**AP Physics 1 Question 129: Answer and Explanation**

### Test Information

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**Question: 129**

**9.**

In the laboratory, a long platform of negligible mass is free to rotate on a fulcrum. A force probe is placed a fixed distance *x* from the fulcrum, supporting the platform. An object of fixed mass is placed a variable distance *d* from the fulcrum. For each position *d*, the force probe is read. It is desired to determine the mass of the object from a graph of data. Which of the following can determine the object’s mass?

- A. Plot the reading in the force probe times
*x*on the vertical axis; plot the gravitational field times*d*on the horizontal axis. The mass is the slope of the line. - B. Plot the reading in the force probe on the vertical axis; plot the distance
*d*on the horizontal axis. The mass is the area under the graph. - C. Plot the reading in the force probe on the vertical axis; plot the distance
*d*multiplied by the distance*x*on the horizontal axis. The mass is the y-intercept of the graph. - D. Plot the reading in the force probe times
*d*on the vertical axis; plot the distance*x*on the horizontal axis. The mass is the slope of the line divided by the gravitational field.

**Correct Answer:** A

**Explanation:**

**A**-Since the platform itself is of negligible mass, only two torques act on the platform: counterclockwise by the force of the force probe (*F*_{P}), and clockwise by the downward force of the object (*mg*). Torque is force times distance from a fulcrum, so set these torques equal: *F*_{P}(*x*) = *mg*(*d*). Solving for the mass, we get . Plot the numerator on the vertical, the denominator on the horizontal, and the slope is the mass *m*.