Block on Inclined Plane with String · CAP 2000 #22

Physics · mechanics

Problem

A block of mass mm is at rest on an inclined plane. The coefficients of static and kinetic friction between the block and the plane are μs\mu_s and μk<μs\mu_k < \mu_s. The angle that the plane makes with the horizontal satisfies tan⁡θ=μs\tan \theta = \mu_s. A string is attached to the block. Is it possible to pull on the string in such a way that the block will slide with constant velocity along a horizontal line? That is to say, can the block slide along a line of constant elevation? (a) Yes (b) Yes, but only if μkmgcos⁡θ<mgsin⁡θ\mu_k mg\cos\theta < mg\sin\theta (c) Yes, but only if μkmgcos⁡θ>mgsin⁡θ\mu_k mg\cos\theta > mg\sin\theta (d) No

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