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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

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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**Title: Analyzing Motion in a Pulley System** **Introduction:** A hanging weight with a mass of \( m_1 = 0.375 \, \text{kg} \) is attached by a string to a block with a mass \( m_2 = 0.865 \, \text{kg} \), as depicted in the accompanying diagram. The string passes over a pulley with a mass \( M = 0.350 \, \text{kg} \). The pulley can be modeled as a hollow cylinder with an inner radius \( R_1 = 0.0200 \, \text{m} \) and an outer radius \( R_2 = 0.0300 \, \text{m} \). The mass of the spokes is considered negligible. As the weight descends, the block moves across the table. The coefficient of kinetic friction between the block and the table is \( \mu_k = 0.250 \). At the instant shown, the block has a velocity \( v_i = 0.820 \, \text{m/s} \) moving toward the pulley. Assume frictionless spinning of the pulley, no stretching of the string, no slip on the pulley, and a negligible mass of the string. **Problem Analysis:** **(a) Energy Method Application:** Determine the velocity of the block (in m/s) after it has moved a distance of \( 0.700 \, \text{m} \) from the initial position provided. - **Solution**: Calculated speed: \( 1.517 \, \text{m/s} \) - **Consideration**: The pulley may have been modeled either as a very thin hollow cylinder with a radius \( R_2 \), or as a solid cylinder with the same radius. More accurately, model it as a hollow cylinder with non-zero thickness. Find the moment of inertia in terms of \( R_1 \) and \( R_2 \). **(b) Determining Angular Speed:** What is the angular speed of the pulley (in rad/s) once the block has moved this specified distance? - **Solution**: Calculated angular speed: \( 50.57 \, \text{rad/s} \) - **Inquiry**: How is angular speed related to linear speed? Determine the block’s final speed from part (a), presented in rad/s.
Transcribed Image Text:**Title: Analyzing Motion in a Pulley System** **Introduction:** A hanging weight with a mass of \( m_1 = 0.375 \, \text{kg} \) is attached by a string to a block with a mass \( m_2 = 0.865 \, \text{kg} \), as depicted in the accompanying diagram. The string passes over a pulley with a mass \( M = 0.350 \, \text{kg} \). The pulley can be modeled as a hollow cylinder with an inner radius \( R_1 = 0.0200 \, \text{m} \) and an outer radius \( R_2 = 0.0300 \, \text{m} \). The mass of the spokes is considered negligible. As the weight descends, the block moves across the table. The coefficient of kinetic friction between the block and the table is \( \mu_k = 0.250 \). At the instant shown, the block has a velocity \( v_i = 0.820 \, \text{m/s} \) moving toward the pulley. Assume frictionless spinning of the pulley, no stretching of the string, no slip on the pulley, and a negligible mass of the string. **Problem Analysis:** **(a) Energy Method Application:** Determine the velocity of the block (in m/s) after it has moved a distance of \( 0.700 \, \text{m} \) from the initial position provided. - **Solution**: Calculated speed: \( 1.517 \, \text{m/s} \) - **Consideration**: The pulley may have been modeled either as a very thin hollow cylinder with a radius \( R_2 \), or as a solid cylinder with the same radius. More accurately, model it as a hollow cylinder with non-zero thickness. Find the moment of inertia in terms of \( R_1 \) and \( R_2 \). **(b) Determining Angular Speed:** What is the angular speed of the pulley (in rad/s) once the block has moved this specified distance? - **Solution**: Calculated angular speed: \( 50.57 \, \text{rad/s} \) - **Inquiry**: How is angular speed related to linear speed? Determine the block’s final speed from part (a), presented in rad/s.
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