**AP Physics 1 Question 311: Answer and Explanation**

### Test Information

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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

**Explanation:**

**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 *F*_{N} = *F*_{g}cos*θ* = *mg*cos*θ.* Next, using Newton's Second Law and defining "up the ramp" as positive, you can say *F*_{Net} = *T* - *F*_{g}sin*θ* - *F*_{f} = 0. Solving for tension and plugging in all the variables gives you *T* = *mg*sin*θ* + μ*mg*cos*θ.*

Next, looking at the hanging block, you can again use Newton's Second Law to determine that *F*_{Net} = *F*_{g} - *T* = *Mg* - (*mg*sin*θ* + µ*mg*cos*θ*) = 0. Thus, solving for μ gives you μ = (*Mg* - *mg*sin*θ*)/(*mg*cos*θ*).