HW31 - homework 31 PAPAGEORGE, MATT Due: Apr 15 2008, 4:00...

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Unformatted text preview: homework 31 PAPAGEORGE, MATT 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 0 . 1 m and 9 . 1 kg mass has a small hole a distance from the disks center that can serve as a pivot point. . 1 m 9 . 1 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 8 . 9 s? (If there are two possible answers, answer with the smaller distance.) Correct answer: 0 . 000254031 m (tolerance 1 %). Explanation: Let : R = 0 . 1 m , m = 9 . 1 kg , T = 8 . 9 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 ) (8 . 9 s) 2 4 2 = 19 . 6829 m and g 2 T 4 16 4- 2 R 2 = (9 . 81 m / s 2 ) 2 (8 . 9 s) 4 16 4- 2 (0 . 1 m) 2 = 387 . 397 m 2 , then = 19 . 6829 m- 387 . 397 m 2 2 = . 000254031 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: 0 . 0707107 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 PAPAGEORGE, MATT 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 m 2 = . 0707107 m . Question 3, chap 15, sect 5. part 3 of 3 10 points What will be the period at this distance? Correct answer: 0 . 754402 s (tolerance 1 %)....
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This note was uploaded on 03/02/2009 for the course PHY 58235 taught by Professor Kleinman during the Spring '09 term at University of Texas at Austin.

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HW31 - homework 31 PAPAGEORGE, MATT Due: Apr 15 2008, 4:00...

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