AP Physics 1 Question 316: Answer and Explanation
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4. Five boxes are linked together, as shown above. If both the flat and slanted portions of the surface are frictionless, what will be the acceleration of the box marked B ?
- A. g sinθ
- B. g sinθ
- C. g sinθ
- D. g cosθ
Correct Answer: B
First, find the net force on the system. Each of the top three blocks will contribute nothing to the net force. The forces on each of the two blocks on the ramp will be the following:
The normal force and the perpendicular component of gravity will cancel out. This leaves just the parallel component of gravity to be a net force. Using Newton's Second Law, you get FNet = Fg,parallel 2mg sin θ = 5ma. The 2 comes in because there are two blocks on the ramp and each one will contribute the net force discussed earlier. The 5 is necessary because the blocks cannot accelerate individually. Either they all move or none do. Solving for a then gives a = gsinθ.