GPE, KE And Pendulums

The different stages in a swinging pendulum are tied to the conversion of g.p.e. to k.e. and k.e. to g.p.e. .

The Stages Of A Pendulum

  1. Maximum g.p.e.: At the highest point of its swing, the pendulum momentarily stops, and its kinetic energy is zero. At this point, the pendulum has maximum gravitational potential energy. This occurs at the extreme ends of its swing.
  2. Conversion of g.p.e. to k.e.: As the pendulum swings downwards towards the lowest point of its path, its g.p.e. is converted into k.e.. The pendulum accelerates as it moves towards the center of the oscillation.
  3. Maximum k.e.: At the lowest point of its swing, the pendulum is moving at its maximum speed, and all of the g.p.e. has been converted to k.e.. At this point, the pendulum's g.p.e. is zero.
  4. Conversion of k.e. to g.p.e.: As the pendulum continues to swing upwards, its k.e. is converted back into g.p.e.. The pendulum decelerates as it moves away from the center of oscillation.
  5. Return to maximum g.p.e.: The pendulum slows down until it reaches the highest point on the opposite side, where its k.e. is zero again, and its g.p.e. is maximized. This completes one full swing, and the process repeats.
Mobirise Website Builder

Pendulum Question Example

  1. Question: Find the maximum speed of the pendulum at its lowest point. 
    Mass of bob is 0.5kg
    h is 6cm
  2. $$\begin{align*} E &= mgh \\ &= 0.5 \times 9.81 \times 0.06 \\ &= 0.2943 \\ \frac{1}{2}mv^2 &= 0.2943 \\ v &= \sqrt{\frac{2 \times 0.2943}{0.5}} \\ &= 1.085 \, ms^{-1} \end{align*}$$
Mobirise Website Builder