Problem 1

A small slider of mass

m

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

L

, inclined at

30^\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

t=\sqrt{\frac{2L}{g\sin30^\circ}}

problems.proof.analysis

Choose the positive root because the elapsed time from release to the bottom is positive. Substitution of the acceleration from the previous step gives the explicit result.