Bin Contents: a stand, the unknown mass, two 10-gram mass hangers, the clamp without bail, and two clamps with bails.

Obtain a 1-meter long ruler – return when finished.

Obtain the two masses you need from your table’s drawer.

Weigh the ruler.

Weigh the clamps with bails; note that the clamp without bail is the pivot, doesn’t contribute torque, and, therefore, doesn’t need to be weighed.

Weigh the 10-gram mass hangers.

Weigh the unknown mass.

Slide the clamp without bail onto the ruler and set it atop the stand.

Note: This experiment is a sequence of measurements that involves balancing the ruler; the images simply outline the shape of the experiment; specific known (or unknown) masses and their positions, etc, are given by the text.

This is exactly how the clamp without bail should be put onto the ruler and onto the stand; no other way achieves equilibrium!

From this image onward, the clamp without bail will be referred to as the pivot.

Use the internal edge at the middle of the pivot to read its position; as shown above, the pivot is at the 52 cm mark.

Note: This is actually how all of the clamps work.

Adjust the location of the pivot until the ruler is balanced; the pivot’s position is the ruler’s center of mass!

Attach the known mass to the given position.

Note: The clamps with bails are attached “up-side-down” as shown.

Attach the unknown mass to the other side of the ruler; shift the position of the unknown mass until the system is at equilibrium.

Note: Keep the objects from swinging as that adds extra forces and torques.

Keep the known mass at the given position BUT remove the unknown mass. Loosen the pivot; slide the ruler about the pivot until you achieve equilibrium.

For this situation, the ruler’s own mass exerts a torque that balances the torque generated by the known mass .

Attach another known mass at another given position onto the ruler. Slide the ruler around the pivot until you achieve equilibrium.

For this situation, the torques generated by the known masses and the torque exerted by the ruler’s own weight all balance.