Momentum

Momentum is defined as the product of an object's mass and its velocity.

p = mv
p = 0.25 kg * 12 m/s
p = 3 kg m/s

The momentum of the ball is 3 kg m/s.

p = mv
v = p/m
v = 0.5 kg m/s / 0.1 kg
v = 5 m/s

The toy car's velocity is 5 m/s.

Impulse = Force x Time = Change in momentum
Impulse = 80 N x 0.12 s = 9.6 Ns
Change in momentum = 9.6 kg m/s

Impulse is the change in momentum, so we calculate force multiplied by time to find the change in momentum.

Impulse = Change in momentum = m(v-u)
Impulse = 0.16 kg x (0 m/s - 35 m/s) = -5.6 Ns
Impulse experienced by the fielder is 5.6 Ns (or -5.6 Ns, depending on direction convention). The negative sign indicates the force acts in the opposite direction to the ball's initial motion. The fielder is experiencing the change in momentum of the ball.

Formula: Total momentum before = Total momentum after
(m₁v₁) + (m₂v₂) = (m₁v₁') + (m₂v₂')

Working:
(2 kg * 3 m/s) + (1 kg * 0 m/s) = (2 kg * 2 m/s) + (1 kg * v₂')
6 kg m/s = 4 kg m/s + (1 kg * v₂')
2 kg m/s = 1 kg * v₂'
v₂' = 2 m/s

Answer: The velocity of the 1 kg trolley after the collision is 2 m/s to the right. (2 marks)

Momentum is conserved in a closed system with no external forces. When the ball hits the ground, the system is NOT closed because the Earth exerts an external force on the ball (and the ball exerts an equal and opposite force on the Earth). While the *total* momentum of the ball + Earth system *is* conserved, the momentum of the ball alone is not. The change in the ball's momentum is equal and opposite to the change in the Earth's momentum, but because the Earth's mass is so large, its change in velocity is negligible. Friction and air resistance also apply external forces.

F = (mv - mu)/t
F = (1200 kg * 25 m/s - 1200 kg * 10 m/s) / 5 s
F = (30000 kg m/s - 12000 kg m/s) / 5 s
F = 18000 kg m/s / 5 s
F = 3600 N

The resultant force is the rate of change of momentum. We calculate the change in momentum and divide by the time taken.