Physics111L_CentripetalAcceleration_291291

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Dec 6, 2023

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Occurs when objects travel in a circular path at a constant speed 1 Uniform circular motion Change in velocity when an object travels in a circular path at a constant speed 2 Centripetal acceleration Points toward the rotational axis of a rotating object, and causes the velocity to change directions without changing the magnitude 3 Centripetal force The distance traced out in a circular path 4 Arc length Force transmitted through a string or similar material that allows a force to act over a distance 5 Tension Physics 111L Centripetal Acceleration Final Report Student Name Kyra Pell Student ID 291291 Lesson Centripetal Acceleration Institution University of Southern Mississippi Session Fall 2023 Course Physics 111L Instructor Sidney Gautrau Test Your Knowledge Match each term with the best description.

Identify each statement as true or false. True False 1 2 The tension of a swinging string can The magnitude and direction of the provide the centripetal force needed to tangential velocity of an object in keep an object on its circular path. uniform circular motion change over time. The speed of an object undergoing uniform circular motion can be The arc length is equal to the subtended determined using the circumference and angle divided by the radius. the period of the motion. Exploration During uniform circular motion, the magnitude and direction of the velocity change. True False The term centripetal means . circular center-seeking towards the margin None of the above Typesetting math: 100%

velocity is the velocity of an object moving in a circular path in uniform circular motion. Tangential Centripetal Circular None of the above The centripetal force always points in the same direction as the centripetal acceleration. True False For circular motion calculations, the angle is measured in units of . degrees radians revolutions None of the above The of an object undergoing uniform circular motion can be determined using the circumference and the period of the motion. acceleration radius speed None of the above

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e velocity is equal to two times pi times the radius, (v = 2πr), v and r are directly proportional. Meaning an increased r will lead to an increased v, as well as a decrease r will lead to a decrease of the velocity, as shown in the equation Fc=m moving v2/r, implying that a doubling of speed will require four times the centripetal force to keep the motion in a circle. this means that the cent provides the centripetal force needed to keep an object swinging on a string on its circular path. Gravity Tension Velocity None of the above Exercise 1 What effect does radius have on the velocity of a rotating object? What effect does the velocity of a rotating object have on the centripetal force exerted on it? The Moon orbits Earth at an average distance of 3.84 x 10 8 m in a path that takes 27.3 days to complete. What is the centripetal acceleration of the Moon? (Remember, you must convert time into seconds.) The centripetal acceleration can be found with the equation ac=v 2 /r. We have to radius 3.84 x 10 8 (m) but we need to find the velocity. To do so we need to use the equation (2πr)/T, where T is the time, it takes to travel the distance. After converting the time, I then received an approximant value of 1025 (m/s) for velocity. We can now plug in the velocity and radius in the centripetal acceleration. This gives us an approximant value of 2.74 x 10 − 3 .

The measured length from my shoulder to the center of a bucket is approximately 82 (m). So, using the equation, velocity =√rg, I find I have an approximant critical velocity of 28.36 (m/s2). When a bucket of water is swung in a vertical circle, the water will remain in the bucket if the velocity is high enough. If you let the bucket slow down too much, the water will spill out. The critical velocity is the slowest velocity necessary to keep the water in the bucket. What is the critical velocity if the formula is velocity = , where r is the radius (the radius of your arm swing including the bucket) and g is the acceleration of gravity ( g =9.81 m/s 2 )? Hint: You must measure or estimate the length from your shoulder to the center of the bucket to determine the radius. Data Table 1: Constants for Varying Radius Number of Washers 20 Mass of all Washers (kg) 0.10156 Average Mass of Single Washer (kg) 0.005078 Rotating Mass (kg) 0.01699 Hanging Mass (kg) 0.03009

al force required to keep an object in circular motion depends on the rotating object's mass, the radius of the circular path, and the square of the angular velocity. However, it can indirectly aff Data Table 2: Varying Radius – Measurements and Calculations Trial Radius (m) Time - 10 rev (s) Circumference (m) Velocity (m/s) F c (N) F g (N) % Error 1 0.70 9.72 4.40 4.53 0.50 0.29 72.4% 2 0.60 9.18 3.77 4.10 0.48 0.29 65.5% 3 0.50 8.80 3.14 3.57 0.43 0.29 48.3% 4 0.40 8.08 2.51 3.10 0.41 0.29 41.4% Exercise 2 What was the effect of increasing the hanging mass on the centripetal force in Part 1 of this exercise?

