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CP A thin, light wire is wrapped around the rim of a wheel

University Physics | 13th Edition | ISBN: 9780321675460 | Authors: Hugh D. Young, Roger A. Freedman ISBN: 9780321675460 31

Solution for problem 49E Chapter 9

University Physics | 13th Edition

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University Physics | 13th Edition | ISBN: 9780321675460 | Authors: Hugh D. Young, Roger A. Freedman

University Physics | 13th Edition

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Problem 49E

CP? A thin, light wire is wrapped around the rim of a wheel (?Fig. E9.45?). The wheel rotates without friction about a stationary horizontal axis that passes through the center of the wheel. The wheel is a uniform disk with radius R = 0.280 m. An object of mass ?m? = 4.20 kg is suspended from the free end of the wire. The system is released from rest and the suspended object descends with constant acceleration. If the suspended object moves downward a distance of 3.00 m in 2.00 s, what is the mass of the wheel?

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Step 1 of 3

Solution 49E We shall have to calculate the acceleration of the suspended object in order to proceed the other calculations. Distance moved by the object s = 3.00 m Time t = 2.00 s 1 2 From the equation s = at 2 we can calculate the acceleration as follows. a = 2s/t2 2 2 a = 2 × 3.00/(2.00) m/s 2 a = 1.5 m/s Let the tension in the wire be T . Since mass is moving downward with an acceleration a, hence the net acceleration on it is = g a Thus, the tension, T = 4.20 × (g a) N T = 4.20 × (9.8 1.5) N = 34.86 N The radius of the wheel R = 0.280 m Torque on the wheel = TR = 34.86 × 0.280 N.m = 9.76 N.m Let M be the mass of the wheel. 1 2 1 2 2 Its moment of inertia is I = MR2= 2 × M × (0.280) kg.m I = 0.0392M kg.m 2 Angular acceleration = a/R = 1.5/0.280 rad/s = 5.35 rad/s 2 From the relation, = I and substituting the calculated values, 2 2 9.76 N.m = 0.0392M kg.m × 5.35 rad/s M = 46.5 kg The mass of the wheel is 46.5 kg .

Step 2 of 3

Chapter 9, Problem 49E is Solved
Step 3 of 3

Textbook: University Physics
Edition: 13
Author: Hugh D. Young, Roger A. Freedman
ISBN: 9780321675460

This full solution covers the following key subjects: wheel, suspended, Object, Wire, mass. This expansive textbook survival guide covers 26 chapters, and 2929 solutions. University Physics was written by and is associated to the ISBN: 9780321675460. The answer to “CP? A thin, light wire is wrapped around the rim of a wheel (?Fig. E9.45?). The wheel rotates without friction about a stationary horizontal axis that passes through the center of the wheel. The wheel is a uniform disk with radius R = 0.280 m. An object of mass ?m? = 4.20 kg is suspended from the free end of the wire. The system is released from rest and the suspended object descends with constant acceleration. If the suspended object moves downward a distance of 3.00 m in 2.00 s, what is the mass of the wheel?” is broken down into a number of easy to follow steps, and 97 words. This textbook survival guide was created for the textbook: University Physics, edition: 13. Since the solution to 49E from 9 chapter was answered, more than 447 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 49E from chapter: 9 was answered by , our top Physics solution expert on 05/06/17, 06:07PM.

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CP A thin, light wire is wrapped around the rim of a wheel