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A hanging weight, with a mass of m, = 0.375 kg, is attached by a string to a block with mass m, = 0.865 kg as shown in the figure below. The string goes over a pulley with a mass of M = 0.350 kg. The pulley can be modeled as a hollow cylinder with an inner radius of R, = 0.0200 m, and an outer radius of R, = 0.0300 m; the mass of the spokes is negligible. As the weight falls, the block slides on the table, and the coefficient of kinetic friction between the block and the table is u, = 0.250. At the instant shown, the block is moving with a velocity of v, = 0.820 m/s toward the pulley. Assume that the pulley is free to spin without friction, that the string does not stretch and does not slip on the pulley, and that the mass of the string is negligible. R (a) Using energy methods, find the speed of the block (in m/s) after it has moved a distance of 0.700 m away from the initial position shown. 1.517 x You may have modeled the pulley as a very thin hollow cylinder with a radius of R,, or as a solid cylinder with a radius of R3. A better approximation is to treat it as a hollow cylinder with a non-zero thickness. What is the moment of inertia in terms of R, and R,? m/s (b) What is the angular speed of the pulley (in rad/s) after the block has moved this distance? 50.57 How is angular sneed related to linear speed? What ie the final speed of the block found in part a12 rad/s

A hanging weight, with a mass of m, = 0.375 kg, is attached by a string to a block with mass m, = 0.865 kg as shown in the figure below. The string goes over a pulley with a mass of M = 0.350 kg. The pulley can be modeled as a hollow cylinder with an inner radius of R, = 0.0200 m, and an outer radius of R, = 0.0300 m; the mass of the spokes is negligible. As the weight falls, the block slides on the table, and the coefficient of kinetic friction between the block and the table is u, = 0.250. At the instant shown, the block is moving with a velocity of v, = 0.820 m/s toward the pulley. Assume that the pulley is free to spin without friction, that the string does not stretch and does not slip on the pulley, and that the mass of the string is negligible. R (a) Using energy methods, find the speed of the block (in m/s) after it has moved a distance of 0.700 m away from the initial position shown. 1.517 x You may have modeled the pulley as a very thin hollow cylinder with a radius of R,, or as a solid cylinder with a radius of R3. A better approximation is to treat it as a hollow cylinder with a non-zero thickness. What is the moment of inertia in terms of R, and R,? m/s (b) What is the angular speed of the pulley (in rad/s) after the block has moved this distance? 50.57 How is angular sneed related to linear speed? What ie the final speed of the block found in part a12 rad/s

Principles of Physics: A Calculus-Based Text
Principles of Physics: A Calculus-Based Text
5th Edition
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter10: Rotational Motion
Section: Chapter Questions
Problem 40P: In Figure P10.40, the hanging object has a mass of m1 = 0.420 kg; the sliding block has a mass of m2...
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A hanging weight, with a mass of m, = 0.375 kg, is attached by a string to a block with mass m, = 0.865 kg as shown in the figure below. The string goes over a pulley with a mass of M = 0.350 kg. The pulley can be modeled as a hollow cylinder with an inner radius of R, = 0.0200 m, and an outer radius of R, = 0.0300 m; the mass of the spokes is negligible. As the weight falls, the block slides on the table, and the coefficient of kinetic friction between the block and the table is u, = 0.250. At the instant shown, the block is moving with a velocity of v, = 0.820 m/s toward the pulley. Assume that the pulley is free spin without friction, that the string does not stretch and does not slip on the pulley, and that the mass of the string is negligible. (a) Using energy methods, find the speed of the block (in m/s) after it has moved a distance of 0.700 m away from the initial position shown. 1.517 You may have modeled the pulley as a very thin hollow cylinder with a radius of Ra, or as a solid cylinder with a radius of R,. A better approximation is to treat it as a hollow cylinder with a non-zero thickness. What is the moment of inertia in terms of R, and R,? m/s (b) What is the angular speed of the pulley (in rad/s) after the block has moved this distance? 50.57 How is angular speed related to linear speed? What is the final speed of the block found in part (a)? rad/s
Transcribed Image Text:A hanging weight, with a mass of m, = 0.375 kg, is attached by a string to a block with mass m, = 0.865 kg as shown in the figure below. The string goes over a pulley with a mass of M = 0.350 kg. The pulley can be modeled as a hollow cylinder with an inner radius of R, = 0.0200 m, and an outer radius of R, = 0.0300 m; the mass of the spokes is negligible. As the weight falls, the block slides on the table, and the coefficient of kinetic friction between the block and the table is u, = 0.250. At the instant shown, the block is moving with a velocity of v, = 0.820 m/s toward the pulley. Assume that the pulley is free spin without friction, that the string does not stretch and does not slip on the pulley, and that the mass of the string is negligible. (a) Using energy methods, find the speed of the block (in m/s) after it has moved a distance of 0.700 m away from the initial position shown. 1.517 You may have modeled the pulley as a very thin hollow cylinder with a radius of Ra, or as a solid cylinder with a radius of R,. A better approximation is to treat it as a hollow cylinder with a non-zero thickness. What is the moment of inertia in terms of R, and R,? m/s (b) What is the angular speed of the pulley (in rad/s) after the block has moved this distance? 50.57 How is angular speed related to linear speed? What is the final speed of the block found in part (a)? rad/s
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