EQUILIBRIUM OF A RIGID BODY
INTRODUCTION
When the angular acceleration of a solid (rigid body) is zero, the system is said to be in equilibrium. In order for this to be true, the sum of the externally applied torques must be zero: St = 0. In this lab we will apply various torques to a meter stick in equilibrium and demonstrate that they do add up to zero.
Note: we treat the unit of gram as if it were weight here, even though it is really a unit of mass. This is because w = mg, and the “g” cancels out on both sides of the equation that we use in this lab, allowing us to treat mass like weight.
PROCEDURE
PART 1: Use torques to find the weight of a meter stick.
1. Weigh the meter stick and record the “weight” in grams to the nearest 0.05g:
Weight of the meter stick: ______g ±______
2. Weigh the two meter stick clamps together and compute their average weight:
Average weight of clamps: ______g ±______
3. Find the center of gravity of the meter stick to the nearest 0.5 mm by balancing it in one of the clamps.
Position of center of gravity of the meter stick:
______cm ±______
4. Put another clamp near one end of the stick and hang a 100-gram weight from it. Then slide the stick through the supporting clamp until the new position of balance is found.
Position of the 100-gram weight: ______cm ±______
Position of balance point: ______cm ±______
PART 2: Show that torques really do add up to zero.
5. Put another clamp near the other end of the stick and suspend a 200-gram weight from it. Leaving the first weight in its place, find the new point of balance by again sliding the meter stick through the supporting clamp.
Position of 200-gram weight: ______cm ±______
Position of new point of balance: ______cm ±______
PART 3: Use torques to find the weight of an unknown object.
6. Remove both weights and their clamps. Slide the meter stick through the support clamp so the support clamp is once again at its center of gravity. Put another clamp near one end of the stick and suspend a body of unknown weight from it. To balance the unknown mass, put another clamp near the other end of the meter stick and hang 200 grams from it. While keeping the support clamp at the center of mass, slide the 200-gram mass until a position of equilibrium is achieved.
Position of unknown mass: ______cm ±______
New position of the 200-gram mass: ______cm ±______
Weigh the unknown mass on the balance, for comparison: ______g ±______
CALCULATION PAGE
For each of the following calculations, indicate the actual locations of the weights, fulcrum, and center of gravity, as in this example:
1. On this page, compute the weight of the meter stick from the data of procedure 4 by the method of moments (St = zero). Calculate the percent difference from the “actual” weight of the meter stick. Indicate the positions below:
2. Using the point of support as the pivot point in Procedure 5, compute the torque of each of the weights and also of the meter stick. (The weight of the meter stick may be treated as if it were located at the center of gravity.) Add all of the torques together, to see if they add up to zero, as they should according to theory. If the sum is not zero, discuss how close it is to zero as compared to the individual torques. Show the actual positions below:
3. Compute the weight of the “unknown” object in Procedure 6 by the method of moments (sum of torques = zero). Calculate the percent difference from the “actual” weight of the body. Show the actual positions below:
ANALYSIS
1. Describe the purpose of each part of the procedure.
2. Describe how you accomplished the procedure.
3. Describe and evaluate the results.
4. Make a comprehensive list of sources of measurement error in this lab.