An Atwood's machine consists of blocks of masses m1 = 13.0 kg and m2 = 16.0 kg attached by a cord running over a pulley as in the figure below. The pulley is a solid cylinder with mass M = 9.10 kg and radius r = 0.200 m. The block of mass m2 is allowed to drop, and the cord turns the pulley without slipping.(a) Why must the tension T2 be greater than the tension T1?(b) What is the acceleration of the system, assuming the pulley axis is frictionless? (Give the magnitude of a.)=________ m/s2(c) Find the tensions T1 and T2.T1= ______NT2= _____N The image depicts a classic physics problem involving a pulley system. Here's a detailed explanation of the components and forces in the diagram:1. **Pulley System**: - A pulley with mass \( M \) and radius \( r \) is shown. The pulley is rigidly fixed to a horizontal support.2. **Masses**: - There are two masses: - \( m_1 \) (represented as a blue sphere) is on the left side of the pulley. - \( m_2 \) (represented as a beige block) is on the right side of the pulley.3. **Tensions**: - \( T_1 \) is the tension in the rope on the side of mass \( m_1 \). - \( T_2 \) is the tension in the rope on the side of mass \( m_2 \).4. **Acceleration**: - The system shows vector \(\vec{a}\) next to each mass, indicating the direction of acceleration. - Mass \( m_1 \) has an upward acceleration (\(\vec{a}\)), and mass \( m_2 \) has a downward acceleration (\(\vec{a}\)).This setup is often used in physics to analyze the dynamics of a system involving rotational motion and linear motion, demonstrating concepts such as Newton's second law, rotational inertia, and torque.

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University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter10: Fixed-axis Rotation

Section: Chapter Questions

Problem 105P: A 2-kg block on a frictionless inclined plane at 45 has a cord attached to a pulley of mass 1 kg and...

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An Atwood's machine consists of blocks of masses m₁ = 13.0 kg and m₂ = 16.0 kg attached by a cord running over a pulley as in the figure below. The pulley is a solid cylinder with mass M = 9.10 kg and radius r = 0.200 m. The block of mass m₂ is allowed to drop, and the cord turns the pulley without slipping.

(a) Why must the tension T₂ be greater than the tension T₁?

(b) What is the acceleration of the system, assuming the pulley axis is frictionless? (Give the magnitude of a.)

=________ m/s²

T1= ______N

T2= _____N

The image depicts a classic physics problem involving a pulley system. Here's a detailed explanation of the components and forces in the diagram:

1. **Pulley System**:
- A pulley with mass \( M \) and radius \( r \) is shown. The pulley is rigidly fixed to a horizontal support.

2. **Masses**:
- There are two masses:
- \( m_1 \) (represented as a blue sphere) is on the left side of the pulley.
- \( m_2 \) (represented as a beige block) is on the right side of the pulley.

3. **Tensions**:
- \( T_1 \) is the tension in the rope on the side of mass \( m_1 \).
- \( T_2 \) is the tension in the rope on the side of mass \( m_2 \).

4. **Acceleration**:
- The system shows vector \(\vec{a}\) next to each mass, indicating the direction of acceleration.
- Mass \( m_1 \) has an upward acceleration (\(\vec{a}\)), and mass \( m_2 \) has a downward acceleration (\(\vec{a}\)).

This setup is often used in physics to analyze the dynamics of a system involving rotational motion and linear motion, demonstrating concepts such as Newton's second law, rotational inertia, and torque.

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