d) By tilting the plane at different angles, you can change the magnitude of the downhill
component of the gravitational force. If the downhill gravitational force is larger than the
maximum value of the static friction, the penny will start to slide downhill. Calculate the
largest angle that the plane can have before the penny starts to slide (this angle is called the
critical angle). i.e., derive an expression for the critical angle in terms one or more of
the following (unspecified) variables: coefficient of friction, mass, acceleration due to
gravity. [Remember that the force of friction depends on the normal force, and the normal
force also changes as we change the angle.]