Rankers Physics

Work Done by Constant and Variable Forces: Practice Problem & Solution

An object of mass m is tied to string of length L and a variable horizontal force is applied on it which starts at zero and gradually increases (it is pulled extremely slowly so that equilibrium exists at all times) until the string makes an angle θ with the vertical. Work done by the gravitational force mg  is : Work Done by Constant and Variable Forces diagram: An object of mass m is tied to
mgL (1 – cosθ)
- mgL (1 – cosθ)
mgL (1 – sinθ)
-mgL (1 – sin θ)

Solution Explained:

To solve this problem, we apply the core principles of Work Done by Constant and Variable Forces. Understanding the underlying formula is key to arriving at the correct answer below:

Be definition of Work, Work Done = F.S. cos θ

Taking F and cos θ together like

W= (F.  cos θ) . s = Component of Force along displacement ×  displacement 

                    Here gravitational force mg is acting downwards and displacement  in upward direction is (L- L cos θ), So

Work done = mg.(L-Lcosθ)cos (180°)= -mgL(1-cosθ)

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