 kg.

4 7. An astronaut whose mass is 80 kg carries an empty oxygen tank with a mass of 20 kg. He throws the tank away from himself with a speed of 2 m/s. With what velocity does he start to move off into space? 8. A 50 kg cart is moving across a frictionless floor at 3 m/s. A 75 kg boy, riding in the cart, jumps off so that he hits the floor with zero velocity. a. What impulse did the boy give to the cart? b. What was the velocity of the cart after the boy jumped? 9. A 2 kg melon is balanced on a bald man's head. His son shoots a 50 g arrow at it with a speed of 30 m/s. The arrow passes through the melon and emerges with a speed of 18 m/s. Find the speed of the melon as it flies off the man's head. 10. Mighty Miquel has a mass of 100 kg and is running towards the end zone at 9 m/s. Jumpin Joey (m = 75 kg), runs at 12 m/s towards Miquel. They collide at the 2-yard line. Does Miquel score a touchdown? Explain.

5 For all solutions, assume motion to the right is positive. 1a. 1b. 1c. 2a. 2b. Both girls had the same change in momentum as given by the law of conservation of momentum. 2c. p = m v Since the younger girl has a smaller mass she had a greater change in velocity.

6 2d. p older + p younger = 0 m o v o + m y v y = 0 v o = m y v m y o 30 kg v o = (10 m/s) 60 kg v o = 5 m/s 3a. The total mass of the loaded freight car is kg kg = kg. 3b. Both cars had the same change in momentum. 3c. The empty car had the greater change in velocity. 3d. p loaded + p empty = 0 m l v l + m e v e = 0 m l (v lf v li ) + m e (v ef v ei ) = 0 m l v f + m e (v f v ei ) = 0 m l v f + m e v f m e v ei = 0 m l v f + m e v f = m e v ei (m l + m e )v f = m e v ei v f = m ev ei m l + m e (3 000 kg)(10 m/s) v f = kg kg v f = 1.7 m/s note: v li = 0 and v lf = v ef = v f 4a.

7 4b. Both the racket and the ball had the same change in momentum. 4c. The ball had the greater change in velocity. 4d. p racket + p ball = 0 m r v r + m b v b = 0 m r (v rf v ri ) + m b (v bf v bi ) = 0 m r v rf m r v ri + m b (v bf v bi ) = 0 m r v rf = m r v ri m b (v bf v bi ) v rf = m rv ri m b (v bf v bi ) 5. m r (1 kg)(30 m/s) (0.2 kg)[25 m/s ( 30 m/s)] v rf = 1 kg v rf = 19 m/s p gun + p bullet = 0 m g v g + m b v b = 0 v g = m b v m b g kg v o = (150 m/s) 2 kg v o = m/s 6. If the girl holds the gun tightly then the effective mass becomes 50 kg (2 kg + 48 kg). Since the mass increases the change in velocity must decrease. v g = m b v m b g kg v o = (150 m/s) 50 kg v o = m/s