A hockey player is initially moving at 5.00m s to the east. Her mass is 50.0 kg. She intercepts and catches on her stick a puck initially moving at 35.0m s at an angle of 30 degrees (Fig. 6.40). Assume that the puck’s mass is 0.50 kg and the two form a single object for a few seconds. (a) Determine the direction angle and speed of the puck and skater after the collision. (b) Was this collision elastic or inelastic? Prove your answer with numbers.

Question

A hockey player is initially moving at 5.00m s to the east. Her mass is 50.0 kg. She intercepts and catches on her stick a puck initially moving at 35.0m s at an angle of 30 degrees (Fig. 6.40). Assume that the puck’s mass is 0.50 kg and the two form a single object for a few seconds. (a) Determine the direction angle and speed of the puck and skater after the collision. (b) Was this collision elastic or inelastic? Prove your answer with numbers.

Answer 1

To answer this question, we need to apply the principles of conservation of momentum and conservation of kinetic energy. Here's a step-by-step approach:

Step 1: Calculate the initial momentum of the hockey player and the puck separately.

Momentum (p) = mass (m) * velocity (v).

For the hockey player:
Mass (m1) = 50.0 kg
Velocity (v1) = 5.00 m/s

Momentum (p1) = m1 * v1 = 50.0 kg * 5.00 m/s = 250 kg·m/s

For the puck:
Mass (m2) = 0.50 kg
Velocity (v2) = 35.0 m/s

Momentum (p2) = m2 * v2 = 0.50 kg * 35.0 m/s = 17.5 kg·m/s

Step 2: Calculate the total momentum after the collision.

The total momentum remains constant before and after the collision, as there are no external forces acting on the system.

Total momentum before collision = Total momentum after collision.

p1 + p2 = p3 + p4

Substituting the values: 250 kg·m/s + 17.5 kg·m/s = (50.0 kg + 0.5 kg) * vf

Step 3: Calculate the final velocity.

vf = (250 kg·m/s + 17.5 kg·m/s) / (50.5 kg)

vf ≈ 4.99 m/s

Now we need to find the direction angle of the final velocity:

The puck and the skater will move in the direction of the resulting momentum.

θ = tan^(-1)((p3 + p4) / (p2 + p4))

θ = tan^(-1)((250 kg·m/s + 17.5 kg·m/s) / (0 + 17.5 kg·m/s))

θ ≈ 85.4 degrees

So, the direction angle of the puck and skater after the collision is approximately 85.4 degrees.

Step 4: Calculate the kinetic energy before and after the collision to determine if it's elastic or inelastic.

The collision is elastic if the total kinetic energy is conserved. It is inelastic if the total kinetic energy is not conserved.

Kinetic energy (KE) = (1/2) * mass * velocity^2

Initial kinetic energy = (1/2) * (50.0 kg) * (5.00 m/s)^2 + (1/2) * (0.50 kg) * (35.0 m/s)^2

Final kinetic energy = (1/2) * (50.5 kg) * (4.99 m/s)^2

Comparing the initial and final kinetic energies will determine whether the collision is elastic or inelastic.

If the initial kinetic energy is equal to the final kinetic energy, the collision is elastic. If they are not equal, the collision is inelastic.

Calculate the initial and final kinetic energies to determine if the collision is elastic or inelastic.