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In an Atwood's machine, one block has a mass of 304.0 g, and the other a mass of 454.0 g. The pulley, which is mounted in horizontal frictionless bearings, has a radius of 6.30 cm. When released from rest, the heavier block is observed to fall 55.0 cm in 1.73 s (without the string slipping on the pulley). m M ↓

In an Atwood's machine, one block has a mass of 304.0 g, and the other a mass of 454.0 g. The pulley, which is mounted in horizontal frictionless bearings, has a radius of 6.30 cm. When released from rest, the heavier block is observed to fall 55.0 cm in 1.73 s (without the string slipping on the pulley). m M ↓

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
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A.) What is the magnitude of the acceleration of the 304.0-g block?

B.) What is the magnitude of the acceleration of the 454.0-g block?

C.) What is the magnitude of the tension in the part of the cord that supports the 304.0-g block?

D.) What is the magnitude of the tension in the part of the cord that supports the 454.0-g block?

 

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**Investigating Dynamics using Atwood's Machine** _A closer look at the apparatus and calculations_ In an Atwood's machine setup, which is commonly used to study the principles of dynamics and mechanics, we have two blocks of different masses connected by a string over a pulley. For this specific example: - Block \(m\) has a mass of 304.0 g. - Block \(M\) has a mass of 454.0 g. - The pulley is mounted on horizontal frictionless bearings and has a radius of 6.30 cm. **Observational Data:** - Upon release from rest, the heavier block \(M\) is observed to fall a distance of 55.0 cm within a time span of 1.73 seconds. - It is assumed that there is no slippage of the string over the pulley. **Detailed Diagram Description:** The diagram illustrates the setup of the Atwood's machine: - A pulley with a radius \(r = 6.30 \, \text{cm}\) is mounted at the top center in the horizontal plane. - Two blocks, \(m\) and \(M\), are hanging on either side of the pulley via a string. - Block \(m\) is on the left side and is moving upwards. - Block \(M\) is on the right side and is moving downwards. - The tension in the string and gravitational forces affect the motion of the blocks. In this system, the primary points of analysis would include calculating the acceleration of the blocks, the tension in the string, and the net forces acting on each block. **Educational Note:** This setup helps in understanding Newton's Second Law of Motion and the interplay between force, mass, and acceleration in a controlled environment. By analyzing the time and distance data, one can deduce the rate of acceleration and other properties of the system, such as the tension in the string and rotational effects if considering the angular motion of the pulley.
Transcribed Image Text:**Investigating Dynamics using Atwood's Machine** _A closer look at the apparatus and calculations_ In an Atwood's machine setup, which is commonly used to study the principles of dynamics and mechanics, we have two blocks of different masses connected by a string over a pulley. For this specific example: - Block \(m\) has a mass of 304.0 g. - Block \(M\) has a mass of 454.0 g. - The pulley is mounted on horizontal frictionless bearings and has a radius of 6.30 cm. **Observational Data:** - Upon release from rest, the heavier block \(M\) is observed to fall a distance of 55.0 cm within a time span of 1.73 seconds. - It is assumed that there is no slippage of the string over the pulley. **Detailed Diagram Description:** The diagram illustrates the setup of the Atwood's machine: - A pulley with a radius \(r = 6.30 \, \text{cm}\) is mounted at the top center in the horizontal plane. - Two blocks, \(m\) and \(M\), are hanging on either side of the pulley via a string. - Block \(m\) is on the left side and is moving upwards. - Block \(M\) is on the right side and is moving downwards. - The tension in the string and gravitational forces affect the motion of the blocks. In this system, the primary points of analysis would include calculating the acceleration of the blocks, the tension in the string, and the net forces acting on each block. **Educational Note:** This setup helps in understanding Newton's Second Law of Motion and the interplay between force, mass, and acceleration in a controlled environment. By analyzing the time and distance data, one can deduce the rate of acceleration and other properties of the system, such as the tension in the string and rotational effects if considering the angular motion of the pulley.
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