Pendulum physics question

Question

:A 250 g pendulum of length 0.500 m is initially at rest 1.00 m from the floor. The pendulum bob is pulled sideways a distance of 0.300 m. What is the potential energy of the pendulum bob in its raised position? Answer: (in reference to the ground, 2.70J. in reference to bottom of pendulum swing, 0.245 J) please show the process to find the answer.

Answer 1

m = 0.25 kg

L = 0.5 m

h = 1 m

x = 0.3 m

First find the increase in height when the pendulum is pulled sideways, using Pythagorean theorem:

Δh = L - sqrt(L² - x²) = 0.5 - 0.4 = 0.1 m

The full height of the pendulum is now h' = h + Δh = 1 + 0.1 = 1.1 m above the floor.

Potential energy: PE = mgh' = 0.25×9.81×1.1 = 2.7 J.