Physics Lab 5

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Dec 6, 2023

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Physics Lab 5 Names: Shri Patil, Ethan Pereira, Sean Kim Introduction: In this lab we will be using a setup involving two different IOLab Devices to find the fraction of gravitational potential energy that is lost at the edge of the table as the system accelerates freely. The setup involves connecting two IOLab devices with a string that is tied to the hook of the force probe sensors. One of the devices will be resting on the top of a table(Device 1), while the other will be freely hanging in the air a distance from the ground(Device 2). Device 1 will be released and will roll off the table. It will be allowed to roll until Device 2 hits the floor. Using the forces measured from each device, the tension of each section of the string can be found. There are two sections in this set-up: the first section is the tension of the string connected to the device on the table, while the other is from the section of the string that is connected to the device that is falling. The difference in these forces will give the force of the table edge acting on the string, and by extension, the devices. The work done by the table edge is the net force times the displacement of the devices. This answer will be the work done by friction as Device 1 rolls to the edge of the table. To find the amount of gravitational potential energy that is lost, simply divide this answer by the change in gravitational potential energy as Device 2 falls to the ground. Methods: 1. Setup the IOLab on a table (“device 1”) so that the force probe is tied to a string which has a hanging IO Lab (“device 2”) on the other end that hangs off a table (diagram shown to the left), have a test run and properly zero the device. 2. Place a ruler next to the device 1, and place device 1 30 cm away (measure with a ruler and mark that spot on the table) from the edge of the table 3. Release device 1, and let it roll till it is at the edge of the table (it traveled 30 cm due to the tension exerted on it by the hanging device 2) 4. Measure the force in N that the force probe registers for both devices, and average the forces for each over the 30 cm displacement each underwent 5. Find the difference of these forces, which would be the absolute value of the difference in their tensions |T 1 - T 2 | and multiply by d to get W edge or work done by friction on the string by they table 6. Measure the initial and final height of Device 1 Device 2 Stri ng Rule

device 2 from the ground using a ruler (see image on right), and find the delta in potential energy (mgh f - mgh i ) = ΔU 7. Record the uncertainty given by each trial 8. Find the ratio between W edge / ΔU 9. Repeat steps 1-8, three more times and find the W edge / ΔU ratio for each 10. This experiment is made under the assumption that the only non-conservative force is the friction force exerted on the string by the table. In reality, there is also static friction between the wheels of device 1 and the table as it rolls across the table (displaces 30 cm). Our equation represents this because we assume that the difference in tensions would be nonzero, hence giving us a non zero ratio for W edge / ΔU. Results: Remote 1 (Rolls on table) Remote 2 (Hangs off table)

Trial 1: T1 = -0.800 N T2 = -0.872 N Trial 2: T1 = -0.801N T2 = -0.871 N Trial 3: T1 = -0.842 N T2 = -0.888 N Trial 4: T1 = -0.837 N T2 = 0.892 N Analysis: (All values are positive to allow for more accurate comparison) Mean T1 = (.800 + .801 + .842 + .837) /4 = .82000 Mean T2 = (.872 + .871 + .888 + .892)/4 = .88075 F edge = |.88075 - .8200| = .06075 W edge = F edge * Distance Distance = 17 inches = 43.18 cm = 0.4318 meters W edge = .06075 * .4318 = .02623 N/m W edge / Δ gravitational energy Δ gravitational energy = m*g*Δ h Δ gravitational energy .2kg * 9.8 m/s 2 * .4318 = .846328 J W edge / Δ gravitational energy = .02623 / .846328 = .03099 = 3%

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Conclusion: The goal of the experiment was to find the ratio of W edge / Δ U, the fraction of U that was lost due to the work of friction at the end of the table. In the experiment it was determined that this value was .03099 or 3.09%. The loss of potential energy being small, can be credited to the small mass of the string. Frictional force is typically determined by the coefficient of friction multiplied by the normal force. Since the string is considered to be near massless, then the frictional force caused by it should also be relatively small. Work done by each person: Shri: Introduction, Methods Sean: Results, Analysis, Conclusion Ethan: Methods

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