Copy of Physics Lab 11

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Apr 3, 2024

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Centripetal Force By: Abby Knapp, Britney Johlfs, Jonathan Deridal, Alora Skustad, Kyra Rodriguez Purpose: The purpose of this lab is to verify the equation F c = ma c = mv 2 /r by measuring the force exerted on an object that is spinning. Procedure: To begin, we assembled the apparatus and set the PVC “T” on top of the metal pole on the stand. We then clamped the ring stand base to the table top and wrapped the string around the PVC base. Next, we placed the hanging mass at one of the three holes. Next, we spun the apparatus and determined the time it took to achieve 10 revolutions. We repeated this for 5 trials per hole (3 holes) and recorded all of our data. We then calculated the period, T, and averaged all the values for the period. We then measured the radius, R, of the canister rotation and repeated for each hole position. Next, we calculated the velocity, v, of the rotation for the canister at the vertical position. We then used the spring scale or nernier sensor to determine the force required to stretch the rubber band or spring to the amount it stretched during the measurement. We then calculated the centripetal force, after measuring the mass of the canister, and compared it to the elastic force F E . We then determined the percentage error between the two values. We repeated this process for each of the three holes. Data: Trial 1 (s) Trial 2 (s) Trial 3 (s) Trial 4 (s) Trial 5 (s) Hole 1 17.03 16.74 17.05 17.01 16.83 Hole 2 15.66 15.70 15.02 15.42 15.62 Hole 3 11.69 12.07 11.87 11.95 12.11 Radius (cm) Hole 1 37.5 Hole 2 31.5 Hole 3 25.0

Spring scale to measure elastic force, F E : F E = 1.7 N for all trials Measure the mass of the canister: m = 4.2 g Sample Calculations: Period (T) Hole 1: Period T = = 1.6932 s (17.03/10) + (16.74/10) + (17.05/10) + (17.01/10) + (16.83/10) 5 Period (T) Hole 2: Period T = = 1.5484 s (15.66/10) + (15.70/10) + (15.02/10) + (15.42/10) + (15.62/10) 5 Period (T) Hole 3: Period T = = 1.1938 s (11.69/10) + (12.07/10) + (11.87/10) + (11.95/10) + (12.11/10) 5 Velocity of rotation of canister for Hole 1: ? = 2π𝑅 𝑇 Conversion of cm to m: (37.5 cm/1)(1m/100cm) = 0.375 m = 1.391 m/s ? = 2π(0.375 ?) 1.6932 ? Velocity of rotation of canister for Hole 2: Conversion of cm to m: (31.5 cm/1)(1m/100cm) = 0.315 m = 1.278 m/s ? = 2π(0.315 ?) 1.5484 ? Velocity of rotation of canister for Hole 3: Conversion of cm to m: (25.0 cm/1)(1m/100cm) = 0.250m = 1.316 m/s ? = 2π(0.250 ?) 1.19384 ? Centripetal Force for Hole 1: F c = ma c = mv 2 /r Conversion of g to kg: (4.2g/1)(1kg/1000g) = 0.0042 kg F c = (0.0042 kg) ( 1.391m/s) 2 / ( ) 0. 375? F c = 0.022 N Centripetal Force for Hole2: F c = (0.0042 kg) ( 1.278m/s) 2 / ( ) 0. 315? F c = 0.022 N Centripetal Force for Hole 3: F c = (0.0042 kg) ( 1.316m/s) 2 / ( ) 0. 250? F c = 0.029 N

Percentage error Hole 1: Percentage error = ?????𝑖???𝑎? ????? − ??𝑎??𝑖? ????? | | ??𝑎??𝑖? ????? 𝑋 100% Percentage error = 0.022 − 1.7𝑁 | | 1.7𝑁 𝑋 100% = 98% Percentage error Hole 2: Percentage error = 0.022 − 1.7𝑁 | | 1.7𝑁 𝑋 100% = 98% Percentage error Hole 3: Percentage error = = 98% 0.029 − 1.7𝑁 | | 1.7𝑁 𝑋 100% Discussion: 1. Sketch all of the forces acting on the weight when it was spinning vertically oriented. 2. What force results in the centripetal force in this lab The force of us pulling the string that caused the canister to spin in a circular motion is what causes the centripetal force in this lab.

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3. Based on your results, does the equation for the centripetal force seem to agree with your measured value of the centripetal force? Based on our results, the equation for centripetal force does not seem to agree with me measured value of the centripetal force. We think this may be because the elastic force may be very inaccurate, leading to a large percent error. It was difficult to use this instrument to accurately measure the centripetal force of the spring that extended from the metal stand. 4. Based on the fact that you took multiple measurements of the period of the weight when the object was spinning vertically, come up with a value for the uncertainty of your calculated centripetal force. Percentage uncertainty = ?????? −𝑎??????? ?𝑎??? | | 𝑎??????? ?𝑎??? 𝑋 100% Standard Deviation Hole 1: 0.124s ((17. 03? − 16. 93?) 2 + (16. 74? − 16. 93?) 2 + (17. 05? − 16. 93?) 2 + (17. 01? − 16. 93?) 2 ) + (16. Standard Deviation Hole 2: 0.25s ((15. 66? − 15. 48?) 2 + (15. 70? − 15. 48?) 2 + (15. 02? − 15. 48?) 2 + (15. 42? − 15. 48?) 2 ) + (15. Standard Deviation Hole 3: 3.66s ((11. 69? − 11. 94?) 2 + (12. 07? − 11. 94?) 2 + (11. 87? − 11. 94?) 2 + (11. 95? − 11. 94?) 2 ) + (16. Average standard deviation: (0.124+0.25+3.66)/3=1.34 So uncertainty is 1.34%. Conclusion: The purpose of this lab was to verify the equation F c = ma c = mv 2 /r by measuring the force exerted on an object that is spinning. After completion of the lab, we were able to accomplish this as well as have a better understanding of centripetal force. Some possible sources of error we could have encountered would have been spring used to measure the force as well as the timing with the stopwatch.