A student holds one end of a string in a fixed position. A ball of mass .2 kg attached to the other end of the string moves in a horizontal circle of radius .5m with a constant speed of 5m/s. How much work is done on the ball by the string during each revolution?

Question

a)0 J
b).5 J
c)1 J
d)2pi J
e)5pi J

Could you please tell me how I would solve this problem? I used F=mv^2/r and then I got 10. Then I used W=fd which gave me W=(10)(.5) and I got 5 as the answer. But this answer isn't in the choices.

The answer is 0 j.

Work done equals displacement times the component of the force in the direction of the displacement. In this case the force exerted by the string on the ball is always at right angles to the direction in which the ball moves.

You can also say that the work done must equal the change in kinetic energy of the ball, but the ball moves at constant speed, only the direction of the velocity changes. So, the kinetic energy stays constant and therefore no work is done on the bal.

Answer 1

It's in a uniform circular motion so no work is done.

Answer 2

Or, you can think of it as you start at an A point on the circle, after one revolution, it returns back to A, means displacement is 0. Since W=Displacement*Force so W=0