Centripetal Force Ex

Lab Report #7: Centripetal Force Elleni Solomon Section 12 Instructor: Megan Varney Experiment Performed: 17 November 2022 Lab Report Due: 1 December 2022

1. Objective a. The reason for this experiment was to observe a mass, m, being rotated in a circle and how the force on the mass while it was being rotated compared to the theoretical value. This would tell us about the centripetal, center seeking, force acting on the mass. The apparatus and setup would allow us to calculate the period T, which is the time for one revolution of the mass, which would then be used to calculate the angular velocity since it is used to express the speed of rotation of an object. Determining the centripetal force using angular velocity is the main objective of this experiment. 2. Description a. In this experiment, the equipment used included the Centripetal Force apparatus, meter stick, ruler, timer, slotted weights, weight hanger, and a digital scale. Different combinations of the slotted weights were used and hung from the weight hanger on the Centripetal Force apparatus to observe how different masses affected the speed of the rotations. Different radii were also used to see how distance from the center of the base pointer to the center of the axis of rotation of the shaft affected the time and angular velocity. 3. Theory a. When the mass is moving in a circle with constant speed, force and acceleration are perpendicular to the velocity and to the point from the particle’s position toward the center of the circle. Force and acceleration are parallel to each other in different cases. While angular velocity, ω measured in rad/s, generally is not constant, it is constant when there is a mass rotating in a circle at constant speed.

b. Part 5: Analysis i. Convert the periods, T, you have measured to angular velocity using the equation: ω= . 2𝛑 𝑇 5. Data and Calculations a. 15 cm radius r= 0.150m M 1 = 0.4469 kg M 2 = 0.650 kg Trial Time (s) for 10 revolutions T (s) ω rad/s Experimental F C (N) Theoretical M 2 g (N) 1 6.56 .656 9.58 6.15 6.38 2 7.25 .725 8.67 5.04 6.38 3 6.72 .672 9.35 5.86 6.38 4 6.43 .643 9.77 6.40 6.38 5 7.08 .708 8.87 5.27 6.38 Average 6.808 .6808 9.248 5.744 6.38 S.D. 0.3103 0.03103 0.4172 0.5155 0 Sample Calculation: 𝑇 = 𝑇𝑖𝑚? 10 = 6.56 10 = 0. 656? ω = 2𝛑 𝑇 = 2𝛑 .656 = 9. 58? F C = mr 2 = (0.4469)(0.15)(9.58) 2 = 6.15N ω M 2 g= (0.650)(9.81) = 6.38N

b. 19 cm radius Trial Time (s) for 10 revolutions T (s) ω rad/s Experimental F C (N) Theoretical M 2 g (N) 1 5.87 .587 10.68 9.69 6.38 2 5.00 .500 12.57 13.42 6.38 3 5.13 .513 12.25 12.74 6.38 4 5.67 .567 11.08 10.42 6.38 5 5.21 .521 12.06 12.35 6.38 Average 5.376 0.5376 11.728 11.724 6.38 S.D. 0.3346 0.03346 0.7225 1.4239 0 6. Questions a. What are the most significant causes of errors in this experiment? i. Human error is the most significant cause of error in this experiment. This was due to the inconsistency in measurement of time as it was difficult to ensure that the timer was being stopped at the exact moment that the mass was lining up with the pointer. Torque was also affected by error because it was difficult to make sure that the mass was directly over the pointer for the duration of all the revolutions for each trial. b. Are the significant errors random or systematic? i. The errors described above are random because they cause the results to skew in both directions, as seen in torque. Systematic error was seen in friction and air resistance as this caused lower angular velocity values.

Therefore, F C will increase upon increase of the radius as its equation is dependent on radius, F C = mr 2 ω 7. Error Analysis a. 15 cm radius: For the 15 cm radius, for almost all the trials (all but 1), M 2 g was larger than F C . This is demonstrated by the percent error shown below: % ???𝑜? = 5.74−6.38 | | 6.38 𝑥 100 = 10. 03% b. 19 cm radius: For the 19 cm radius, M2g was significantly lower than Fc for all trials. This is because to keep the masses in line with the pointer, the speed of rotation was much faster, causing the amount of time to complete 10 revolutions to be lower than a 15 cm radius. This caused a much higher percent error for the 19cm trials as shown below: % ???𝑜? = 11.72−6.38 | | 6.38 𝑥 100 = 83. 70% The 19cm radius experienced more variation as its standard deviation is higher than the 15 cm radius trials. By comparing the % errors and standard deviation values for both radii, it appears that the 15cm trials were generally closer to the theoretical values expected. 8. Conclusion a. This experiment did have significant errors due to unexpected human and systematic errors affecting the data, mainly from inconsistency among each trial in measurement of the time as the mass lined up with the pointer. Random errors were also caused by issues, such as the torque, while systematic errors included friction and air resistance. There were human, random, and systematic errors, and the data did not enable us to estimate any of these errors, however, we were still

able to investigate the given theories. These were still observed, as seen in the data where a larger radius and a constant mass gives a larger centripetal force, f . A possible improvement for this experiment would be to obtain measurements through methods with less human, random, and systematic errors by eliminating non-conservative forces.