An object of mass m is tied to a string of length l and a variable force F is applied on it which brings the string gradually at angle $θ$ with the vertical. Find the work done by the force F.

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Solution

Given,

$m a s s = m, l e n g t h = l, f o r c e = f, a n g l e = θ$

By the work energy theorem, since the change in KE is zero, so the total work done by all forces must equal to zero.

Thus,

$W_{f} + W_{g} = 0$

Where $W_{f}$ is the final work done, $W_{G}$ is the initial work done.

$W_{f} = - W_{g}$

$W_{f} = - m g l (1 - c o s θ)$

Since $W_{g} = m g l (1 - c o θ)$

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An object of mass m is tied to a string of length l and a variable force Fis applied on it which brings the string gradually to an angle with the vertical. The work done by the force F is

An object of mass m is tied to a string of length l and a variable force F is applied on it which brings the string gradually to an angle $θ$ with the vertical. The work done by the force F is