Question

A pendulum that weighs 1.0 kg is pulled sideways so that it is raised a vertical distance of 3 m above its resting position. Find the maximum speed the pendulum reaches after being released.

Answer 1

According to the conservation energy law, the maximum potential energy of the pendulum is equal to its maximum kinetic energy. Writing down the expressions for each energy, obtain:

$$mgh_{max} = \dfrac{mv^2_{max}}{2}$$

where $m$ is the mass of the pendulum, $h_{max} = 3m$ is the initial (and maximum) height, $g = 9.81m/s^2$ is the gravitational acceleration, and $v_{max}$ is the maximum speed. Thus, obtain:

$$v_{max} = \sqrt{2gh_{max}}\\ v_{max} = \sqrt{2\cdot 9.81\cdot 3} \approx 7.67m/s$$

Answer. 7.67 m/s.