# Impulse momentum theorem  problems

These impulse momentum theorem problems will help you clearly see how to apply the impulse-momentum theorem. Study the solution we give carefully so you can tackle other similar problems.

Earlier in impulse and momentum, we saw that Ft = ▲mv

In many situations, the mass will not change. In this case, we can also rewrite the formula as Ft = m▲v  or Ft = m(final speed - initial speed)

Problem #1:

What average force is required to push a 20-kg stroller with your toddler in it for 5 seconds if the  weight of the toddler is 15 kg? Suppose that you can push with a speed of 1 m/s and the stroller is initially at rest.

Solution:

You are pushing a total mass of 20 kg + 15 kg = 35 kg

Ft = m(final speed - initial speed)

F × 5 = 35 kg × (1 m/s - 0)

F × 5  = 35

Since 7 × 5 = 35, F = 7 newtons.

## Interesting impulse momentum theorem problems

Problem #2:

An average force of 50 N is exerted on a 4-kg cart for 2 seconds.

a. What is the impulse?

b. What is the change in momentum?

c. What is the mass's change in velocity?

Solution:

a. Impulse  =  F × t

Impulse  = 50 N × 2

Impulse  = 100 N.s

b.

Impulse  = change in momentum

So, change in momentum  = impulse  = 100 N.s

c.

The mass's change in velocity is ▲v

F × t = m▲v

100 N.s = 4 × ▲v

Since 100 = 4 × 25, ▲v = 25 m/s

Problem #3:

A soccer ball is heading toward a wall with a speed of 20 meters per second. After hitting the wall, the ball bounces back with a speed of 25 meters per second. The ball was in contact with the wall for 0.003 second. What is the average force the wall exerted on the ball?

Solution:

F × t = m(final speed - initial speed)

The final speed is 25 meters per second

The initial speed is -20 meters per second. This speed is negative because the ball is going to the other direction.

The mass of a soccer ball is 0.45 kg

F × 0.003 = 0.45 (25 - -20)

F × 0.003 = 0.45 (45)

F × 0.003 = 20.25

F = 20.25 / 0.003

F = 6750 N

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