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# The Atwood’s Machine. Figure P10.59 illustrates an

ISBN: 9780321675460 31

## Solution for problem 67P Chapter 10

University Physics | 13th Edition

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Problem 67P

The Atwood’s Machine. Figure P10.59? illustrates an Atwood’s machine. Find the linear accelerations of blocks A and B, the angular acceleration of the wheel C, and the tension in each side of the cord if there is no slipping between the cord and the surface of the wheel. Let the masses of blocks A and B be 4.00 kg and 2.00 kg, respectively, the moment of inertia of the wheel about its axis be and the radius of the wheel be 0.120 m.

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Solution 67P Let us have a look at the free body diagram as shown below. = For the mass B, let T be the tension on the left side of the cord. 1 T 1 2g = 2a…..(1) For the mass A, let T 2e the tension on the right side of the rope. 4g T 2 = 4a…..(2) Adding equations (1) and (2), T 1 T 2= 6a 2g T 2 T 1= 2g 6a…..(3) Now, the radius of the wheel is = 0.120 m Therefore, the torque on the wheel is = (T T ) × 0.120 N.m 2 1 = (2g 6a) × 0.120 N.m…..(4) Again, torque = Moment of inertia × angular acceleration = 0.220 kg.m × , where is angular acceleration. Now, angular acceleration = a/radius, a is linear acceleration. a =...

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The Atwood’s Machine. Figure P10.59 illustrates an

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