J ,i i! 7 you? data from table 5, what is the relationship . 1y? Use your data and equations to justify your a Conclusion: 1. Using your data in table 2, what is the relationship between centripetal force and velocity? Use your data and equations to justify your answer. If it is linear, what two variables would be graphed? 2. Using your data in table 4, what is the relationship between radius and velocity? Use your data and equations to justify your answer. If it is linear, what two variables would be graphed? 93% 52OF Sun O W Pew Tools Help Circular Motion and Centripetal Force Name. Objective: This experiment involves determining the relationships between the centripetal force and the effect on velocity of the stopper, the radius and the effect on velocity of the stopper, and the moving mass and the effect on velocity of the stopper. Experiment: 1. Go to the following website: https://www.thephysicsaviary.com/Physics/Programs/Labs/ClassicCircularForceLab/inde x.html 2. Click BEGIN on the bottom right of the simulation. 200 radius, r Moving Mass 25 g moving mass, mm Elapsed Time 0.0 s hanging mass, mh # Washers: 7 Click on masking tape to change radius w 92% 52 Type here to searchTable 2: Analysis: Relationship Between Force and Velocity T = 10 W= T Run T (s) Utmeas Utcale Fe = mng w (rad /s) (m/s) (m/s) F. (N) doerror 2 3 4 5 Part B - Relationship Between Radius and Velocity 1. SET the radius to ~30 cm. Record your exact radius, (r) in Row 1, Column 1 of Table 3. 2. SET the hanging mass, mr to (~150 g) and the moving mass, mm to (~50 g). Record your exact values in meters (m) and kilograms (kg) in the space provided. 3. Click Start for 10 complete revolutions. Hit Pause. Record the time under the t, column of Table 1. Click Reset. Repeat 2 more times. Calculate and Record the average tavg. 4. Click on the yellow tab 1-2 times to increase the radius. Record the exact (r) value in -1-t - TLI. 1 93% ] 52OF SU re to search O Pata Analysis: 1. Calculate the Period, T for each run. Record your result in the Analysis Table. 2. Calculate the angular velocity, w for each run. Record your result in the Analysis Table. 3. Calculate the tangential velocity, of for each run. Record your result in the Analysis Table. 4. Calculate the Centripetal Force, Fc for each run. Record your result in the Analysis Table. Table 4: Analysis - Relationship Between Radius and Velocity T = aug W = F. = mng 10 Ut = WT Run r (m) T (s) w (rad/s) Ut (m/s) F. (N) 1 2 3 4 52OF Sunny 93% w searchTable 5: Data: Relationship Between Mass and Velocity Run mm (kg) t1 (s ) t2 ( s) t3 ( s ) tavg (S) 1 2 3 4 5 mn = kg r = m Data Analysis: 1. Calculate the Period, T for each run. Record your result in the Analysis Table. 2. Calculate the angular velocity, w for each run. Record your result in the Analysis Table. 3. Calculate the tangential velocity, v, for each run. Record your result in the Analysis Table. 4. Calculate the Centripetal Force, F. for each run. Record your result in the Analysis Table. Table 6: Analysis - Relationship Between Mass and Velocity 93% ] 52OF Sunny WMm = kg r= m Data Analysis: 1. Calculate the Period, T for each run. Record your result in the Analysis Table. 2. Calculate the angular velocity, w for each run. Record your result in the Analysis Table. 3. Calculate the measured tangential velocity, Utmeas = wr for each run. Record your result in the Analysis Table. 4. Calculate the theoretical tangential velocity, Utcare for each run using Equation 6. Record your result in the Analysis Table. 5. Calculate the Centripetal Force, F- for each run. Record your result in the Analysis Table. Table 2: Analysis: Relationship Between Force and Velocity 93% 52OF Sunny O w P to searchTheory: According to Newton's First Law, an object in motion tends to stay in motion in a straight line at a constant speed if there is no external net force applied to the object. An object undergoing uniform circular motion (motion in a circle at constant speed) must be acted on by a non-zero net force called the centripetal force which must point toward the center of the circle. The magnitude of the centripetal force required to keep an object in a circular path depends on the inertia (or mass) and the acceleration of