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Get Full Access to University Physics - 13 Edition - Chapter 6 - Problem 61p
Get Full Access to University Physics - 13 Edition - Chapter 6 - Problem 61p

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# Rotating Bar. A thin, uniform 12.0-kg bar that is 2.0 m

ISBN: 9780321675460 31

## Solution for problem 61P Chapter 6

University Physics | 13th Edition

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Problem 61P

Rotating Bar?. A thin, uniform 12.0-kg bar that is 2.0 m long rotates uniformly about a pivot at one end, making 5.0 complete revolutions every 3.00 seconds. What is the kinetic energy of this bar? (?Hint?: Different points in the bar have different speeds Break the bar up into infinitesimal segments of mass ?dm? and integrate to add up the kinetic energies of all these segments.)

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Solution 61P Kinetic energy is calculated from the equation K = mv , where m is the mass of an 2 object and v is its speed. We are asked to consider a segment in the bar that has a mass of dm. Therefore, if the segment has a speed of v , its kinetic energy is given by dK = dm × v …..(1) 2 Let the length of the segment be dx. 12.0 kg is the mass of the rod and it has a length of 2.0 m. Therefore, the mass per unit 12 kg kg length of the rod is = 2 m = 6 m Therefore, the mass of the segment dx is = 6dx kg Or, dm = 6dx…..(2) Let the segment is located at a distance of x from the pivot. So, its speed is given by v = x , where is angular speed of the segment. Now, 5 revolutions = 10 rad Therefore, = 10/3 rad/s Therefore, v = x × 10/3 m/s v = 10.47x m/s Now, substituting the values of dm and v in equation (1), dK = 1× 6dx × (10.47x) 2 2 2 dK = 329x dx…..(3) Now, integrating this equation from x = 0to x = 2.0 m 2 dK = 329 x d 2 0 K = 329 × ( ) x3 2 3 0 8 K = 329 × 3 J K = 877 J Therefore, the approximate kinetic energy of the bar is 877 J.

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##### ISBN: 9780321675460

This full solution covers the following key subjects: bar, segments, kinetic, making, end. This expansive textbook survival guide covers 26 chapters, and 2929 solutions. This textbook survival guide was created for the textbook: University Physics, edition: 13. The answer to “Rotating Bar?. A thin, uniform 12.0-kg bar that is 2.0 m long rotates uniformly about a pivot at one end, making 5.0 complete revolutions every 3.00 seconds. What is the kinetic energy of this bar? (?Hint?: Different points in the bar have different speeds Break the bar up into infinitesimal segments of mass ?dm? and integrate to add up the kinetic energies of all these segments.)” is broken down into a number of easy to follow steps, and 66 words. University Physics was written by and is associated to the ISBN: 9780321675460. Since the solution to 61P from 6 chapter was answered, more than 552 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 61P from chapter: 6 was answered by , our top Physics solution expert on 05/06/17, 06:07PM.

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