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.
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