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OMPhQuiz_07_p58-66 - chapter 7 Work and Energy Work Work in...

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58 PhysiQuiz Contents Work Work in one dimension: (Section 7.1, part 1) The following two problems involve pulleys and may be used after Example 2 in Section 7.1: 1. Atwood machine 2. Raising m by a distance x Work in two dimensions: (Section 7.1, part 2) 3. Work against gravity • Context in the textbook: After Example 3 in Section 7.1. Work–energy and gravitational potential energy (Section 7.4) Exercises to be used in conjunction with Section 7.4: 4. Sliding down an incline 5. Comparing final kinetic energies 6. Stopped pendulum 7. Sliding down a dome: The “stay-on” condition 8. Sliding down a dome: Equations of motion chapter 7 Work and Energy
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Two blocks with masses m 1 and m 2 are connected by a light string passing over a light frictionless pulley. Assume m 2 m 1 . Determine the potential energy released by the system as block 2 starts from rest and falls by h /2: A B C Potential energy released m 2 gh /2 ( m 2 m 1 ) gh /2 m 1 gh /2 Hint: Remember that as block 2 descends by h /2, block 1 rises correspondingly by a height h /2. Explanation: When block 2 falls by a distance h /2, block 1 goes up by h /2. The potential energy lost by block 2 is m 2 gh /2. The potential energy gained by block 1 is m 1 gh /2. So the net potential energy lost is ( m 2 m 1 ) gh /2. Answer B. Block 1 Block 2 m 1 m 2 h 1. Atwood Machine PhysiQuiz 59
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Consider the mass–pulley system shown. Determine the distance d covered by the force F as it lifts the block by a height x : A B C Distance of F d x /2 d x d 2 x Explanation: As the block is lifted by height x , the length of each of the two strings supporting the moving pulley will be reduced by x , so d 2 x . Answer C. Comment: Notice that conservation of energy implies that the increase of the potential energy equals the input mechanical energy: mg x F d 2 x F. Solving for F gives F mg /2. In other words, the applied force required is half of the weight.
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