Experiment 6: Centripetal Force


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1 Name Section Date Intoduction Expeiment 6: Centipetal oce This expeiment is concened with the foce necessay to keep an object moving in a constant cicula path. Accoding to Newton s fist law of motion thee must be foces acting on an object moving in a cicula path since it does not move off in a staight line. The second law of motion ( = ma) also indicates foces since an unbalanced foce is equied to change the motion of an object. An object moving in a cicula path is continuously being acceleated since it is continuously changing diection. This means that thee is a continuous unbalanced foce acting on the object that pulls it out of a staightline path. The foce that pulls an object out of a staightline path and into a cicula path is called a centipetal foce. The magnitude of the centipetal foce equied to keep an object in a cicula path depends on the inetia (o mass) and the acceleation of the object, as you know fom the second law ( = ma). The acceleation of an object moving in unifom cicula motion is a = v /, so the magnitude of the centipetal foce of an object with a mass (m) that is moving with a velocity (v) in a cicula obit of adius () can be found fom mv =. The distance (cicumfeence) aound a cicle is π. The velocity of an object moving in a cicula path can be found fom v = d/t, o v = π/t whee π is the distance aound one complete cicle and T is the peiod (time) equied to make one evolution. Substituting fo v, = m T o π = m 4π T, 4π m 1 = T m = 4π. T This is the elationship between the centipetal foce (c), the mass (m) of the object in cicula motion, the adius () of the cicle, and the time (T) equied fo one complete evolution. 65
2 Pocedue 1. The equipment setup fo this expeiment consists of weights (washes) attached to a sting, and a ubbe stoppe that swings in a hoizontal cicle. You will swing the stoppe in a cicle and adjust the speed so that the stoppe does not have a tendency to move in o out, thus balancing the centipetal foce ( c ) on the stoppe with the balancing foce ( b ), o mg, exeted by the washes on the sting. Plastic o glass tube (small diamete) Stoppe (m) Place clip hee Washes ( = mg) igue 6.1. Place some washes on the sting and pactice otating the stoppe by placing a finge next to the sting, then moving you hand in a cicula motion. You ae tying to move the stoppe with a consistent, balancing motion, just enough so the stoppe does not move in o out. Keep the stoppe moving in a faily hoizontal cicle, without the washes moving up o down. An alligato (o pape) clip placed on the sting just below the tube will help you maintain a consistent motion by poviding a point of efeence as well as helping with length measuements. Be caeful of the moving stoppe so it does not hit you in the head. 3. Afte you have leaned to move the stoppe with a constant motion in a hoizontal plane, you ae eady to take measuements. The distance fom the sting at the top of the tube to the cente of the stoppe is the adius () of the cicle of otation. The mass (m) of the stoppe is detemined with a balance. The balancing foce ( b ) of the washes is detemined fom the mass of the washes times g ( b = mg). The peiod (T) is detemined by measuing the time of a numbe of evolutions, then dividing the total time by the numbe of evolutions to obtain the time fo one evolution. o example, 0 evolutions in 10 seconds would mean that 10 0, o 0.5 seconds, is equied fo one evolution. This data is best obtained by one peson acting as a counte speaking aloud while anothe peson acts as a time. 66
3 4. Make fou o five tials by otating the stoppe with a diffeent numbe of washes on the sting each time, adding o emoving two washes (about 0 g) fo each tial. o each tial, ecod in Data Table 6.1 the mass of the washes, the adius of the cicle, and the aveage time fo a single evolution. Data Table Centipetal oce Relationships Tial Mass of washes (m) Balancing Radius Time Centipetal foce foce ( b ) () (t) (c) (kg) (N) (m) (s) (N) Mass of stoppe kg 67
4 5. Calculate and ecod the balancing foce ( b ) fo each tial fom the mass of washes times g (9.8 m/s ), o b = mg. 6. Calculate and ecod the centipetal foce ( c ) fo each tial fom m = 4π. T Consideing the balancing foce ( b ) as the accepted value, and the calculated centipetal foce ( c ) as the expeimental value, calculate you pecentage eo fo each tial of this expeiment. Analyze the pecentage eos and othe vaiables to identify some tends, if any. Tial 1 : Tial : Tial 3 : = 10% 100 = 7.% = 1.% 7 Tial 4 : = 5.% 1 Tial 5 : = 5.% 1 68
5 Results 1. Did the balancing foce ( b ) equal the centipetal foce ( c )? Do you conside them equal o not equal? Why o why not? The balancing foce and the centipetal foce ae basically equal. The balancing foce ceates the tension in the sting which keeps the stoppe moving in a cicle. The data suppots this since the eo is less than 10%.. Analyze the eos that could be made in all the measued quantities. What was pobably the geatest souce of eo and why? Discuss how these eos could be avoided and how the expeiment in geneal could be impoved. Thee ae at least two majo souces of eos: (a) time measuement, and (b) adius measuement The eos in the time measuement can be educed by timing a numbe of evolutions and finding the aveage. The eo in the adius measuement can be educed by choosing a easonable adius and making it on the sting. Then you will swing the stoppe at such a ate to make the sting stay at the mak. This also helps the student keep a constant speed thoughout the timing pocess 3. Discuss any tends that wee noted in you analysis of pecentage eo fo the diffeent tials. Analyze the meaning of any obseved tends o discuss the meaning of the lack of any tends. Thee is moe eo when the time fo a evolution is too long. This is because it is difficult to keep the stoppe moving at a constant speed. Thus, as the hanging mass inceases, and the time of evolution deceases, thee will be less eo. o the tial with a small hanging mass, it is best to make the adius small as well. This will educe the time fo a evolution and help keep the eo down. 69
6 4. Was the pupose of this lab accomplished? Why o why not? (You answe to this question should be easonable and make sense, showing thoughtful analysis and caeful, thoough thinking.) (The student should be able to explain the basics of centipetal acceleation. They should be able to explain how the centipetal acceleation (o centipetal foce) changes when the adius changes o when the time of evolution changes. They should also undestand that the tension; in the sting, o indiectly the hanging weight, supplies the foce needed to keep the stoppe moving in a cicle.) Invitation to Inquiy 1. Did you eve ty to figue out which is a cooked egg and which is a aw one without beaking the shell? One way to accomplish this is by spinning the eggs on a plate, and the wellcooked one will continue to spin while the uncooked egg will ock back and foth. The yolk is heavie than the white, but why would an uncooked egg spin moe slowly? Use you undestanding of centipetal foce to develop some ideas about why eggs should behave this way, then design a demonstation o expeiment to test you idea.. Expeiment with some things that otate, such as olling cylindes. Roll lage, small, solid, hollow, and vaious combinations of lage and solid cylindes, small and solid cylindes down an incline. Pedict ahead of time which will each the bottom of the incline fist. Then test you pedictions. 3. A hollow and solid cylinde of the same size do not have the same weight. If you oll the two cylindes down an incline slope togethe, side by side, the solid cylinde should win. Yet if you attach stings of equal lengths to make pendulums fom the same hollow and solid cylindes, then you will find that they swing togethe, side by side. Is this tue? Expeiment to find out, then be pepaed to explain you findings. 4. Exploe elationships between mass distance fom an axis and how had it is to set an object into otational motion. Conside using a baton with some kind of movable masses that can be fixed to the baton diffeent distances fom the axis of otation. A lage wooden dowel od and lumps of clay might be a good expeimental altenative to a baton. 70
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