Question

A pendulum with a bob of mass m is oscillating on either side from its resting position A between the extremes B or C at a vertical height h above A. What is the kinetic energy k and potential energy U when the pendulum is at B.
A) K=0; U=mgh
B) K=0; U=-mgh
C) K=mgh; U=0
D) K=0; U=0

Answer 1

Hint: If we swing a pendulum from its resting position we observe a to and fro motion. This to and fro motion is harmonious i.e. The pendulum covers equal distances on both sides. This is known as simple harmonic motion. We have to find out the potential and kinetic energy of the pendulum moving in either extremes at a certain time.

Formula used:
The formula for kinetic energy and potential energy is given below:-
$K.E = \dfrac{1}{2}m{v^2}$;
Where:
K.E = Kinetic Energy;
m = Mass of the pendulum;
v = Velocity of the pendulum
Potential Energy is given by:-
$U = mgh$;
Where:
U = Potential Energy
m = Mass of the pendulum
g = acceleration due to gravity (Approx. $10m/{s^2}$)
h = Height.

Complete step by step answer:

Here in this question we have been asked to find out the potential energy and kinetic energy of the pendulum at the extreme position B (see above diagram). At the extreme position of the pendulum the Kinetic energy has to be zero because there would be no velocity of the pendulum.
The velocity of the pendulum would be zero at the extreme point at B. So, the k.E would be $K.E = 0$. Since K.E is Zero we are left with the potential energy.
The potential energy would be P.E = mgh. The bob has mass; hence gravity would act so it tends to move downwards. Hence the direction would be negative. So the Potential Energy would be $P.E= -mgh$.
Therefore,
$K.E=0$;
$P.E= -mgh$;

The correct answer is K=0, U=-mgh. Therefore, Option B is correct.

Additional Information:
The pendulum follows the principle of Simple Harmonic Motion or SHM. The pendulum moves in harmony, that is the movement is linear. The mass does not affect the period of the pendulum. It uses the principle of energy. There is a direct relation between the angle and the velocity of the pendulum.

Note:
Here we have to apply our conceptual knowledge. Here the kinetic energy of the pendulum will be zero because at the extreme point of the pendulum the velocity of it would be zero, so there would be no kinetic energy and only potential energy. The direction of the potential energy would be negative as the direction is downwards. The negative sign is used for showing the direction.