Question

A pendulum is made of a 250 g metal ball suspended 50.0 cm below a support by a string. The ball is moved sideways along the swing arc so that it is 3.0 cm higher than it is at the bottom of its swing. The ball is then released.
Calculate the speed of the ball at the bottom of the swing.
Show your work.

Answer 1

The speed of the ball at the bottom of the swing is approximately 0.767 meters per second.

In this case, the speed of the ball at the bottom of the swing is related to maximum translational kinetic energy ($K$), in joules, which is equivalent to maximum gravitational potential energy ($U_{g}$), in joules, by the principle of energy conservation:

$U_{g} = K$ (1)

By definitions of translational kinetic energy and gravitational potential energy:

$m\cdot g \cdot h = \frac{1}{2}\cdot m\cdot v^{2}$

$v = \sqrt{2\cdot g\cdot h}$ (2)

If we know that $g = 9.807\,\frac{m}{s^{2}}$ and $h = 0.03\,m$, then the speed of the ball at the bottom of the swing is:

$v = \sqrt{2\cdot \left(9.807\,\frac{m}{s^{2}} \right)\cdot (0.03\,m)}$

$v\approx 0.767\,\frac{m}{s}$

The speed of the ball at the bottom of the swing is approximately 0.767 meters per second.

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