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JCUSSIUN: When a body moves at constant speed in a circular path, it is undergoing uniform circa motion. Because the velocity of the body which is tangent to the circular path at every point) is continually changing directie nanging direction, the body is accelerating. The acceleration is constant in magnitude and directed towards the center of the circle, perpendicular to the velocity vector. According to Newton's second law, this acceleration is produced by the centripetal force, F given by MV R where Mand vare the body's mass and speed, respectively, and R is the radius of the circle. The quantity V/ R is the centripetal acceleration. In this experiment, you will swine a rubber stonner, attached to a string, in a horizontal circle. The ce is provided by the weight of a stack of washers tied to the opposite end of the string. See Figure 4.1. You will swing the stopper for Nrevolutions, and determine the time taken. Since one revolution covers a distance 2R (the circumference of a circle), the total distance traversed by the stopper is ZIRN. The speed is then the total distance divided by the time: 21 RN (4.2) You will compare the calculated centripetal force (Eq.4.1) with the weight w of the washers, w = mg. where m is the mass of the washers, and gis 9.80 m/s?. Ideally, the weight and centripetal force should be the same, but, as always, experimental error is unavoidable. You will also investigate the effect of increasing the weight of the washers. Rubber stopper Hollow tube Circular path Washers - E (w= (w = mg) Paper clip Figure 4.1 Centripetal force apparatus

Centripetal Force PROCEDURE le rubber stopper (M 1. Weigh a one-hole rubber stopper ( Mar 0.1 8. Record the masses in kilograms 2. Assemble the apparatus shown in Figur be either glass (fire-polished at and a stack of four washers with a paper clip (m) to the team Pass the free end of the string through the distance is the radius (R) of apparatus shown in Figure 4.1. The string should be at about I m long. The tube should ass hire-polished at both ends) or smooth plastic. Loop the string through the hole in the Stopper, and tie a double (or triple) knot to ensure that stopper will not fly loose when swung. the string through the tube far enough that the distance from the center of the rubber per to the point on the string that makes contact with the top of the tube is 50.0 cm (0.500 m). This s the radius (R) of the circle. Place a small piece of masking tape on the string where it passes through the bottom of the tube. This reference point will allow you to see whether the radius is when swinging the stopper over your head. The strip of masking tape must not move higher han this point during the trials. Now loop the free end of the string at the bottom of the tube several times through the stack of washers so that they will be positioned about an inch below the Masking tape. (If the washers are too far below this point, they will tend to swing wildly when the Stopper is swung.) Secure the washers by attaching the paper clip to the string just below the washers. 5. Move to an area where there is PLENTY OF ROOM, and practice swinging the stopper horizontally WELL ABOVE YOUR HEAD at a speed that maintains the position of the masking tape reference at the bottom of the tube. Do not allow the tape to move above or below this point. Make certain that your hand does not move in wide circles as you swing and that the stopper moves in a horizontal plane, nor ar a large angle. After sufficient practice, prepare for the first trial. 4. Count and time the revolutions in the following way: Start swinging the stopper at the appropriate speed to maintain a constant radius, and when you are ready, shout "NOW!" as a signal to your lab partner to start the stopwatch. When the stopper has made one revolution, say (or mentally note) "ONE." etc. Note: The stopwatch must be started at the beginning of the first revolution, so saying "NOW" will be followed by "ONE" for the first complete rotation, not the second. Continue counting and timing for at least 30 revolutions. When the last revolution is completed, shout "STOP" to signal your partner to stop the stopwatch. Record the number of revolutions, N. and the time for Trial 1. 5. For Trial 2, weigh two more washers, add this mass to the mass of the original four washers plus the paper clip, and record their total mass, m, in kilograms. Add the two extra washers to the original four washers by re-looping the string through all six, attaching the paper clip below them, and repeat the procedure. This time, you will have to swing a little faster. 6. For Trial 3, repeat the procedure with two more washers (eight in all). 7. Finally, for Trial 4, repeat the procedure with two more washers, a total of 10 washers. 8. For each trial, calculate the speed v (Eq.4.2), centripetal force F (Eq.4.1). and balancing weight wof the washers and paper clip. 27 Centripetal Force

Experiment 4 Centripetal Force Name Date REPORT SHEET Mass of stopper Radius of circle Time Speed of stopper Centripetal Weight of force Washers + clip Trial Mass of No. of washers revol- + clip K utions 2452130 139,3 130 5262130 1 4 165.15 30 mis 1492 6,3 39.69 1.4 1.241 14.7516,39 140,837,44 .385 11478 6.38 1407 1.43 1.500 13,56 6195 48,3 1,70 1639) Sample calculations

Centripetal Force Experiment 4 Centripetal Force Name Date QUESTIONS 1. Were the calculations for the centripeta close? Discuss several sources of experimental Is for the centripetal force and the weight of the washers (plus paper clip) reasonably ral sources of experimental error that might have caused them to significantly differ 2. How was the speed of the stopper affected when more washers were added? Explain this effect refer to Eq. 4.1). 3. Graph the washer/paper clip weights (w) on the y-axis vs. the squares of the stopper speed (A) on the x-axis. Draw the best-fit line that passes through the origin. ATTACH THIS GRAPH TO YOUR LAB REPORT. a. Do the data points appear to "line up"? b. Calculate the slope of the line. Indicate the point(s) chosen for the calculation. You may choose one of the points to be the origin. What physical quantity does this value represent? Centripetal Force