AP Physics 1 Question 311: Answer and Explanation

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Question: 311

9. A block of mass m is connected by a string which runs over a frictionless pulley to a heavier block of mass M. The smaller block rests on an inclined plane of angle θ, and the larger block hangs over the edge, as shown above. In order to prevent the blocks from moving, the coefficient of static friction must be

  • A.
  • B.
  • C.
  • D.

Correct Answer: C



If nothing is moving, then you know that the net force will be 0. Looking first at the forces perpendicular to the plane, you get FN = Fgcosθ = mgcosθ. Next, using Newton's Second Law and defining "up the ramp" as positive, you can say FNet = T - Fgsinθ - Ff = 0. Solving for tension and plugging in all the variables gives you T = mgsinθ + μmgcosθ.

Next, looking at the hanging block, you can again use Newton's Second Law to determine that FNet = Fg - T = Mg - (mgsinθ + µmgcosθ) = 0. Thus, solving for μ gives you μ = (Mg - mgsinθ)/(mgcosθ).