Question

In the conical pendulum of Example 5.20 (Section 5.4), which of the forces do work on the bob while it is swinging?

Short answer

No forces act on the bob of the conical pendulum when it is swinging.

Step-by-step solution

Describe the Work

The expression for the work is given by,

$\mathit{W}\mathbf{=}\overrightarrow{\mathbf{F}}\mathbf{.}\overrightarrow{\mathbf{s}}$

Here,$\overrightarrow{\mathbf{F}}$is the force and $\overrightarrow{\mathbf{s}}$is the displacement.

Find the forces work on the bob while it is swinging

Draw the free-body diagram of conical pendulum

The centripetal force$\left(\frac{m{v}^2}{r}\right)$ and displacement of the pendulum is perpendicular to each other. So, centripetal force does not do work on the bob while it swinging.

The weight of the bob$\left(mg\right)$ and displacement of the pendulum are perpendicular to each other. So, the weight of the bob does not do work on the bob while it is swinging.

The tension$\left(T\right)$ in string and displacement of the bob made an angle $90°$. Hence, the tension$\left(T\right)$ does not work on the bob while it is swinging.

Therefore, no forces act on the bob of the conical pendulum when it is swinging