Question

A pendulum with a length of 35 cm swings back and forth as shown in the figure above, at each turn around point it stops and it starts accelerating until reaching maxium velocity at the botton (equilibrium position), at which point it starts slowing down. If the maximum angle is 48 degrees, what is its maximum velocity in m/s? (Use g = 10.0 m/s2 and assume there is no friction)

Answer 1

Consider the image

To solve this problem we will apply conservation of energy

Let us first calculate some distances using trigonometry.

and

Let us take the gravitational reference point at C.

We know at point A the velocity of the pendulum is zero so all the energy is in the form of potential energy which is provided by the gravity. So total energy when the pendulum is at point A is given by

And at point C the potential energy due to gravity is zero ( as we took it as the reference point to calculate the gravitational potential energy at point A). So it has only kinetic energy which is given by

This velocity is the maximum velocity of the pendulum.

Now applying conservation of energy

So the maximum velocity is 1.52 m\s.