the object, as you know from the second law (F = ma). The acceleration of an object moving in uniform circular motion is a = ", so the magnitude of the centripetal force of an object can be found from F. = (1) Where (m) is the mass of the object moving in a circle in a circular orbit of radius (r) with a tangential velocity (v). The distance (circumference) around a circle is 2mr. The velocity of an object moving in a circular path can be found from v = =. For uniform circular motion, the tangential speed is given by: U = (2) T where 2ar is the distance around one complete circle and T is the period (time) required to make one revolution. Now if we substitute for v into Equation (1) yields: An2mr2 An? mr 4x-mmT = F. = (3) Fe = T2 r T2 + T2 52OF Sunny P 93% W4. Click on the yellow tab 1-2 times to increase the radius. Record the exact (r) value in Table 1. Repeat Step 3. Then do this step 3 more times to complete Table 1. Table 3: Data - Relationship Between Radius and Velocity Run r (m) ty (s ) t2 ( s ) t3 ( s) tavg (s) 2 3 4 5 mn = kg mm = kg 52 OF 93% W PClick on masking tape to change radius Start Click on washers to change #washers Each washer has a mass of 10 grams 3. Adjust the hanging mass, mm Click the Icon to randomly add more washers. As indicated above, the mass of each washer is 10 grams. 4. Adjust randomly the moving mass, mm to increase and to decrease. 5. The Yellow Flag allows you to adjust randomly the radius, r. 6. Take a few minutes to CLICK on each of these to get used to how they work. 92% ] 52 P O W to searchFor this experiment, mass mm is the mass of the moving mass moving at a constant tangential speed of vt at the end of a string of length r. The centripetal force will be supplied by a hanging mass me that is attached to the bottom of the string. See the figure on page 1. The weight of this hanging mass is determined by the equation: Fu = mn . g (4) Therefore, the weight of the hanging mass is the centripetal force applied to mass mm, keeping it in a horizontal circular orbit. Fc = Fu or: (5) mm = mh g T Thus the calculated tangential velocity Utcare required to keep this system in equilibrium, will be: mh (6) Utcale erg mm The measured tangential velocity Utmea, is determined by: 2x/rey in rad /sec. Utmeas = W . r where (w) is the angular velocity given by w - Trev 52OF Su 93% n O W ere to search1 2 3 4 5 Part C - Relationship Between Mass and Velocity 1. SET the moving mass to ~25 (g). Record the exact value in Row 1, Column 1 of Table 5. 2. SET the hanging mass, me to ~150 g and the radius, r to ~180 cm. Record your exact values in kilograms (kg) and meters (m) in the space provided. 3. Click Start for 10 complete revolutions. Hit Pause. Record the time under the t, column of Table 1. Click Reset. Repeat 2 more times. Calculate and Record the average tavg. 4. Click on the UP arrow to increase the moving mass. Record the exact (mm) value in Table 1. Repeat Step 3. Then do this step 3 more times to complete Table 1. 52OF Sunny O w P 93%3. Calculate the tangential velocity, v for each run. Record your result in the Analysis Table. 4. Calculate the Centripetal Force, F. for each run. Record your result in the Analysis Table. Table 6: Analysis - Relationship Between Mass and Velocity T - fave Run 10 W= T Ut = WT Fe = mng mm (kg) T (s) w (rad/s) Ut (m/s) Fe (N) 2 3 4 5 52OF Sunny w P 93% O earchPart A - Relationship Between Force and Velocity 1. Place a small number of washers ( ~8) on the end of the string. Record your exact hanging mass, (mn) which is the # of washers x 10g in Row 1, Column 1 of Table 1. 2. SET a radius of (~200 cm) and mass of the moving mass, mm to a value in the range of 60-90 g. Record your exact values in meters (m) and kilograms (kg) in the space provided. 3. Click Start for 10 complete revolutions. Hit Pause. Record the time under the t column of Table 1. Click Reset. Repeat 2 more times. Calculate and Record the average tavg. 4. Click on the washers 1-2 times to add more mass. Record the exact (mh) value in Table 1. Repeat Step 3. Then do this step 3 more times to complete Table 1. Table 1: Data - relationship Between Force and Velocity: Run Mn (kg) T 1 (s) T2 ( s ) T3 (s ) Tavg (s ) 1 3 4 5 93% 52OF SL w @ 2 re to search