A pendulum bob with a mass of 0.400 kg is attached to a 1.5 m long string as sho

Question

A pendulum bob with a mass of 0.400 kg is attached to a 1.5 m long string as shown. As the pendulum bob swings from, point A, where the angle theta = 30.0 degree, to point B at the bottom, of its are, determine the change in the gravitational potential energy of the pendulum bob-earth system. Where is a convenient location for zero gravitational potential energy? What is it about this location that makes it convenient? Recall that the change in gravitational potential energy may be expressed as the final minus the initial potential energy. What is the height of the pendulum bob when it is at each location? How can you use the length of the string and the angle to determine the height of the pendulum bob at point A? At you expecting a negative or a positive value for the change in potential energy?

Explanation / Answer

m = 0.4 kg ; L = 1.5 m ; theta = 30 deg ;

The diffrence in height of the points A and B is required.

D = 1.5 - x

x = L cos(theta)

x = 1.5 x cos30 = 1.3

D = 1.5 - 1.3 = 0.2 m

The change potential energy would be:

delta-U = m g h

delta-U = 0.4 x 9.81 x 0.2 = 0.785 J

Hence, delta-U = 0.785 J

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