i understand how if when the object is swung in a vertical circle the total grav

Question

i understand how if when the object is swung in a vertical circle the total gravitational work and tension work is = to zero and i understand the gravitational work when swung in a semi - circle from the lowest point to the highest point is = to the mg*(2*l) cos 180 which gives you the work in joules which is greater then zero. my question is why does the gravitational force give significant work done on the object and the tension force give a zero work done on the object when swung in a vertical semicirle both from lowest to highest points. please be very clear and explain each step.

Explanation / Answer

Work done by body is given as                    W = Fs cos Here F is the net force and s is the dispalcement of the object and is the angle between force and dispalcement. The tension in the string is always perpendicular to the dispalcement of the object when it is in a circular motion. Then the angle between tension force and dispalcement of the object are perpendicualr to each other then the angle = 90 thus the work done by tension in the string is zero and this tension provides the necessary centripetal force to move a object in circular motion. Since when an object in a vertical circular motion its velocity is not constant so there should be some force which is acting on the object to accelerate. That force is gravity and which does a work                 W = Fs cos Here gravitational force and dispalcement are parallel to each other so angle = 180 therefore the work done by gravity even though work done by tension becomes zero.                 W = - F(2l)   

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