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Sandra Gutierrez Physics 151 L Section 1103 Hamed Goli Yousefabad Due October 13, 2022 Equilibrium of Non-Current Forces Objectives: We will be seeing how the law of moments works and verifying it. We will also be looking at the requirements to balance unequal masses and the principles of parallel forces. Apparatus: For this experiment a meter stick, fulcrum with knife edge, scale, balance, rigid support, known mass set, with a pair of looped threads, and two unknown masses was used. A balance beam was set on top of the fulcrum trying to keep it in the middle, with one mass on each side. Theory: The law of moments says that an object such as a scale will be in equilibrium. The horizontal object can either rotate clockwise or counterclockwise. At equilibrium, the torques can be equated. Some force with a given lever or moment arm is the same as half the force with twice the lever arm, and this gives a mechanical advantage in the use of a lever The left side is the counterclockwise side and the torque for this side (mass times length) will be equal to the right side’s torque (mass times length) known as the clockwise side. By knowing the left side mass, left side length and right side length, we can solve for the right side mass (our unknown mass). Procedure: For part 1, we tested the conditions of equilibrium. First we will find the center of gravity of the meter stick and place different masses on each side and position them until they are in equilibrium. For part 2, we used torques to calculate the mass of the meter stick. We will adjust the knife edge so that it is on 30 cm of the meter stick and place different masses on each side until equilibrium is reached. For part 3, we determined an unknown mass by placing an unknown mass on one end of the meter stick. Pre-lab Questions: What are the two conditions for equilibrium of a rigid body? How would this experiment demonstrate their validity? The first condition is the net force acting upon the object must be zero. The second is that the net torque acting upon the object must be zero.

This experiment would show that by testing if the meter stick stays still (balanced) when both torques are equal. Why do you not need to take into consideration the force exerted on the meter stick by the support? Because you are adding the moments about the fulcrum so any force that passes through the fulcrum will contribute to this. In part 3, you can calculate the moment of the known mass and use that to determine the unknown mass, but explain how the unknown mass can be determined without directly calculating the torque (hint: use ratios). The torques should be equal so you can find the unknown mass by calculating the left torque divided by the right length. This is according to the equation M(L)xL(L)=M(R)xL(R). What defines the center of gravity of a rigid body? How does it relate to center of mass? The center of gravity is the point where weight is evenly distributed in all directions. The center of mass is where mass distribution is even. Assume a 150g meter stick with center of mass at the 48cm mark is supported by the 60cm mark. There are two masses placed on the meter stick; m=50g and is placed at the 16cm mark and m is an unknown mass at an undisclosed location. The meter stick is in equilibrium. What is the torque induced by each of the masses (don’t forget about the mass of the stick itself)? Now, supposing m is located on the 100cm mark, what must its mass be? What if it is at the 80cm mark? torque due to mass of scale = 1800 gcm anti clockwise torque due to mass of scale = 1800 gcm anti clockwise Mass must be 100 g on the 100 cm mark and 200 g on the 80 cm mark. Equations: Mean moment: (clockwise torque + counterclockwise torque)/2 % difference: (clockwise torque- counterclockwise torque)/ mean torque

Data: Notes/Computations:

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Post-lab Questions:

1. How well do your experimental results compare to the expected results? Did you confirm the theory you were testing? Cite your results and errors specifically. Our experimental results were pretty accurate to the expected results because our % difference was fairly low, usually under 50%. We did confirm the theory that we were testing because the clockwise moment and the counterclockwise moment were equal when our meter stick was in equilibrium. We were able to find our unknown mass by setting the two torques equal to each other. 2. In most cases, the balancing position of the meter stick (unloaded) is not on the 50cm mark. Why is that the case? What does that mean about the center of mass of the meter stick? The balancing position is usually not on the 50 cm mark because of inconsistencies with the material that the meter stick is made from. This means that the center of mass is probably not right in the middle for the meter stick. 3. What are the largest sources of error in your experiment? The largest sources of error are the hangers, the unequal weight of the meter stick, and unequal platform. The biggest source of error is probably the set screws not tightening enough and shifting. 4. Explain how the old fashioned scales in doctors’ offices and gyms (with all of the sliding blocks) work. TThese scales work in the same sense that our meter stick worked. They work as a lever where the beam is fixed on a pivot and the weight is moved until the beam is balanced on the pivot. Once it is in equilibrium, the actual weight of the person is shown.

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