InterviewSolution
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InterviewSolution
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A uniform board of length L is sliding along a smooth (frictionless) horizontal plane as in figure. The board then slides across the boundary with a rough horizontal surface. The coefficient of kinetic friction between the board and the second surface surface is `mu_k` a. Find the acceleration of the board at the moment its front end has traveled a distance x beyond the boundary. b. The board stops at the moment its back end reaches the boundary, as in figure. Find the initail speed `v` of the board. |
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Answer» a. Let `m` be the mass of the whole board. The portion on the rough surface has mass `mx//L`. The normal force supporting it is `mxg//L` and the frictional force is `mu_kmgx//L=ma`. Then `a=mu_kgx//L` opposite to the motion. b. In an incremental bit of forward motion `dx`, the kinetic energy converted into internal energy is `f_xdx=(mu_kmgx)/(L)dx`. The whole energy converted is `1/2mv^2=underset0oversetLint(mu_kmgx)/(L)dx=(mu_kmg)/(L)x^2/2 :|_0^L=(mu_kmgL)/(2)` `v=sqrt(mu_kgL)` |
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