9.1

Rotational Equilibrium

Student Notes

With this simulation, you can investigate the basic principles of equilibrium. For the beam to remain at equilibrium, the net force on the beam must be zero and the net torque on the beam should also be zero. The 100-cm long beam is assumed to be uniform, so its center-of-gravity is at the center of the beam.
Here are some things to try to see if you fully understand the concepts. If possible, predict what you think will happen and then make the changes to see if you are correct.

1. | The support forces are determined using the conditions for equilibrium, which are that the sum of all the forces must be zero and the sum of all the torques must be zero. For a particular set of weights and positions, use the equilibrium conditions to set up equations you can use to solve for the support forces. When you solve the equations, do you agree with the values calculated by the simulation?
2. | If you move the support on the right toward the right end of the board, does the force provided by the support change? If so, how? Is the sum of all the forces still zero? Is the sum of all the torques still zero?
3. | By adjusting the positions (and possibly weights) of the objects you should be able to make the force from one support equal zero. The other support would then support all the weight. In this situation, one of the two supports would have to be placed at the center-of-gravity of the system. Which support is it, the one supporting no weight or the one supporting all the weight?
4. | If you think of the beam as simply resting on the two supports, the beam would stay in equilibrium as long as each support was applying an upward force. Can you set up a situation where the beam tips over? Where is the center-of-gravity of the system in this situation? Does this explain why the system is unstable?

Self-test

1. | There are two basic conditions for equilibrium. One pertains to the sum of all the forces on an object, while the other applies to the sum of the torques. What are these conditions? You should be able to express them in words, as well as writing them as equations.
2. | Both conditions for equilibrium must be met for a system to be in equilibrium. What would happen if the net force was zero but there was a net torque? What would happen if the net torque was zero but there was a net force?
3. | In this simulation five forces are shown on the free-body diagram. The positions of four of these, the two support forces and the weights of the two boxes, are easy to position on the free-body diagram. The other force is the weight of the beam. Where is this force placed on the free-body diagram? Why is it placed there, and why is it important to place each of the forces in its proper location along the beam?
4. | If you and a friend are lifting a heavy piece of furniture, and your friend is much stronger than you are, which one of you should lift the furniture at one end and which one of you should be closer to the center-of-gravity?

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