Problem 1

A small slider of mass

m

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

L

, inclined at

45^\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

v=at=\sqrt{2gL\sin45^\circ}

problems.proof.analysis

The final speed follows from $v=at$ , or equivalently $v^2=2aL$ ; both expressions agree. Since acceleration is mass-independent, neither the speed nor the time contains $m$ .