The Pendulum Accelerometer · AI Generator #GEN-F32CACA2

Physics · mechanics

Problem

A simple pendulum consists of a small mass

m = 0.5\;\text{kg}

attached to a rigid rod of length

L = 1.2\;\text{m}

and negligible mass. The pendulum is mounted inside a car that accelerates horizontally with constant acceleration

a

. When the car reaches steady acceleration, the pendulum bob comes to rest at an angle

\theta = 15°

from the vertical (as measured in the car's reference frame). The car then encounters a speed bump, causing it to decelerate uniformly and come to a complete stop in time

t = 2.0\;\text{s}

. During this deceleration phase, find the maximum angle

\theta_{max}

that the pendulum makes with the vertical in the car's reference frame. Assume the pendulum oscillates as a simple pendulum about its new equilibrium position during deceleration. Take

g = 9.8\;\text{m/s}^2

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