AP Physics 1 Exam Question:

A 0.25 kg hockey puck is sliding on a frictionless horizontal ice rink with an initial velocity of 4 m/s. The puck collides with a stationary 0.35 kg goalie mask and rebounds in the opposite direction with a velocity of 2 m/s. Assume the collision is elastic.

a) Calculate the impulse experienced by the hockey puck during the collision with the goalie mask. b) Determine the change in momentum of the hockey puck during the collision. c) Calculate the magnitude and direction of the impulse experienced by the goalie mask during the collision.

Answer:

a) In an elastic collision, the impulse experienced by an object can be determined using the equation:

Impulse = Change in momentum

The change in momentum of an object can be found using the equation:

Change in momentum = (Final velocity - Initial velocity) * mass

Given: Initial velocity of the puck, v1 = 4 m/s Mass of the puck, m1 = 0.25 kg Final velocity of the puck, v2 = -2 m/s (since it rebounds in the opposite direction)

Change in momentum of the puck = (v2 - v1) * m1

Substituting the values:

Change in momentum of the puck = (-2 - 4) * 0.25

Change in momentum of the puck = -1.5 kg·m/s

Therefore, the impulse experienced by the hockey puck during the collision with the goalie mask is -1.5 kg·m/s.

b) The change in momentum of the hockey puck can be calculated using the same equation mentioned earlier:

Change in momentum = (Final velocity - Initial velocity) * mass

Given: Initial velocity of the puck, v1 = 4 m/s Mass of the puck, m1 = 0.25 kg Final velocity of the puck, v2 = -2 m/s

Change in momentum of the puck = (v2 - v1) * m1

Substituting the values:

Change in momentum of the puck = (-2 - 4) * 0.25

Change in momentum of the puck = -1.5 kg·m/s

Therefore, the change in momentum of the hockey puck during the collision is -1.5 kg·m/s.

c) Since the collision is elastic, the total momentum before and after the collision must be conserved.

Initial momentum of the system = Final momentum of the system

Since the goalie mask is stationary, its initial velocity is 0 m/s.

Momentum of the goalie mask = Final momentum of the hockey puck

Momentum of the goalie mask = Mass of the hockey puck * Final velocity of the hockey puck

Given: Mass of the goalie mask, m2 = 0.35 kg Final velocity of the hockey puck, v2 = -2 m/s

Momentum of the goalie mask = m2 * v2

Substituting the values:

Momentum of the goalie mask = 0.35 * -2

Momentum of the goalie mask = -0.7 kg·m/s

Hence, the magnitude of the impulse experienced by the goalie mask during the collision is 0.7 kg·m/s, and the direction of the impulse is opposite to that of the hockey puck.