What is the Work done by Gravity on an object having Horizontal circular motion?

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What is the Work done by Gravity on an object having Horizontal circular motion? Is it positive, negative, or zero work?
We will set up a quick experiment for easy observation.

How to set up an experiment to find out work done by gravity on a horizontally circulating object?

Let’s tie a piece of stone to one end of a string and another end of the string is tied with a finger. Then start to rotate the stone with the help of the string in a horizontal plane. The stone starts moving in the horizontal circular track without any intention to drop towards the earth.

So how is this possible? How is it avoiding the effect of gravity?

Let’s find out. We all know that gravity works towards the center of the earth. As the stone is maintaining a circular path in a horizontal plane, its motion is at a right angle with the line of action of the gravity.

So do you think gravity has any effect on the stone piece rotating there?

centripetal force diagram1
Diagram-1

Work Done by Gravity on an object having Horizontal circular motion is zero. How?

We can quickly check from the definition and formula of work done. Work done depends on the Cosine of the angle between the line of force and the displacement of the object. W = FS Cos θ.

But here what is the angle θ between the rotating stone and the line of gravity? Yes! It’s 90 degrees. And cos 90 degrees is zero.

What does this mean? This means work done on the horizontally rotating stone by the gravitational force of earth (gravity) is  ZERO. Therefore the gravity has no effect on its motion. Reference: Diagram-1

Summary

What is the Work done by Gravity on an object having Horizontal circular motion? Is it positive, negative, or zero work?
And the answer is zero. Work done by Gravity on an object having Horizontal circular motion is zero.

What is the Work done by Gravity on an object having Horizontal circular motion?
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