10.7 Data and Results
10.8 Calculations
Force Calculation: The force exerted by each mass was calculated using the formula F =
m * g, where m is the mass and g is the acceleration due to gravity. For example, for a mass of
50g, the force would be F = 50/1000 * 981 = 48.05 x 10³ dyne.
Torque Calculation: The torque produced by each force was calculated using the formula τ = F *
x, where F is the force and x is the position. For example, for a force of 48.05 x 10³ dyne at a
position of 5 cm, the torque would be τ = 48.05 * 5 = 245250 dyne-cm.
Sum of Torques: The sum of the torques in the counterclockwise (ccw) and clockwise (cw)
directions were calculated by adding up the individual torques. For example, the sum of the ccw
torques would be Στccw = τ1 + τ2 + τ3.
Percent Difference: The percent difference between the sum of the ccw and cw torques was
calculated using the formula % difference = (|Στccw - Στcw| / ½ (Στccw + Στcw)) * 100. This
gives a measure of how close the system is to equilibrium.
10.9 Guide Questions
1. Can a small force exert a greater torque than a larger force? Explain.
Yes, a small force can exert a greater torque than a larger force. Torque is the rotational
equivalent of linear force and is calculated as the product of the force and the distance from the
pivot point (or fulcrum) at which the force is applied. This distance is often referred to as the
lever arm. Therefore, if the lever arm is long enough, a small force can produce a large torque.
This is the principle behind tools like wrenches and door handles.
2. A meter stick is found to balance at the 49.7-cm mark when placed on a fulcrum. When
a 50.0-g mass is attached at the 10.0-cm mark, the fulcrum must be moved to the 39.2-cm
mark for balance. What is the mass of the meter stick?
m = (M * d2) / d1 = (0.05 kg * 0.392 m) / 0.497 m ≈ 0.039 kg or 39 g
So, the mass of the meter stick is approximately 39 g.
3. Two people are carrying a uniform wooden board that is 3.00 m long and weighs 160 N.
If one person applies an upward force equal to 60 N at one end, at what point does the
other person lift? Begin with a free-body diagram of the board.
F1 * 0 = Fg * d
d = F1 / Fg = 60 N / 160 N = 0.375 m
10.10 Discussion
The experiment revolves around the principle of torque and the equilibrium of a lever.
The experiment demonstrated that a system achieves equilibrium when the sum of
counterclockwise and clockwise torques are equal. However, in the scenario involving an
inclined force, a small discrepancy was observed, indicating the system was not in perfect
equilibrium. This could be due to experimental errors or imperfections in the setup. The
experiment underscores the importance of careful measurements and setup in understanding
and applying the principles of torque and equilibrium in physics.
10.11 Conclusion
The conclusion of the experiment is that the principle of torque and equilibrium was
successfully demonstrated using a lever system. The system achieved equilibrium when the
sum of counterclockwise and clockwise torques were equal. However, when an inclined force
was introduced, a slight discrepancy was observed, indicating the system was not in perfect
equilibrium. This suggests that even minor deviations can lead to noticeable differences in
equilibrium. Therefore, careful experimental setup and accurate measurements are crucial in
physics experiments involving torque and equilibrium.