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7 - homework 07 JACOBS AMBER Due 1:00 am Question 1 chap 10...

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homework 07 – JACOBS, AMBER – Due: Mar 18 2008, 1:00 am 1 Question 1, chap 10, sect 10. part 1 of 1 10 points Given: 1 hp=746 W An automobile engine develops a torque of 500 N m and is rotating at a speed of 2000 rev / min. What horsepower does the engine generate? Correct answer: 140 . 375 hp (tolerance ± 1 %). Explanation: ω = (2000 rev / min) parenleftbigg 2 π rad 1 rev parenrightbigg parenleftbigg 1 min 60 sec parenrightbigg = 209 . 44 rad / s . We have P = τ ω = (500 N m) (209 . 44 rad / s) = (104720 W) parenleftbigg 1 hp 746 W parenrightbigg = 140 . 375 hp . Question 2, chap 11, sect 11. part 1 of 2 10 points A child of mass 51 . 6 kg sits on the edge of a merry-go-round with radius 2 m and moment of inertia 150 . 672 kg m 2 . The merry-go-round rotates with an angular velocity of 1 . 5 rad / s. What radial force does the child have to exert to stay on the merry-go-round? Correct answer: 232 . 2 N (tolerance ± 1 %). Explanation: Basic Concepts: Conservation of Angu- lar Momentum. Centripetal Force: F = m v 2 r = m ω 2 r The force the child needs to exert in the radial direction to hold on is simply the centripetal force: F = m v 2 r = m ω 2 r Question 3, chap 11, sect 11. part 2 of 2 10 points The child then walks towards the center of the merry-go-round and stops at a distance 0 . 88 m from the center. Now what is the angular velocity of the merry-go-round? Correct answer: 2 . 80966 rad / s (tolerance ± 1 %). Explanation: When the child moves inward, the moment of inertia of the system i MGR + i child (the merry- go-round plus the child) changes. Therefore, to conserve angular momentum, the angular velocity of the system must change. Specifi- cally: L init = L final ( i child + i MGR ) ω = ( i child, 2 + i MGR ) ω 2 The moment of inertia of the child is m r 2 . Therefore ω 2 = m r 2 + i MGR m r 2 2 + i MGR ω . Question 4, chap 11, sect 11. part 1 of 1 10 points If the polar ice caps of the Earth were to melt, the oceans would be deeper by about 30m. What effect would this have on the Earth’s rotation? 1. It depends on mass. 2. Faster. 3. No change. 4. Slower. correct Explanation: In accord with the conservation of angular momentum, if mass moves farther from the axis of rotation, rotational speed decreases. So the Earth would slow in its daily rotation. Question 5, chap 11, sect 11. part 1 of 1 10 points
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homework 07 – JACOBS, AMBER – Due: Mar 18 2008, 1:00 am 2 A figure skater on ice spins on one foot. She pulls in her arms and her angular speed increases. Physically, this happens because . . . ? Choose the reason from the list below; if two or more reasons seem plausible, choose the most important reason. 1. Her angular speed increases because she is undergoing uniformly accelerated angular motion. 2. Her angular speed increases because by pulling in her arms she creates a net torque in the direction of rotation. 3. Her angular speed increases because her angular momentum increases. 4. Her angular speed is unrelated to her arms. She pulls them in at the same time as she speeds up her spin because it looks better this way.
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