Problem 39.

A body of mass 10g is set to rotate in a circular path by means of a string 200 cm long. If it makes 3 complete revolutions in 2s, find the tension of the string.

Solution:

The first step is to convert all variables into SI units:

mass should be measures in kg: ;

length should be measured in meters: .

Now we can solve the problem. The body moves in a circle with constant speed. This is the motion with acceleration – centripetal acceleration. The acceleration is pointing towards the center of the circle. The magnitude of acceleration is

Here is the speed of the body (the speed is constant) and is the radius of the circle, which is equal to the length of the string. Therefore, to find the magnitude of the centripetal acceleration we need to know the speed of the body.

We know that the body makes 3 complete revolutions in 2 seconds. During one revolution the body travels a distance of , then during 3 revolutions it travels a distance of in . Then the speed of the body is

Now we can find the magnitude of centripetal acceleration:

The centripetal acceleration is provided by the tension in the string. Then from the second Newton's law we obtain the tension in the string: