hw 31 - homework 31 HETTIGER, CHRISTOF Due: Apr 15 2008,...

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Unformatted text preview: homework 31 HETTIGER, CHRISTOF Due: Apr 15 2008, 4:00 am 1 Question 1, chap 15, sect 5. part 1 of 3 10 points A uniform disk of radius 1 . 5 m and 4 . 6 kg mass has a small hole a distance from the disks center that can serve as a pivot point. 1 . 5 m 4 . 6 kg The acceleration of gravity is 9 . 81 m / s 2 . What should be the distance so that the period of this physical pendulum is 5 . 6 s? (If there are two possible answers, answer with the smaller distance.) Correct answer: 0 . 147145 m (tolerance 1 %). Explanation: Let : R = 1 . 5 m , m = 4 . 6 kg , T = 5 . 6 s , and g = 9 . 81 m / s 2 . Using the parallel-axis theorem, I = I cm + m 2 = 1 2 m R 2 + m 2 . The period of a physical pendulum is T = 2 radicalBigg I m g T = 2 radicaltp radicalvertex radicalvertex radicalbt 1 2 m R 2 + m 2 m g T 2 = radicaltp radicalvertex radicalvertex radicalbt 1 2 R 2 + 2 g T 2 g 4 2 = 1 2 R 2 + 2 2- g T 2 4 2 + R 2 2 = 0 . Applying the quadratic formula, = g T 2 4 2 radicalbigg g 2 T 4 16 4- 2 R 2 2 . Since g T 2 4 2 = (9 . 81 m / s 2 ) (5 . 6 s) 2 4 2 = 7 . 79265 m and g 2 T 4 16 4- 2 R 2 = (9 . 81 m / s 2 ) 2 (5 . 6 s) 4 16 4- 2 (1 . 5 m) 2 = 56 . 2254 m 2 , then = 7 . 79265 m- 56 . 2254 m 2 2 = . 147145 m . Question 2, chap 15, sect 5. part 2 of 3 10 points What should be the distance so that this physical pendulum will have the shortest pos- sible period? Correct answer: 1 . 06066 s (tolerance 1 %). Explanation: The period is T = 2 radicalBigg R 2 2 g 1 + g and its derivative is T d = 2 1 2 parenleftbigg R 2 2 g + g parenrightbigg 1 / 2 parenleftbigg- R 2 2 g 2 + 1 g parenrightbigg . homework 31 HETTIGER, CHRISTOF Due: Apr 15 2008, 4:00 am 2 For minimum period, T d = 0, so- R 2 2 g 2 + 1 g = 0 2 = R 2 2 = R 2 = 1 . 5 m 2 = 1 . 06066 m . Question 3, chap 15, sect 5. part 3 of 3 10 points What will be the period at this distance?...
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This note was uploaded on 05/09/2010 for the course PHYSICS PHY 301k taught by Professor Turner during the Spring '10 term at University of Texas-Tyler.

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hw 31 - homework 31 HETTIGER, CHRISTOF Due: Apr 15 2008,...

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