Physic Labs

Problem 1

A block of mass m=4.0 kgm=4.0\,\mathrm{kg} starts from rest and slides s=6.0 ms=6.0\,\mathrm m down a 30∘30^\circ incline. The kinetic-friction coefficient is μ=0.10\mu=0.10; take g=10 m s−2g=10\,\mathrm{m\,s^{-2}}. The plane is fixed and the block remains in contact with it throughout the slide. The coefficient μ\mu is constant along the path, and kinetic friction opposes the motion. The block moves in a straight line down the plane with constant acceleration from its starting point to the stated endpoint. (a) Find the normal force and the acceleration along the plane. (b) Determine the speed at the end of the descent. (c) Calculate the time for the slide, assuming constant acceleration.
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mgssin⁡30∘−μmgscos⁡30∘=12mv2mg s\sin30^\circ-\mu mg s\cos30^\circ=\frac12mv^2
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The gravitational work minus frictional work equals the gain in kinetic energy. Its agreement with the kinematic result checks the friction sign and magnitude.