Momentum and impulse – problems and solutions

1. A small ball is thrown horizontally with a constant speed of 10 m/s. The ball hits the wall and reflected with the same speed. What is the change in linear momentum of the ball?

Known :

Mass (m) = 0.2 kg

Initial speed (v_o) = -10 m/s

Final speed (v_t) = 10 m/s

The plus and minus sign indicates that the objects moves in opposite direction.

Wanted : the change in linear momentum (Δp)

Solution :

Formula of the change in linear momentum :

Δp = m v_t – m v_o = m (v_t – v_o)

The change in linear momentum :

Δp = 0.2 (10 – (-10)) = 0.2 (10 + 10)

Δp = 0.2 (20)

Δp = 4 kg m/s

2. A 10-gram ball falls freely from a height, hits the floor at 15 m/s, then reflected upward at 10 m/s. Determine the impulse!

Known :

Mass (m) = 10 gram = 0.01 kg

Initial velocity (v_o) = -15 m/s

Final velocity (v_t) = 10 m/s

Wanted : Impulse (I)

Solution :

The impulse (I) equals the change in momentum (Δp)

I = m v_t – m v_o = m (v_t – v_o)

Impulse :

I = 0.01 (10 – (-15)) = 0.01 (10 + 15)

I = 0.01 (25)

I = 0.25 kg m/s

3. A 200-gram ball thrown horizontally with a speed of 4 m/s, then the ball was hit in the same direction. The duration of the ball in contact with the bat is 2 milliseconds and the ball speed after leaving the bat is 12 m/s. The magnitude of force exerted by the batter on the ball is …

Known :

Mass (m) = 200 gram = 0.2 kg

Initial velocity (v_o) = 4 m/s

Final velocity (v_t) = 12 m/s

Time interval (t) = 2 milliseconds = (2/1000) seconds = 0.002 seconds

Wanted : The magnitude of the force (F)

Solution :

Formula of impulse :

I = F t

Formula of the change in momentum :

m v_t – m v_o = m (v_t – v_o)

The impulse (I) equals the change in momentum (Δp)

I = Δp

F t = m (v_t – v_o)

F (0.002) = (0.2)(12 – 4)

F (0.002) = (0.2)(8)

F (0.002) = 1.6

F = 1.6 / 0.002

F = 800 Newton

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1. Linear momentum problems and solutions
2. Momentum and impulse problems and solutions
3. Perfectly elastic collisions in one dimension problems and solutions
4. Perfectly inelastic collisions in one dimension problems and solutions
5. Inelastic collisions in one dimension problems and solutions