a hockey puck with a mass of 0.16 kg travels at a velocity of 42 m/s toward a goalkeeper. the goalkeeper has a mass of 122 kg and is at rest. assuming a closed system, find the total momentum of the goalkeeper and puck after the puck i caught by the goalkeeper. which object has the greater momentum after the puck is caught, the puck or the goalkeeper? and why?
To solve this problem, we can use the principle of conservation of momentum. According to this principle, the total momentum of a closed system remains constant before and after a collision.
The momentum of an object can be calculated by multiplying its mass and velocity. Therefore, the momentum of the puck (m1) before the collision is given by:
Momentum of puck (before) = mass of puck × velocity of puck
= 0.16 kg × 42 m/s
= 6.72 kg·m/s
Since the goalkeeper is initially at rest, the momentum of the goalkeeper (m2) before the collision is 0 kg·m/s.
After the puck is caught by the goalkeeper, they move together as one system. The total momentum of the system (m_total) after the collision can be calculated by adding the individual momenta of the puck and the goalkeeper.
Total momentum (after) = momentum of puck (after) + momentum of goalkeeper (after)
However, since the goalkeeper has caught the puck, they move together at the same velocity. Therefore, the velocity of the combined system is the same as the velocity of the puck before the collision (42 m/s).
Therefore, the total momentum of the system after the collision is:
Total momentum (after) = (mass of puck + mass of goalkeeper) × velocity
= (0.16 kg + 122 kg) × 42 m/s
= 5136 kg·m/s
Comparing the total momentum of the goalkeeper and the puck after the collision, we find that the goalkeeper has greater momentum. This is because the goalkeeper's mass is significantly higher compared to the mass of the puck. Thus, even though the puck's velocity is initially higher than the goalkeeper's, the goalkeeper's greater mass allows him to have greater momentum after the catch.