Serway & Jewett — The Laws of Motion: Problem 21

A simple accelerometer is constructed inside a car by suspending an object of mass \( m \) from a string of length \( L \) that is tied to the car’s ceiling. As the car accelerates the string–object system makes a constant angle of \( \theta \) with the vertical. (a) Assuming that the string mass is negligible compared with \( m \), derive an expression for the car’s acceleration in terms of \( \theta \) and show that it is independent of the mass \( m \) and the length \( L \). (b) Determine the acceleration of the car when \( \theta = 23.0^\circ \).