AP Physics 1 Question 326: Answer and Explanation
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4. As it is, the system above is not balanced. Which of the following changes would NOT balance the system so that there is 0 net torque? Assume the plank has no mass of its own.
- A. Adding a mass equal to m2 on the far left side and a mass equal to m1 and on the far right side
- B. Stacking both masses directly on top of the fulcrum
- C. Moving the fulcrum a distance L/3 to the right
- D. Moving both masses a distance L/3 to the left
Correct Answer: A
In this situation, the left-hand block will provide counterclockwise torque, and the right-hand block will provide clockwise torque. Therefore, the two must be equal in magnitude for the system to be balanced. You know that the formula for torque is τ = Frsinθ. In this problem, θ will always be 90 degrees, and sin 90° = 1, so that term will be neglected for the rest of the explanation. Furthermore, the only forces involved in this problem are the forces of gravity on the blocks, and you know Fg = mg.
For (A), the net counterclockwise torque (left side of the system) would be τ = (m2g)(2L) + (m1g)(L) = (2m1g)(2L) + (m1g)(L) = 5m1gL. The clockwise torque (right side of the system) would be τ = (m2g)(L) + (m1g)(2L) = (2m1g)(L) + (m1g)(2L) = 4m1gL. Thus, it would not be balanced. Choice (B) would make both torques 0, so that would be balanced. Choices (C) and (D) both result in the fulcrum being twice as far from m1 as it is from m2, which would counteract the difference in their weights.