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 30∘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 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⁡30∘, N=mgcos⁡30∘, t=2Lgsin⁡30∘, v=2gLsin⁡30∘\boxed{a=g\sin30^\circ,\ N=mg\cos30^\circ,\ t=\sqrt{\frac{2L}{g\sin30^\circ}},\ v=\sqrt{2gL\sin30^\circ}}
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Collect the directions as well as magnitudes: acceleration is downhill and the reaction is outward normal to the track; time and speed are positive scalars. Their dimensions are respectively acceleration, force, time, and speed.