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Get Full Access to University Physics - 13 Edition - Chapter 9 - Problem 47e
Get Full Access to University Physics - 13 Edition - Chapter 9 - Problem 47e

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# A frictionless pulley has the shape of a uniform solid ISBN: 9780321675460 31

## Solution for problem 47E Chapter 9

University Physics | 13th Edition

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Problem 47E

A frictionless pulley has the shape of a uniform solid disk of mass 2.50 kg and radius 20.0 cm. A 1.50-kg stone is attached to a very light wire that is wrapped around the rim of the pulley (?Fig. E9.43?), and the system is released from rest. (a) How far must the stone fall so that the pulley has 4.50 J of kinetic energy? (b) What percent of the total kinetic energy does the pulley have?

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Solution 47E Since the system is released from rest, therefore there will be loss in potential energy of the system and gain in its kinetic energy. Therefore, Loss in potential energy = gain in (kinetic energy of the pulley + kinetic energy of the stone)…..(1) Let the stone falls by a distance of h. Given, mass of the pulley disk m = 2.p0 kg Its radius r = 20.0 cm = 0.2 m 1 2 Its moment of inertia I = m r2 p 2 2 I = 2 × 2.50 kg × 0.2 m 2 I = 0.05 kg.m Given, kinetic energy of the pulley disk = 4.50 J If is the angular velocity of the pulley, 1 2 2I = 4.50 J 1 × 0.05 kg.m × = 4.50 J 2 2 9 2 2 = 0.05rad /s = 180 rad /s 2 2 2 2 2 2 v = 180 × (0.2) m /s 2 2 2 v = 7.2 m /s Given, mass of the stone m = 1.s0 kg 1 2 2 Its kinetic energy = 2 × 1.50 kg × 7.2 m /s = 5.4 J 2 Potential energy loss of the stone = 1,50 kg × 9.80 m/s × h (a) Therefore, from equation (1), w get 1.50 kg × 9.8 m/s × h = 4.5 J + 5.4 J h = 9.9 J 1.50 kg×9.8 m/s h = 0.673 m So, the stone must fall by a distance of 0.673 m. (b) Total kinetic energy of the system = 9.9 J Kinetic energy of the pulley = 4.50 J 4.50 J The pulley’s fraction of kinetic energy = 9.9 J = 0.455 = 45.5% Therefore, the pulley has 45.5% of the total kinetic energy.

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##### ISBN: 9780321675460

Since the solution to 47E from 9 chapter was answered, more than 656 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 47E from chapter: 9 was answered by , our top Physics solution expert on 05/06/17, 06:07PM. This full solution covers the following key subjects: pulley, kinetic, stone, Energy, around. This expansive textbook survival guide covers 26 chapters, and 2929 solutions. This textbook survival guide was created for the textbook: University Physics, edition: 13. University Physics was written by and is associated to the ISBN: 9780321675460. The answer to “A frictionless pulley has the shape of a uniform solid disk of mass 2.50 kg and radius 20.0 cm. A 1.50-kg stone is attached to a very light wire that is wrapped around the rim of the pulley (?Fig. E9.43?), and the system is released from rest. (a) How far must the stone fall so that the pulley has 4.50 J of kinetic energy? (b) What percent of the total kinetic energy does the pulley have?” is broken down into a number of easy to follow steps, and 76 words.

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