Question

An object of mass m is tied to a string of length l and a variable horizontal force is applied on it which starts at zero and gradually increases until the string makes an angle with the vertical. Work.Done by the force f is

Answer 1

The work done by the force is W(F) = mgl(1−cosθ).

Explanation:

According tot he statement of the question three forces are acting on the object:

1 - Tension (T)

2 - Weight (mg) and

3 - Applied force (F)

Using work-energy theorem:

W(net) = ΔK.E

OR W(T)+W(mg)+W(F) = 0  ...(i)

As we know that

ΔK.E = 0

Because initial K.E is equal to Final K.E which is zero.

Ki = Kf= 0

WT=0 (As tension is always perpendicular to displacement)

W(mg) = −mgh

or W(mg) = − mgl(1−cosθ)

W(F) = mgl(1−cosθ)

Thus the work done by the force is W(F) = mgl(1−cosθ)

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