Question

A small sphere is suspended by a string from the ceiling of a car. If the car begins to move with a constant acceleration a, prove that the inclination of the string to the vertical is \(\sf tan^{-1} (a/g)\)

Answer 1

\[T \sin \theta = m a\]
\[m = \frac{ T \sin \theta }{a }\]
\[T \cos \theta = m g\]
\[m = \frac{ T \cos \theta }{ g }\]
thus \[\frac{ T \cos \theta }{ g } = \frac{ T \sin \theta }{ a }\]
\[\tan \theta = \frac{ a }{ g }\]
\[\theta = \tan^{-1} (\frac{ a }{ g })\]
Q.E.D.