Physic Labs

Problem 1

A small block of mass m=2.0 kgm=2.0\,\mathrm{kg} is released from rest at the top of a straight, smooth plane inclined at α=30∘\alpha=30^\circ to the horizontal. It travels a distance s=10.0 ms=10.0\,\mathrm{m} measured along the plane. Take g=9.80 m s−2g=9.80\,\mathrm{m\,s^{-2}}, neglect air resistance, and choose downhill as positive. (a) Find the block’s acceleration and the normal force exerted by the plane. (b) Find the travel time and its speed at the bottom. (c) Find the work done by gravity and its average power during the descent.
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s=12at2,t=2s/a=2.02 ss=\tfrac12at^2,\quad t=\sqrt{2s/a}=2.02\,\mathrm{s}
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The acceleration is constant and the block starts from rest, so the along-plane displacement is s=at2/2s=at^2/2. Solving gives t=2.02 st=2.02\,\mathrm{s}.