A pendulum of length L = 1.02 m has a bob of mass M = 122 g. Without using the s

Question

A pendulum of length L = 1.02 m has a bob of mass M = 122 g. Without using the small angle approximation, the magnitude of the restoring force on the pendulum bob along the trajectory is found to be 0.55 N when the bob is at its maximum angular deviation with respect to the vertical.

Ignore air resistance as it swings, and use the gravitational acceleration g = 9.8 m/s2 for the following questions.

a. Without using the small angle approximation, find the maximum angular deviation of the pendulum bob with respect to the vertical.

b. Without using the small angle approximation, find the magnitude of the acceleration of the bob along the trajectory when the bob is at the maximum angular deviation.

Explanation / Answer

a) Magnitude of restoring force = mg(sin)

Now, mg(sinmax) = 0.55

=> Maximum angular deviation, max = sin-1(0.55/mg) = sin-1[0.55/(0.122*9.8)] = 27.39o

b) Magnitude of acceleration at maximum deviation, a = g(sinmax) = 9.8 * sin(27.39o) = 4.51 m/s2

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