Problem 10.

A constant force of 80 N acts for 8 s on a box of mass 10 kg horizontally that initially rests on a horizontal frictionless surface.

(a) Find the change in the box's momentum.

(b) Calculate the final speed of the box after the 8 s have passed.

Solution:

In this problem we need to use the definition of an impulse of a force and the relation between the impulse and the chance of the momentum of the box.

If a constant force acts on a box for a time then the impulse of the force is

In the present problem a constant force of 80 N acts for 8 s. Then and . Then the impulse is

(a) The change in the box's momentum is equal to the impulse of the force acting on the box:

(b) The initial speed of the box is zero. Then the initial momentum of the box is zero. The change of the momentum is equal to the difference between the final momentum and the initial momentum (which is zero). Then

Now we know the final momentum of the box. To find the final speed we just need to divide the final momentum by the mass of the box: