Question

A pendulum bob is released from some initial height such as the speed of the bob at the bottom of the swing is 1.0 m/s. What is the initial height of the bob? Answer in units of m

Answer 1

Answer on Question#37802 -Physics - Mechanics | Kinematics | Dynamics

A pendulum bob is released from some initial height such as the speed of the bob at the bottom of the swing is $1.0 \, \text{m/s}$. What is the initial height of the bob? Answer in units of m

Solution:

We can use conservation on Energy equation:

$$W_{\text{top}} = W_{\text{bottom}}$$

So for any increase in KE, there is an equal decrease in PE.

At the initial height all the energy is PE since the mass isn't moving ($W_{\text{KE}} = 0$). At the bottom of the swing, where $v = 1 \, \frac{\text{m}}{\text{s}}$, the energy is all converted to KE ($W_{\text{PE}} = 0$).

$$\begin{array}{l} \mathrm{mgh} = \frac{\mathrm{mv}^2}{2} \\ \mathrm{h} = \frac{\mathrm{v}^2}{2\mathrm{g}} = \frac{\left(1 \, \frac{\text{m}}{\text{s}}\right)^2}{2 \cdot 9.8 \, \frac{\text{m}}{\text{s}^2}} = 51 \times 10^{-3} \, \text{m} \end{array}$$

Answer: height of the bob is $51 \times 10^{-3} \, \text{m}$.