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In this lesson, we will learn how to calculate the change in motion of objects that collide elastically and inelastically.

Q1:

A 90.0-kg ice hockey player hits a 0.150-kg puck, giving the puck a velocity of 45.0 m/s. If both are initially at rest and if the ice is frictionless, how far does the player recoil in the time it takes the puck to reach the goal 15.0 m away?

Q2:

A child sleds down a hill and collides at 5.6 m/s into a stationary sled that is identical to his. The child is launched forward at the same speed, leaving behind the two sleds that lock together and slide forward more slowly. What is the speed of the two sleds after this collision?

Q3:

Two carts on a straight track collide head on. The first cart was moving at 3.6 m/s in the positive 𝑥 direction and the second was moving at 2.4 m/s in the opposite direction. After the collision, the second cart continues moving in its initial direction of motion at 0.24 m/s. If the mass of the second cart is 5.0 times that of the first, what is the mass of the first cart?

Q4:

An alpha-particle undergoes an elastic collision with a stationary uranium-235 nucleus. What percent of the kinetic energy of the alpha-particle is transferred to the uranium nucleus? Assume the collision is one-dimensional.

Q5:

Two hockey players of unequal masses collide with each other head-on, each moving at a speed of 15 m/s. After the collision, the hockey players move in the same direction as each other, each at the speed of 5.0 m/s. How many times greater is the mass of the more massive hockey player than the mass of the other hockey player?

Q6:

In an elastic collision, a bumper car of mass 250 kg collides directly from behind with a bumper car of mass 315 kg that is traveling in the same direction. The initial speed of the leading bumper car is 4.3 m/s and that of the trailing car is 5.2 m/s.

What is the speed of the 250 kg bumper car after the collision?

What is the speed of the 315 kg bumper car after the collision?

Q7:

A proton is traveling at 3 . 8 × 1 0 6 m/s in the positive 𝑥 -direction. The proton collides elastically with a stationary alpha particle that has four times the mass of the proton. After the collision, the proton moves in a direction 7 3 ∘ above the positive 𝑥 -direction. What percentage of the proton’s kinetic energy before the collision does the proton have after the collision?

Q8:

Two identical pucks, puck 1 and puck 2, are on an air hockey table. Puck 1 is initially at rest. Puck 2 approaches puck 1, moving west at a speed of 4.7 m/s. The pucks collide elastically. After the collision, puck 2 moves in a direction 2 7 ∘ north of west.

What is the speed of puck 1 after the collision?

At what angle south of west is the direction of the motion of puck 1 after the collision?

Q9:

A billiard ball, labeled Ball_{1}, moves in the positive 𝑥 -direction at 2.56 m/s. Ball_{1} collides with another, stationary, billiard ball, labeled Ball_{2}. Both balls’ masses are 230 g. After the collision, Ball_{1} has a speed of 0.340 m/s and moves in a direction 4 3 . 0 ∘ above the positive 𝑥 -direction.

What is the speed of Ball_{2} after the impact?

At what angle below the positive 𝑥 -direction is the motion of Ball_{2}?

Q10:

Two identical billiard balls, Ball A and Ball B, collide. Ball A is initially traveling at m/s and Ball B is travelling at m/s. The balls collide elastically when the center of Ball A is at the origin and the center of Ball B is at the point where is the radius of the balls.

What is the velocity of Ball A after the collision?

What is the velocity of Ball B after the collision?

Q11:

In an elastic collision, a 400 kg bumper car collides directly from behind with a second, identical bumper car that is traveling in the same direction. The initial speed of the leading bumper car is 5.60 m/s and that of the trailing car is 6.00 m/s. Assume that the mass of the drivers is negligible.

What is the final speed of the leading bumper car?

What is the final speed of the trailing bumper car?

Q12:

Two asteroids of different sizes are on a collision course with each other. The large asteroid’s mass is 4 4 × 1 0 3 kg and the small asteroid’s mass is 1 2 × 1 0 3 kg. The large asteroid’s speed is 1 1 2 0 m/s and the small asteroid’s speed is 688 m/s. The large asteroid moves in the positive 𝑥 -direction and the small asteroid moves in a direction 2 7 ∘ above the positive 𝑥 -direction. When the asteroids collide, they stick together.

At what speed do the asteroids move after the collision?

At what angle above the positive 𝑥 -direction is the motion of the asteroids after the collision?

Q13:

A child of mass 34 kg rides a sled with a mass of 18 kg down a hill. At the bottom of the hill, the sled moves horizontally and collides elastically at a speed of 4.8 m/s with a stationary sled that has the same mass as the sled he is riding. The child is launched forward from his sled at 4.8 m/s, landing clear of both sleds. After the collision, the sled that the child was launched from continues to move.

After the collision, what is the speed of the sled that the child was launched from?

After the collision, what is the speed of the sled that was initially at rest?

Q14:

An egg of mass 3.7 g falls from an 84 cm high counter and breaks. What magnitude impulse is exerted by the floor on the egg?

Q15:

A billiard ball with velocity m/s collides elastically with a wall that runs parallel to the direction. What is the velocity of the billiard ball after the collision?

Q16:

Two identical billiard balls are labeled ball and ball . Ball has velocity m/s. Ball has velocity m/s. The billiard balls collide elastically when the center of ball is at the origin and the center of ball is at the point . Assume that the force between the balls is directed perpendicularly to the point of contact between them and that there is no friction force between the balls when they collide.

What is the velocity of ball after the collision?

Q17:

Two projectiles, labeled Projectile One and Projectile Two, have masses of 150 g and 225 g respectively. These projectiles are both launched at a speed of 55.0 m/s at an angle of 2 6 . 0 ∘ above the horizontal. The horizontal motions of the projectiles are in opposite directions, with the projectiles moving horizontally toward each other’s launch positions. The horizontal distance between the launch points of the two projectiles is 550 m. The projectiles collide when at the maximum upward vertical displacement from their launch positions. After the collision, they move together. At what displacement from the launch point of Projectile Two in the direction of Projectile One do the projectiles land?

Q18:

What is the coefficient of restitution for perfectly elastic impact?

Q19:

What is the coefficient of restitution for perfectly plastic impact?

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