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?
To find the total momentum of the goalkeeper and the puck after the puck is caught, we need to consider the law of conservation of momentum, which states that in a closed system, the total momentum before an event is equal to the total momentum after the event.
The momentum (p) of an object is calculated by multiplying its mass (m) by its velocity (v):
momentum (p) = mass (m) × velocity (v)
Given:
Mass of the puck (m1) = 0.16 kg
Velocity of the puck (v1) = 42 m/s
Mass of the goalkeeper (m2) = 122 kg
Velocity of the goalkeeper (v2) = 0 m/s (since the goalkeeper is at rest)
The total momentum before the puck is caught is the sum of the momentum of the puck and the momentum of the goalkeeper:
Total momentum before = momentum of puck + momentum of goalkeeper
= m1 × v1 + m2 × v2
= (0.16 kg) × (42 m/s) + (122 kg) × (0 m/s)
= 6.72 kg*m/s
After the puck is caught, the goalkeeper and the puck are at rest. Therefore, the velocity of both objects is zero (v1' = 0 m/s and v2' = 0 m/s).
Now we can find the total momentum after the puck is caught:
Total momentum after = momentum of puck + momentum of goalkeeper
= m1 × v1' + m2 × v2'
= (0.16 kg) × (0 m/s) + (122 kg) × (0 m/s)
= 0 kg*m/s
Comparing the total momentum before and after the puck is caught, we see that the total momentum is conserved in this closed system. The total momentum of the system is zero after the event, meaning there is no net momentum.
Therefore, neither the puck nor the goalkeeper has momentum after the puck is caught.