Problem 1
A small slider of mass starts from rest at the top of a straight track of length , inclined at to the horizontal. The track is smooth, the slider may be treated as a point particle, and the gravitational acceleration has constant magnitude ; take down the track as positive. (a) Find the acceleration and the normal reaction. (b) Determine the time to traverse and the speed at the bottom. (c) Check the final speed using the change in gravitational potential energy, and state which results are independent of the mass.
problems.proof.stepOf
problems.proof.analysis
There is no acceleration normal to the track because the constraint keeps the slider on its surface. The reaction balances the perpendicular component of gravity and is positive.
problems.proof.pitfall. Constraint condition: Do not use as the downhill force; it is perpendicular to the plane and is balanced by the normal reaction.