A Pendulum and a Truck

A flatbed truck has a box of mass \(M\) riding on the bed of the truck. There is a hanger on the box which supports a simple pendulum. As the truck accelerates with acceleration \(A\), the box slides toward the rear of the truck but, due to friction, experiences an acceleration of \(a\) in the forward direction. This causes the string of the pendulum to make an angle of \(\theta\) with the vertical direction.

What is the measure of angle \(\theta\) to the nearest tenth of a degree?

Details and Assumptions:

• Assume that the pendulum bob has a negligible mass of \(m\).

• The coefficient of kinetic friction between the box and the truck bed is \(\mu_{k}=0.5774\).