A hockey puck with a mass of 160 g slides at a speed of 12 m/s on frictionless ice. The puck runs into a small box with a mass of 850 g that is initially at rest. Assuming that the collision is elastic, what is the speed of the hockey puck after the collision?
Question
A hockey puck with a mass of 160 g slides at a speed of 12 m/s on frictionless ice. The puck runs into a small box with a mass of 850 g that is initially at rest. Assuming that the collision is elastic, what is the speed of the hockey puck after the collision?
Solution
In an elastic collision, both momentum and kinetic energy are conserved.
First, let's convert the masses from grams to kilograms, because in physics, we usually use SI units. So, the mass of the puck (m1) is 0.16 kg and the mass of the box (m2) is 0.85 kg. The initial speed of the puck (u1) is 12 m/s and the initial speed of the box (u2) is 0 m/s (since it's at rest).
The final speed of the puck (v1) and the box (v2) can be found using the following equations derived from the conservation of momentum and kinetic energy:
v1 = ((m1 - m2) / (m1 + m2)) * u1 + ((2 * m2) / (m1 + m2)) * u2
v2 = ((2 * m1) / (m1 + m2)) * u1 - ((m1 - m2) / (m1 + m2)) * u2
Substituting the given values into these equations, we get:
v1 = ((0.16 - 0.85) / (0.16 + 0.85)) * 12 + ((2 * 0.85) / (0.16 + 0.85)) * 0 = -5.4 m/s
The negative sign indicates that the puck is moving in the opposite direction after the collision. So, the speed of the hockey puck after the collision is 5.4 m/s.
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