There are two conditions for an object to be in equilibrium: 1) The sum of the forces on the object must be zero, and 2) the sum of the torques on the object about any axis must be zero. In this lab you will check these conditions for the particular case of the static equilibrium (v = 0 and ω = 0) of a beam carrying various weights. (The “beam” will actually be a meter stick balanced on a fulcrum. It is considered to be in equilibrium, or in balance, when is it level and stationary.) Since the meter stick itself has mass, gravity exerts a force on the meter stick which must be taken into account. This can be done by considering the entire force of gravity to be applied at the center of gravity of the meter stick. If your meter stick has a uniform mass distribution, its center of gravity should be at its midpoint. However, due to variations in wood, this will probably not be the case, and you will have to experimentally determine the center of gravity of the meter stick.
Materials
Meter stick with knife edge, support stand, electronic balance, spring balance, hooked masses, string
Procedure
· Use an electronic balance to mass the meter stick with and without the knife edge. Record these two masses.
· Using the knife edge and support, determine and record the location of the meter stick’s center of gravity.
Part I:
· Place the knife edge at the meter stick’s center of gravity and place it on the support stand.
· Use string to hang these masses on your meter stick “beam:”
o 500 g at the 5.00-cm mark
o 200 g at the 20.00-cm mark
o 200 g at the 75.00-cm mark
o 100 g at the 95.00-cm mark
· When attaching the string loops to hang the masses, you want to make sure the loops are short enough so that the masses don’t drag on the table when the beam is balanced. You will also want to make the strings tight enough on the beam so that the strings will not slide along the beam.
· Hook the spring balance on the beam at the 10.00-cm mark and measure the upward force necessary to balance the beam, which you will call the “equilibrant.” (Note the spring balance measures force, not mass.)
· Draw a free-body diagram of your beam, showing all the forces involved. This free-body diagram should be turned in with your report.
1. If you were to sum the torques about the fulcrum in this Part I, would it be necessary to include the mass of the knife edge?
· Taking the center of gravity of the beam as the rotation axis, calculate the expected value of the equilibrant. Consider torques that would produce a counterclockwise rotation to be positive; torques that would produce clockwise rotations are negative.
Part II:
· Move the knife edge to the 20.00-cm mark and place the beam on the support.
· Use string to hang these masses on your beam:
o 1,000 g at the 5.00-cm mark
o 500 g at the 10.00-cm mark
o 200 g at the 80.00-cm mark
o 100 g at the 95.00-cm mark
· Measure the mass which must be placed at the 15.00-cm mark to achieve equilibrium.
· Draw a free-body diagram of your beam, showing all the forces involved. This free-body diagram should also be included with your report.
2. In this Part II, when you consider the torque about the fulcrum produced by the beam itself, should you use the mass of the meterstick with or without the knife edge?
· Taking the 20.00-cm mark as the rotation axis, calculate the expected value of the equilibrant (force) needed at the 15-cm mark.
Questions
3. From Part I, calculate a % error for your measured equilibrant. The calculated value is the “standard.”
4. Calculate the normal force on the knife edge from the support in Part I. (Pay attention to whether to use the mass of the meterstick with or without the knife edge here.)
5. From Part II, calculate a % error for your measured equilibrant.