Problem 1

A small slider of mass

m

starts from rest at the top of a straight track of length

L

, inclined at

60^\circ

to the horizontal. The track is smooth, the slider may be treated as a point particle, and the gravitational acceleration has constant magnitude

g

; take down the track as positive. (a) Find the acceleration and the normal reaction. (b) Determine the time to traverse

L

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.prevStep problems.proof.nextStep

mgL\sin60^\circ=\frac12mv^2

problems.proof.analysis

The vertical drop is $L\sin\alpha$ , so the loss $mgL\sin\alpha$ of gravitational potential energy becomes kinetic energy. Cancelling the mass reproduces the kinematic speed, providing an independent physical and dimensional check.