Problem 9.

A skater of mass 80 kg initially at rest speeds up to a final speed of 10.0 m/s along a straight line and towards the East direction.

(a) Find the momentum of the skater while at rest.

(b) Find the momentum of the skater while traveling with its final speed.

(c) Find the change in momentum of the skater.

(d) Find the impulse acted on the skater.

(e) If that impulse exerted on the skater acts for 4 s, find the average force acting on the skater.

Solution:

In this problem we need to use the definition of momentum and impulse.

Momentum of an object is a vector, which is defined as the product of a mass of the object and its velocity:

Therefore the direction of momentum is the same as the direction of velocity and the magnitude of momentum is equal to the product of the mass of the object and its speed (the magnitude of velocity).

(a) If the skater is at rest then its speed is zero. Then the momentum of the skater is 0.

(b) The final speed of the skater is10 m/s, its mass is 80 kg, then the final momentum is

(c) The change in the momentum is equal to the difference between the final momentum and initial momentum:

(d) The impulse acted on the skater is equal to the change of its momentum:

(e) At the same time he impulse acted on the skater is equal to the product of the (average) force acted on the skater and the time

We know time: . Then we can find the force: