A crate of mass 451 kg is being lifted by the mechanism shown in the figure. The two cables are wrapped around their respective pulleys, which have radii of 0.600 and 0.200 m. The pulleys are fastened together to form a dual pulley and turn as a single unit about the center axle, relative to which the combined moment of inertia is 51.0 kg · m2. The cables roll on the dual pulley without slipping. A tension of magnitude 2150 N is maintained in the cable attached to the motor. Find (a) the angular acceleration of the dual pulley and (b) the tension in the cable connected to the crate. The image consists of three parts, illustrating the mechanics of a dual pulley system. Below is a detailed explanation suitable for an educational website:### (a) Dual Pulley and Crate System- **Description**: This section shows a dual pulley system connected to a motor. The pulley is attached to a crate, which is being lifted vertically. The motor drives the rotation of the pulley, enabling the lifting of the crate.### (b) Free-Body Diagram of Pulley- **Components**: - The pulley is depicted with two radii: \(\ell_1 = 0.600 \, \text{m}\) and \(\ell_2 = 0.200 \, \text{m}\). - **Forces**: - \(\vec{T}_1\) and \(\vec{T}_2\) are tension forces acting at different distances from the axis. - \(\vec{P}\) represents force applied by the motor. - \(\vec{w}_p\) indicates the weight of the pulley. - **Axis**: The center of the pulley denotes the axis of rotation.### (c) Free-Body Diagram of Crate- **Components**: - The crate experiences a tension force \(\vec{T}_2\) directed upwards. - The gravitational force \(m\vec{g}\) acts downward. - The crate accelerates upwards with an acceleration \(\vec{a}_y\).### Coordinate System Inset- Shows the positive directions for the coordinate system: - Positive \(y\)-axis is upwards. - Positive \(x\)-axis is to the right. - Positive torque (\(+\tau\)) direction shown with a counterclockwise arrow.This diagram helps to understand the forces and mechanics involved in lifting a crate using a dual pulley system, which is essential for studying rotational dynamics and mechanical systems.

Given data: crate mass (m) = 451 kg cable radius (r1) =0.60 m cable radius (r2) =0.20 m Moment of…

Answered: Dual pulley Motor 4 = 0.600 m- - l2 =…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

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A crate of mass 451 kg is being lifted by the mechanism shown in the figure. The two cables are wrapped around their respective pulleys, which have radii of 0.600 and 0.200 m. The pulleys are fastened together to form a dual pulley and turn as a single unit about the center axle, relative to which the combined moment of inertia is 51.0 kg · m². The cables roll on the dual pulley without slipping. A tension of magnitude 2150 N is maintained in the cable attached to the motor. Find (a) the angular acceleration of the dual pulley and (b) the tension in the cable connected to the crate.

The image consists of three parts, illustrating the mechanics of a dual pulley system. Below is a detailed explanation suitable for an educational website:

### (a) Dual Pulley and Crate System
- **Description**: This section shows a dual pulley system connected to a motor. The pulley is attached to a crate, which is being lifted vertically. The motor drives the rotation of the pulley, enabling the lifting of the crate.

### (b) Free-Body Diagram of Pulley
- **Components**:
- The pulley is depicted with two radii: \(\ell_1 = 0.600 \, \text{m}\) and \(\ell_2 = 0.200 \, \text{m}\).
- **Forces**:
- \(\vec{T}_1\) and \(\vec{T}_2\) are tension forces acting at different distances from the axis.
- \(\vec{P}\) represents force applied by the motor.
- \(\vec{w}_p\) indicates the weight of the pulley.
- **Axis**: The center of the pulley denotes the axis of rotation.

### (c) Free-Body Diagram of Crate
- **Components**:
- The crate experiences a tension force \(\vec{T}_2\) directed upwards.
- The gravitational force \(m\vec{g}\) acts downward.
- The crate accelerates upwards with an acceleration \(\vec{a}_y\).

### Coordinate System Inset
- Shows the positive directions for the coordinate system:
- Positive \(y\)-axis is upwards.
- Positive \(x\)-axis is to the right.
- Positive torque (\(+\tau\)) direction shown with a counterclockwise arrow.

This diagram helps to understand the forces and mechanics involved in lifting a crate using a dual pulley system, which is essential for studying rotational dynamics and mechanical systems.

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