m=39.9 g

M=119.7g

Results: Data Table: Circular Motion Length of Radius of Period of sin 0 String, L Orbit, R Revolution, T (cm) (cm) (s) R ( o) 20 18 0.5 40 35 0 .7 60 54 0. 8 80 69 0 9 100 90 1. 1 Graphs: Attach your two graphs to the back of this report. Analysis and Concluding Questions: 1. Calculate the average value of angle 0 found from using the formula sin 0 = R/L. 2. Compare your calculated value with the value of 0 predicted using cos 0 = m/M. What is the percent difference between the two results? 3. According to the results, what is the mathematical relationship between the period, T, of the orbiting mass and the length, L? 4. Determine the slope of your final, straight-line graph, and express it in the appropriate units.Results: Data Table: Circular Motion Length of Radius of Period of sin 0 String, L Orbit, R Revolution, T (cm) (cm) (s) R ( o) 20 18 0.5 40 35 0 .7 60 54 0. 8 80 69 0 9 100 90 1. 1 Graphs: Attach your two graphs to the back of this report. Analysis and Concluding Questions: 1. Calculate the average value of angle 0 found from using the formula sin 0 = R/L. 2. Compare your calculated value with the value of 0 predicted using cos 0 = m/M. What is the percent difference between the two results? 3. According to the results, what is the mathematical relationship between the period, T, of the orbiting mass and the length, L? 4. Determine the slope of your final, straight-line graph, and express it in the appropriate units.Purpose: To investigate factors involved in the uniform circular nylon motion of a mass revolving at the end of a string. thread glass tube m - 3 washers Introduction: Some aspects of circular motion can be studied using the simple equipment shown in the adjacent figure, Figure #1. A small mass m (a bundle of 3 washers) 'orbits' on the end of a string. A large mass M experiences a force of gravity, Mg. M - 9 washers In this investigation, M is chosen to be a bundle of 9 identical washers, so that M = 3m. Figure #1 : ) The glass tube is smoothly polished at the top, and strong, smooth nylon thread joins the two masses. In effect, the edge of the tube acts like a pulley, changing the direction of the tension force in the string without changing in magnitude. When the small mass m is made to 'orbit' around the top end of the glass tube, mass M remains static, so the tension in the string along its length L is equal to the downwards force of gravity on M, which is Mg. ... m The radius of the orbit is not L, however, but R (the horizontal M Figure #2 distance from m to the vertical glass tube). See Figure #2. When the small mass m is made to 'orbit' the top of the glass tube, we will assume the upward force on the stationary mass M has a magnitude of Mg. The reaction force exerted on m through the strin has the same magnitude (Mg), but is exerted in the opposite direction. In Figure #3, the tension for is labelled Fr = Mg. Consider the two components of FT. The vertical component, Fry, balances the downwards force of gravity on m, so Fry = mg. The horizontal component of Fr is the centripetal force, so FTX = FC. FT = Mg FT, =mg FT.=mg m FTX = Fc M Figure #3 mg5. Write the specific equation for your straight line, incorporating the slope (make sure to include units). You can use the results of your experiment to do a check on the formula for centripetal force. Since therefore, T2 _ man2R 72 Fc Figure 2 shows that R = L sin 0 , and Figure 3 makes it clear that Fc = FTx = Mg sin 0. Therefore, we can write: T2 _ man Lsin e Mg sin 0 Mg Thus, the theoretical slope of a graph of T2 vs. L should be - man2 Mg 6. What is the theoretical value of your slope? 7. What is the percent difference between your graph's actual slope and the theoretical slope? Discuss sources of error in this experiment and how you might be able to reduce their effects