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Torques, Equilibrium, and Center of Mass: Some Theory Torque is defined as force times the length of the lever arm. If an object is not rotating, then the sum of the torques acting on the object must be zero. In this case, we say that the object is in static equilibrium. In this experiment, we will place an object in static equilibrium and then sum the clockwise and counterclockwise torques to see if they are indeed equal. Note: 1) Use meters and kilograms for all measurements. 2) In all cases, x should be measured from the zero end of the meter stick. 3) The length of the lever arms will always be |x - xo|, where xo is the center of mass of the meter stick. 4) Obtaining a perfect balance is often difficult. If the meter stick refuses to remain level, record the value that seems to work best. Equipment: - Meter Stick (Non-Metal End) - Knife Edge Clamps – 3 with hooks and one without - Torque Balance - Hooked Masses - Beam Balance - Metal Cylinder - String Procedure: 1) Measure and record the mass of the three clamps with hooks (C1-3). Remember which clamp is which. 2) Measure and record the mass of a 50 g mass, a 100 g mass, and a 200 g mass. C1 = 17.24 g 50 g mass = 50.0 g C2 = 17.30 g 100 g mass = 99.9 g C3 = 17.30 g 200 g mass = 199.6 g 3) Insert your meter stick through the hookless clamp and position it on the torque balance so that the zero end is to the left. 4) Find the exact center of mass of the meter stick by finding the balance point. Record this position as xo = 50.0 cm (0.50 m) and tighten the clamp at that position. CASE I: a) With the meter stick balanced, attach the first clamp at x1 = 30.0 cm and suspend the 50 g mass from it. Also, attach the second clamp at x2 = 20.0 cm and suspend the 100 g mass from it. b) Using the third clamp with the 200 g mass hanging from it, find and record the position x3 that balances the system. c) Record M1 = C1 + 50 g mass, M2 = C2 + 100 g mass, and M3 = C3 + 200 g mass. d) Calculate the length of the lever arms l, the appropriate forces, and the magnitudes of the clockwise and counterclockwise torques (tcw and tcc). Then determine the percent difference between the torques. Show all of your work on a separate sheet of paper. x1 = 0.300 m l1 = M1 = 67.24 g F1 = x2 = 0.200 m l2 = M2 = 117.2 g F2 = x3 = l3 = M3 = 216.9 g F3 = tcc = tcw = __ Percent Difference =

          Torques, Equilibrium, and Center of Mass: Some Theory

Torque is defined as force times the length of the lever arm. If an object is not rotating, then the sum of the torques acting on the object must be zero. In this case, we say that the object is in static equilibrium. In this experiment, we will place an object in static equilibrium and then sum the clockwise and counterclockwise torques to see if they are indeed equal.

Note:
1) Use meters and kilograms for all measurements.
2) In all cases, x should be measured from the zero end of the meter stick.
3) The length of the lever arms will always be |x - xo|, where xo is the center of mass of the meter stick.
4) Obtaining a perfect balance is often difficult. If the meter stick refuses to remain level, record the value that seems to work best.

Equipment:
- Meter Stick (Non-Metal End)
- Knife Edge Clamps – 3 with hooks and one without
- Torque Balance
- Hooked Masses
- Beam Balance
- Metal Cylinder
- String

Procedure:
1) Measure and record the mass of the three clamps with hooks (C1-3). Remember which clamp is which.
2) Measure and record the mass of a 50 g mass, a 100 g mass, and a 200 g mass.

C1 = 17.24 g
50 g mass = 50.0 g
C2 = 17.30 g
100 g mass = 99.9 g
C3 = 17.30 g
200 g mass = 199.6 g

3) Insert your meter stick through the hookless clamp and position it on the torque balance so that the zero end is to the left.
4) Find the exact center of mass of the meter stick by finding the balance point. Record this position as xo = 50.0 cm (0.50 m) and tighten the clamp at that position.

CASE I:
a) With the meter stick balanced, attach the first clamp at x1 = 30.0 cm and suspend the 50 g mass from it. Also, attach the second clamp at x2 = 20.0 cm and suspend the 100 g mass from it.
b) Using the third clamp with the 200 g mass hanging from it, find and record the position x3 that balances the system.
c) Record M1 = C1 + 50 g mass, M2 = C2 + 100 g mass, and M3 = C3 + 200 g mass.
d) Calculate the length of the lever arms l, the appropriate forces, and the magnitudes of the clockwise and counterclockwise torques (tcw and tcc). Then determine the percent difference between the torques. Show all of your work on a separate sheet of paper.

x1 = 0.300 m
l1 = __________
M1 = 67.24 g
F1 = __________

x2 = 0.200 m
l2 = __________
M2 = 117.2 g
F2 = __________

x3 = __________
l3 = __________
M3 = 216.9 g
F3 = __________

tcc = __________
tcw = __________
Percent Difference =

Added by Angela M.

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