Work done by couple - Any Learn Nepal

Before going through work done by couple, make sure to check torque and couple meaning from here.

Consider a wheel of radius ‘r’ rotating about an axis through a center due to the application of a couple of magnitude ‘F’ at points A and B.

Let’s consider a wheel covers angular displacement ‘ $\theta$ ‘ such that the wheel moves from A to A^‘ as shown in the figure.

Work done in displacing from A to A^‘ is given by: $W_{AA^'}$ = $F \times AA^'$

$W_{AA^'}$ = $F \times \theta r \qquad [ \theta = \frac{l}{r} \quad \rightarrow \quad \theta = \frac{AA^'}{r}]$

Similarly, Work done in displacing from B to B^‘ is given by:

$W_{BB^'}$ = $F \times \theta r$

The total work done by a couple can be calculated by adding work done by both forces.

$W = W_{AA^'} \quad + \quad W_{BB^'}$

$W = F \times \theta r + F \times \theta r$

$W = 2 F \theta r$

$W = F \times (2r) \theta$

$\boxed{W = \tau \theta}$

Where $\tau$ is the torque due to a couple which is calculated by the product of either force with the distance between them.

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