A pendulum of length L = 1.2 m has a bob of mass M = 169 g. Using the small angl

Question

A pendulum of length L = 1.2 m has a bob of mass M = 169 g. Using the small angle approximation, the magnitude of the acceleration of the pendulum bob along the trajectory is calculated to be 1.52 m/s2when 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) Under the small angle approximation, what is the maximum angular deviation of the pendulum bob with respect to the vertical?
°

(b) Under the small angle approximation, what is the magnitude of the restoring force on the bob along its trajectory when it is at the maximum angular deviation?
N

Explanation / Answer

a) Let theta is the maximum angular deviation.

so, a = g*sin(theta)

sin(theta) = a/g

theta = sin^-1(a/g)

= sin^-1(1.52/9.8)

= 8.92 degrees

b) Restoring force = m*g*sin(theta)

= 0.169*9.8*sin(8.92)

= 0.257 N

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