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Question
An object of unknown mass is provided to a student. Without using a scale, design an experimental procedure detailing how the magnitude of this mass could be experimentally found. Your explanation must include the concept of torque and all steps should be provided in an orderly sequence. You may include a labeled diagram of your setup to help in your description. Include enough detail so that another student could carry out your procedure.
Get a uniform board, a fulcrum, a known mass, and a ruler.

1. Measure the length of the board, $L$
2. Position the fulcrum in the middle of the board, and the known mass at one end.
3. Find $r_2$ such that the board is balanced.
4. Solve $m_2gr_2=m_1gr_1$ for $m_2$.
Solution Video

# OpenStax College Physics for AP® Courses Solution, Chapter 9, Problem 8 (Test Prep for AP® Courses) (1:28)

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Video Transcript
This is College Physics Answers with Shaun Dychko. We have an unknown mass and we want to figure out what its mass is without using a regular scale. So we are gonna setup an experimental procedure to figure it out... I would say get an uniform board and the word 'uniform' means that the mass is distributed uniformly along its length so that its center of mass is located at the geometric center of the board and measure the length of the board— that's step (1)— so you also need a ruler by the way and a fulcrum for the board to pivot on in the middle and a known mass that's m 1. Now step (2) is position the fulcrum in the middle and and put the known mass at the end of the board and step (3) is find r 2 such that the board is balanced. So m 2 has to be placed somewhere such that this board is balanced. I guess with the m 1 at the very end m 2 must be some mass that's a little bit more than m 1 but anyway, this could be... it doesn't have to be strictly at the end, it could be a little bit closer to the fulcrum. In any case, you need to solve this equation which says that the clockwise torque has to equal the counterclockwise torque and solve it for m 2 and then there you go!