PHYS 110_Formal Lab_Exp8_Revisions.docx

Step 6 changing to the close to furthest distance

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- Step 6: Changing to the close to furthest distance from the vertical rotating shaft. Redo from Step 2 to Step 4, to record the r, m, M, t to fill in the table. - Step 7: Changing to the close to closest distance from the vertical rotating shaft. Redo from Step 2 to Step 4, to record the r, m, M, t to fill in the table. Part II: Varying the Rotating Mass - Step 8: Keep the radius of Step 7, and adding 50g to the mass of the rotating object. Then repeat Step 2 to Step 4, to record the r, m, M, t to fill in the table. - Step 9: Keep the radius of Step 7, and adding 100g to the mass of the rotating object. Then repeat Step 2 to Step 4, to record the r, m, M, t to fill in the table. - Step 10: Use calculator to calculate object’s angular velocity ω , ω 2 , centripetal force F c , Hanging Weight ( Mg ) , and % Diff (Error) F c Mg .
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IV. Data Tables and Graphs 1. Data Tables: Note Measure time (3 times) Time, t (s) ω (ra d/s) = 2 π 50 t ω 2 (rad/s) 2 Rotating Mass, m (kg) Radius r (m) F c = m ω 2 r (N) M (kg) Hanging Weight = Mg (N) % Diff (Error) F c & Mg Furthest t 1 = 48.09s t 2 = 46.13s t 3 = 47.46s 47.23 (s) 6.6517 (rad/s) 44.2450 (rad/s) 2 453.20g =.45320 kg 20.50cm =.2050m 4.1106 (N) 470g = .470 (kg) 4.6107 (N) 11.47% Closet t 1 = 53.82s t 2 = 51.70s t 3 = 51.38s 52.30 (s) 6.0069 (rad/s) 36.0825 (rad/s) 2 453.20g =.45320 kg 16.00cm =.1600m 2.6164 (N) 450g = .450 (kg) 4.4145 (N) 51.15% Close to Furthest t 1 = 47.17s t 2 = 46.91s t 3 = 47.55s 47.21 (s) 6.6545 (rad/s) 44.2825 (rad/s) 2 453.20g =.45320 kg 19.00cm =.1900m 3.8131 (N) 420g = .420 (kg) 4.1202 (N) 7.74% Close to Closest t 1 = 46.17s t 2 = 47.32s t 3 = 47.54s 47.01 (s) 6.6828 (rad/s) 44.6601 (rad/s) 2 453.20g =.45320 kg 17.50cm =.1700m 3.5420 (N) 420g = .420 (kg) 4.1202 (N) 15.09% Adding 50g to Rotating Mass t 1 = 44.97s t 2 = 44.31s t 3 = 47.35s 45.54 (s) 6.8985 (rad/s) 47.5898 (rad/s) 2 503.20g =.50320k g 17.50cm =.1700m 4.1908 (N) 350g = .350 (kg) 3.4335 (N) 19.86% Adding 100g to Rotating Mass t 1 = 52.79s t 2 = 49.71s t 3 = 50.47s 50.99 (s) 6.1612 (rad/s) 37.9603 (rad/s) 2 553.20g= .55320 kg 17.50cm =.1700m 3.6749 (N) 340g = .340 (kg) 3.3354 (N) 9.69%
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C e nt ri p et al F or c e ( F c ) 2. Graphs a. Graph (1) between Centripetal Force ( F c = m ω 2 r ) and the radius of rotation ( r ): Radius of the rotation ( r ) b. Graph (2) between the Hanging Weight ( Mg ) and radius of rotation ( r ):
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H a n g i n g W e i g h t ( M g ) Radius of the rotation ( r ) V. Sample Calculations 1. Conversion: a. Converting the Rotating mass 1 from gram (g) into kilogram (kg): 453.20 g = 453.20 1 kg 10 3 g = .45320 kg b. Converting the Radius of rotation 1 from cm into m: 20.50 cm = 20.50 cm× 1 m 10 2 cm = .2050 m c. Converting the Hanging mass 1 from gram (g) into kilogram (kg):
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470 g = 470 1 kg 10 2 g = .470 kg d. To find the average time add the t values and divide by 3 t avg = t 1 + t 2 + t 3 3 = 48.09 s + 46.13 s + 47.46 s 3 = 47.23 s 2. Calculate object’s angular velocity ω ω = 2 π 50 t = 2 π 50 47.23 s = 6.6517 ( rad / s ) 3. Calculate ω 2 ω 2 =( 6.6517 rad / s ) 2 = 44.2450 ( rad / s ) 2 4. Calculate centripetal force F c F c = 2 r ¿ ( .45320 kg ) × ( 44.2450 ( rad / s ) 2 ) × ( .205 m )= 4.1106 ( N ) 5. Calculate Hanging Weight HangingWeight = Mg =( .470 kg ) × ( 9.81 m / s 2 )= 4.6107 ( N ) 6. Calculate % Diff (Error) F c Mg Diff ( Error ) F c Mg = | F c Mg ( F c + Mg ) 2 | × 100 = | 4.1106 N 4.6107 N ( 4.1106 N + 4.6107 N ) 2 | × 100 = 11.47 VI. Results: Note ω (rad/s ) = 2 π 50 t ω 2 (rad/s) 2 F c = m ω 2 r (N) Hanging Weight = Mg (N) % Diff (Error) F c & Mg Furthest 6.6517 (rad/s) 44.2450 (rad/s) 2 4.1106 (N) 4.6107 (N) 11.47% Closet 6.0069 (rad/s) 36.0825 (rad/s) 2 2.6164 (N) 4.4145 (N) 51.15% Close to Furthest 6.6545 (rad/s) 44.2825 (rad/s) 2 3.8131 (N) 4.1202 (N) 7.74% Close to Closest 6.6828 (rad/s) 44.6601 (rad/s) 2 3.5420 (N) 4.1202 (N) 15.09%
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Adding 50g to Rotating Mass 6.8985 (rad/s) 47.5898 (rad/s) 2 4.1908 (N) 3.4335 (N) 19.86% Adding 100g to Rotating Mass 6.1612 (rad/s) 37.9603 (rad/s) 2 3.6749 (N) 3.3354 (N) 9.69% Based on the data above:
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