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Homework 5-solutions

Homework 5-solutions - pels(kcp389 Homework 5 hill(666 This...

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pels (kcp389) – Homework 5 – hill – (666) 1 This print-out should have 36 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 (part 1 of 3) 10.0 points The moon has a mass of 7 . 4 × 10 22 kg and completes an orbit of radius 3 . 8 × 10 8 m about every 28 days. The Earth has a mass of 6 × 10 24 kg and completes an orbit of radius 1 . 5 × 10 11 m every year. What is the speed of the Moon in its orbit? Correct answer: 986 . 442 m / s. Explanation: Let : r 1 = 3 . 8 × 10 8 m and t 1 = 28 days . The speed of the Moon is v = s t = 2 π r 1 t 1 = 2 π (3 . 8 × 10 8 m) 28 days · day 24 h · h 3600 s = 986 . 442 m / s . 002 (part 2 of 3) 10.0 points What is the kinetic energy of the Moon in orbit? Correct answer: 3 . 60035 × 10 28 J. Explanation: Let : m 1 = 7 . 4 × 10 22 kg and v 1 = 986 . 442 m / s . The kinetic energy of the Moon is K 1 = 1 2 m 1 v 2 1 = 1 2 (7 . 4 × 10 22 kg) (986 . 442 m / s) 2 = 3 . 60035 × 10 28 J . 003 (part 3 of 3) 10.0 points What is the kinetic energy of the Earth? Correct answer: 2 . 67676 × 10 33 J. Explanation: Let : r 2 = 1 . 5 × 10 11 m , t 2 = 1 year , and m 2 = 6 × 10 24 kg . The speed of the Earth is v 2 = s t = 2 π r 2 t 2 = 2 π (1 . 5 × 10 11 m) 1 year · year 365 d · d 24 h · h 3600 s = 29870 . 6 m / s . The kinetic energy of the Earth is K 2 = 1 2 m 2 v 2 2 = 1 2 (6 × 10 24 kg) (29870 . 6 m / s) 2 = 2 . 67676 × 10 33 J . 004 10.0 points Which of the two object shown below has the greatest kinetic energy? A m B 1 2 m v 2 v 1. B correct 2. A 3. Unable to determine. 4. Kinetic energies are the same. Explanation: For mass A, K A = 1 2 m v 2 .
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pels (kcp389) – Homework 5 – hill – (666) 2 For mass B, K B = 1 2 parenleftbigg 1 2 m parenrightbigg (2 v ) 2 = m v 2 . So B has more kinetic energy. 005 10.0 points Which of the following is the best example of kinetic energy? 1. a tornado correct 2. a television set 3. a tank of gasoline 4. a loaded gun 5. a strawberry shortcake 6. a calculator battery 7. a piece of chewing gum 8. a Jolt Cola 9. a stick of dynamite 10. boulder dam Explanation: Kinetic energy is the energy of motion. The only system that is in motion is the tornado. 006 (part 1 of 2) 10.0 points A simple Atwood’s machine uses two masses m 1 and m 2 . Starting from rest, the speed of the two masses is 9 . 3 m / s at the end of 6 . 7 s. At that time, the kinetic energy of the system is 51 J and each mass has moved a distance of 31 . 155 m. The acceleration of gravity is 9 . 81 m / s 2 . 31 . 155 m m 1 m 2 Find the value of heavier mass. Correct answer: 0 . 673098 kg. Explanation: Let : v = 9 . 3 m / s , t = 6 . 7 s , K = 51 J , = 31 . 155 m , and g = 9 . 81 m / s 2 . The total kinetic energy of the system is K = 1 2 ( m 1 + m 2 ) v 2 m 1 + m 2 = 2 K v 2 = 2 (51 J) (9 . 3 m / s) 2 = 1 . 17933 kg a = parenleftbigg m 1 - m 2 m 1 + m 2 parenrightbigg g summationdisplay F = ( m 1 + m 2 ) a ( m 1 - m 2 ) g = ( m 1 + m 2 ) a a = parenleftbigg m 1 - m 2 m 1 + m 2 parenrightbigg g The velocity is v = a t = ( m 1 - m 2 ) g t m 1 + m 2 m 1 - m 2 = ( m 1 + m 2 ) v g t = (1 . 17933 kg) (9 . 3 m / s) (9 . 81 m / s 2 ) (6 . 7 s) = 0 . 166868 kg .
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pels (kcp389) – Homework 5 – hill – (666) 3 m 1 + m 2 = 1 . 17933 kg m 1 - m 2 = 0 . 166868 kg m 1 = 1 . 17933 kg + 0 . 166868 kg 2 = 0 . 673098 kg .
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