Assignment 6.3 – Conservation of Momentum
1. A steel ball with a mass of 2 kg is traveling at 3 m/s west. It collides with a stationary ball that has a mass
of 1 kg. Upon collision, the smaller ball moves to the west at 4 m/s. What is the velocity of the larger ball?
2. A boy and a girl are riding in bumper cars at an amusement park. A 75-kg boy and car are moving to the
east at 3.00 m/s toward a 50-kg girl and car who are moving west toward him at 1.80 m/s. If they have a
totally inelastic collision, what will be their final velocity?
3. In a hockey game, an 80.0-kg player skating at 10.0 m/s overtakes and bumps from behind a 100.0-kg
player who is moving in the same direction at 8.00 m/s. As a result of being bumped from behind, the
100.0-kg player’s speed increases to 9.78 m/s. What is the 80.0-kg player’s velocity (speed and direction)
after the bump?
4. A 3-kg hard steel ball collides head-on with a 1-kg hard steel ball. The balls are moving at 2 m/s in opposite
directions before they collide. Upon colliding, the 3-kg ball stops. What is the velocity of the 1-kg object
after the collision?
5. A 50 g marble moving at 2.0 m/s strikes a 20 g marble at rest. What is the speed of each marble
immediately after the elastic collision?
6. A 45-kg female figure skater and her 75-kg male skating partner begin their ice-dancing performance
standing at rest in face-to-face position with the palms of their hands touching. When their dance-music
starts, both skaters “push off” with their hands to move backward. If the female skater moves at 2.0 m/s
relative to the ice, what is the velocity of the male skater?
7. A 0.35 kg tennis racquet moving to the right at 20.0 m/s hits a 0.060-kg tennis ball that is moving to the left
at 30.0 m/s. The racquet continues moving to the right after the collision, but at a reduced speed of 10.0
m/s. What is the velocity of the tennis ball after it is hit by the racquet?
8. A proton (𝑚 = 1.67 𝑥 10−27 𝑘𝑔) traveling at 2.50 𝑥 105 𝑚⁄𝑠 collides with an unknown particle initially at
rest. After the collision, the proton reverses direction and travels at 1.10 𝑥 105 𝑚/𝑠. Determine the change
in momentum of the unknown particle.
9. An astronaut at rest in space fires a thruster pistol that expels 35 g of hot gas at 875 m/s. The combined
mass of the astronaut and pistol is 84 kg. How fast and in what direction is the astronaut moving after firing
the pistol?
10. 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?
11. Two titanium spheres approach each other head-on with the same speed and collide elastically. After the
collision, one of the spheres, whose mass is 300 g, remains at rest. What is the mass of the other sphere?
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Assignment 6.3 – Conservation of Momentum
12. A cart with mass 340 g moving on a frictionless linear air track at an initial speed of 1.2 m/s undergoes an
elastic collision with an initially stationary cart of unknown mass. After the collision, the first cart
continues in its original direction at 0.66 m/s. (a) What is the mass of the second cart? (b) What is its
speed after impact?
13. The ballistic pendulum was used to measure the speeds of bullets before electronic timing devices were
developed. The version shown in the figure below consists of a large block of wood of mass M = 5.4 kg,
hanging from two long cords. A bullet of mass m = 9.5 g is fired into the block, coming quickly to rest.
The block + bullet then swing upward, their center of mass rising a vertical distance h = 6.3 cm before the
pendulum comes momentarily to rest at the end of its arc. What is the speed of the bullet just prior to the
collision?
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