A block rests on a horizontal surface

PHYSICS · Subjective · AP · Physics 1: Algebra-based · Force and Translational Dynamics · Force and Translational Dynamics

Problem

A 3 kg3\,\text{kg} block rests on a horizontal surface. It is pulled to the right by a light horizontal string with tension 8 N8\,\text N while a horizontal push of 10 N10\,\text N acts to the left. The coefficients of friction between the block and the surface are μs=0.5\mu_s=0.5 and μk=0.35\mu_k=0.35. Take g=10 m s−2g=10\,\text{m\,s}^{-2}. (a) Will the block remain at rest under these forces? Justify your answer. (b) Determine the magnitude and direction of the frictional force acting on the block in this situation. (c) If the leftward push is increased to 25 N25\,\text N while the tension remains 8 N8\,\text N, find the acceleration of the block just after it starts sliding.

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