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ncreasing the mass of a rotating object does affect its velocity. As Data table 4 shows, as the mass increases, the angular velocity decreases to keep the angular momentum constant, and vice Did increasing the mass of the rotating object affect its velocity in Part 2 of this exercise? Explain your answer by referencing Data Table 4.

otating mass increases so does its velocity, its tangential velocity to be specific. This relationship holds because points farther from the axis of rotation need to cover a larger distance in one ro d have measured my radiuses, revolutions, and masses incorrectly or not precise enough. In the case of incorrect calculations, I could have made a mistake in my calculations leading to an er correct and precise enough. Finally, If I had more time, I could have practiced using my apparatuses so that I could get the most accurate measurements. oing uniform circular motion and the radius, r, of the circular path. The simulations in Exercise 2 have contributed to my understanding of how the velocity and the radius of centripetal accele ng a centripetal force apparatus lets you see first-hand the effects of centripetal acceleration. What effect did increasing the radius of the rotating mass have on its velocity? Reference Data Table 5 in your answer. How do these results compare to those recorded in Exercise 1? What factors introduced error in both Exercise 1 and Exercise 2? How could the error have been reduced? 5. How did using the simulations in Exercise 2 contribute to your understanding of centripetal acceleration? Did you find them more or less effective than the physical experiment in Exercise 1? Explain your answer.

Data Table 3: Varying Hanging Mass - Measurements and Calculations Rotating Mass (kg) 0.025 Radius (m) 2.00 Circumference (m) 12.6 Trial Hanging Mass (kg) Time - 10 rev (s) Time T - 1 rev (s) Velocity (m/s) F c (N) F g (N) % Error 1 0.10 14.2 1.42 8.87 0.98 0.98 0.00% 2 0.13 12.4 1.24 10.16 1.29 1.27 1.57% 3 0.20 10.0 1.00 12.60 1.98 1.96 1.02% 4 0.26 8.8 0.88 14.32 2.56 2.55 0.39% Data Table 4: Varying Rotating Mass - Measurements and Calculations Hanging Mass (kg) 0.13 Radius (m) 2.00 Circumference (m) 12.6 Trial Rotating Mass (kg) Time - 10 rev (s) Time T - 1 rev (s) Velocity (m/s) F c (N) F g (N) % Error 1 0.025 12.4 1.24 10.16 1.29 1.27 1.57% 2 0.047 17.1 1.71 7.37 1.28 1.27 0.79% 3 0.056 18.6 1.86 6.77 1.28 1.27 0.79% 4 0.065 20.1 2.01 6.27 1.28 1.27 0.79% Data Table 5: Varying Radius - Measurements and Calculations Rotating Mass (kg) 0.025 Hanging Mass (kg) 0.13 Trial Radius (m) Time - 10 rev (s) Time T - 1 rev (s) Circumference (m) Velocity (m/s) F c (N) F g (N) % Error 1 0.25 4.4 0.44 0.39 0.89 0.08 1.27 93.7% 2 0.50 6.1 0.61 1.57 2.57 0.33 1.27 74.0% 3 0.75 7.1 0.71 3.53 4.97 0.82 1.27 35.4% 4 1.00 8.7 0.87 6.28 7.22 1.30 1.27 2.4%

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Competency Review Uniform circular motion occurs when objects travel in a circular path at a constant . velocity direction speed All of the above The centripetal acceleration points towards the center of the circle. True False The centripetal acceleration is always to the tangential velocity. perpendicular tangential central All of the above The centripetal force is proportional to the . mass velocity squared inverse of the radius All of the above The force provides the tension force in the centripetal force apparatus.

spring gravitational incline All of the above The tension force is greater than the centripetal force in the centripetal force apparatus. True False An object moving in uniform circular motion with a radius of 0.6 m and a period of 0.4 s has a tangential velocity of m/s. 2 4 9 None of the above The centripetal force acting on a 0.30 kg object moving with a tangential velocity of 12 m/s in a 0.80 m radius circle is N. 4.5 54 380 None of the above The centripetal acceleration acting on a 0.30 kg object moving with a tangential velocity of 12 m/s in a 0.80 m radius circle is m/s 2 .

15 180 480 None of the above In Exercise 1, the theoretical centripetal force was calculated from the . tension velocity weight None of the above Extension Questions For each of the following scenarios, describe the force providing the centripetal force for the motion:

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vided by the friction between the car's tires and the road. As the car turns, the tires push against the road surface in the direction of the center of the turn, causing a frictional force that keep petal force is provided by the tension force in the string, chain, or rope that the child is holding onto as they swing. The tension force always acts towards the center of the circular motion, allo rousel, the centripetal force is provided by both the normal force exerted by the bench on the person and the frictional force between the two. The normal force is the force exerted by a surfa e to the movement of the carousel. In this case, the normal force, and the frictional force acts towards the center of the circular motion, keeping the pers e is provided by the tension force in the string. The tension force always acts towards the center of the circular motion, which allows the rock to maintain its circular path as it swings back and force is provided by the gravitational force between the Sun and the Earth. The gravitational force is always directed towards the center of the circular orbit, keeping the Earth in its path arou a. a car making a turn b. a child swinging around a pole c. a person sitting on a bench facing the center of a carousel d. a rock swinging on a string e. the Earth orbiting the Sun.

Physics111L_CentripetalAcceleration_291291

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