Physic Labs

Problem 1

A small slider of mass mm starts from rest at the top of a straight track of length LL, inclined at 60∘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 gg; take down the track as positive. (a) Find the acceleration and the normal reaction. (b) Determine the time to traverse LL 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.
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a=gsin⁡60∘a=g\sin60^\circ
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Gravity has a component mgsin⁡αmg\sin\alpha down the plane, the only force along the chosen axis. Newton’s second law therefore gives a constant acceleration directed downhill.

problems.proof.pitfall. Axis and sign choice: Do not use mgcos⁡αmg\cos\alpha as the downhill force; it is perpendicular to the plane and is balanced by the normal reaction.