Lab 6 _ Centripetal Force Justin Fan

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Indiana University, Bloomington *

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P221

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Mechanical Engineering

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Jan 9, 2024

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Lab 6 :Centripetal Forcex Introduction Per Newton's First Law, objects maintain their motion unless acted upon by an external force. For circular movement, this external force is termed centripetal force, computable via Newton's second law. In our lab, we used a rotating setup and spring to measure this force and compared it with direct spring readings. We also estimated an unidentified weight's mass, validating it against a digital scale measurement. Procedure A. Determining Centripetal Force Period of Motion - Set up the apparatus with the lighter red bob, measure and record its mass using the balance, hang it from the crowbar, adjust the pointer to align with the center of the bob, and attach the spring to the bob. - Rotate the bob by twirling the center rod to maintain a constant speed, ensuring the bob swings above the pointer in each revolution. Have one partner rotate the bob while the other times and record ten complete rotations, switching roles for several trials to minimize error. - Estimate the uncertainty in the radius of rotation by determining the uncertainty in measuring the clicker’s distance from the vertical rod's center, measuring the width of the clicker, observing any wobble while rotating the bob, and calculating the overall uncertainty in radius using the given formula. - Determine the period T + δT from your table of times (remembering you timed ten revolutions), use Equation 3 to calculate the centripetal force F C,I, and calculate the uncertainty in centripetal force δF C,I considering δT and δr. Direct Measurement Connect a string to the outer edge of the bob, align it with the pulley, hang a 50g weight from the other loop, add slotted masses until the bob is pulled directly over the clicker, calculate the weight W = mg, and estimate the uncertainty δF C,II for the weight. B. Unknown Bob Mass

- Set up the apparatus with the heavier bob without moving the clicker or using the pulley, and measure the rotational period in a similar manner to Step 2. - Determine the period T + δT from your table of times (again, you timed ten revolutions), use Equation 4 to calculate the unknown mass, m2, and calculate the uncertainty in centripetal force δm2. - Measure and record the actual value of the unknown mass using the scale. Analysis ( for calculation, measurements, and diagram please check the appendix) Table for Part A Trial (10 rev) Period (s) 1 10.07 2 10.34 3 10.39 4 10.27 5 10.50 average 10.31+/- 0.0716 Table for Part B Trial (10 rev) Period (s) 1 17.37 2 18.60 3 18.25 4 17.26 5 17.80 average 17.86 +/- 0.288

A. Determining Centripetal Force Period of Motion • Mass of the aluminum bob measured with the balance. • Question: Why is it important to mark the position of the clicker as the bob hangs Vertically? Marking the position of the clicker as the bob hangs vertically is crucial for maintaining consistent experimental conditions and ensuring accuracy. It serves as a reference for measuring the radius of the circular motion, which is pivotal for determining the centripetal force. Additionally, this marked position minimizes systematic errors across trials, especially when roles are switched between partners, and aids in the accurate alignment during the direct measurement phase. Without this reference, uncertainties could significantly impact results, reducing the experiment's reliability. • Table of times from ten revolutions. • Estimate of δrruler (uncertainty of your measurement of the clicker’s distance) • Measurement of W clicker (width of the clicker) • Radius of wobble while rotation, or statement that it seemed stable • Calculation of the uncertainty in radius δr • Period of rotation T + δT • Calculation of centripetal force and its uncertainty F C,I + δF C,I Direct Measurement • Mass required to stretch the spring • Calculation of the directly measured centripetal force (weight) F C,II + δF C,II • Question: Do your two measures F C,I and FC,II agree within their uncertainties? Yes, our two measurements of F C I and F C II agree within their uncertainties. B. Unknown Bob Mass • Table of times from ten revolutions. • Period of rotation T + δT • Calculation of unknown mass and its uncertainty m2 + δm 2 • Mass of the unknown bob measured with the balance. • Question: Does your calculated unknown mass agree with the actual value within its Uncertainty? Yes, Our calculated results of the unknown mass agrees with the actual value measured within its uncertainty.

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Conclusion In this lab, we verified Newton’s second law for rotational motion by contrasting a direct measurement of the centripetal force required to sustain a specific mass in circular motion at a consistent speed with the force anticipated from the lab manual's equation [3]. Our direct measurement of the spring force and the force derived from the circular motion geometry and equation [3] were mutually consistent. Furthermore, we validated that equation [4] is applicable in determining an unknown mass using the ratio of rotational periods in the same setup. When we later gauged this unknown mass with a digital scale, the result was in line and within one error bar of our earlier prediction, confirming the reliability of our experimental approach. Appendix