If M = 2m, find the tension in the cord (in mg).

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If M = 2m, find the tension in the cord (in mg).

This image illustrates a pulley system, which includes the following components:

- **Pulley Wheel:** The wheel is divided into two sections labeled "R" and "M." This suggests that the pulley has radius \( R \) and mass \( M \).

- **Block/Weight:** Attached to the pulley is a block hanging vertically. The block is subject to gravitational force, indicated by the label \( mg \), where \( m \) represents the mass of the block and \( g \) is the acceleration due to gravity.

- **Tension Forces:** The strings connected to the block show two tension forces, both labeled \( T \), acting upwards. This indicates that the tension in the rope/string on both sides of the block is equal.

### Explanation

The diagram represents the mechanics of a simple pulley system. In a system like this, the weight of the block creates a downward force due to gravity, while the tension in the string counteracts this force.

- **Gravitational Force (\( mg \))**: Acts downward on the block due to its mass.
- **Tension (\( T \))**: Acts upward on the block, balancing the gravitational force.

This setup is typically analyzed using Newton's laws of motion to determine the acceleration of the block and/or the angular acceleration of the pulley. The parameters such as \( R \) (radius of the pulley) and \( M \) (mass of the pulley) may be used to calculate rotational inertia, which is essential for evaluating the system's dynamics.
Transcribed Image Text:This image illustrates a pulley system, which includes the following components: - **Pulley Wheel:** The wheel is divided into two sections labeled "R" and "M." This suggests that the pulley has radius \( R \) and mass \( M \). - **Block/Weight:** Attached to the pulley is a block hanging vertically. The block is subject to gravitational force, indicated by the label \( mg \), where \( m \) represents the mass of the block and \( g \) is the acceleration due to gravity. - **Tension Forces:** The strings connected to the block show two tension forces, both labeled \( T \), acting upwards. This indicates that the tension in the rope/string on both sides of the block is equal. ### Explanation The diagram represents the mechanics of a simple pulley system. In a system like this, the weight of the block creates a downward force due to gravity, while the tension in the string counteracts this force. - **Gravitational Force (\( mg \))**: Acts downward on the block due to its mass. - **Tension (\( T \))**: Acts upward on the block, balancing the gravitational force. This setup is typically analyzed using Newton's laws of motion to determine the acceleration of the block and/or the angular acceleration of the pulley. The parameters such as \( R \) (radius of the pulley) and \( M \) (mass of the pulley) may be used to calculate rotational inertia, which is essential for evaluating the system's dynamics.
Expert Solution
Step 1

Given data

The mass of the disk is: M = 2m

The tension in the cord is: T

The radius of the disk is: R

The mass of the block is: m

 

Let a be the acceleration of the block in a downward direction. The tension in the cord is in an upward direction, while the weight on the block in a downward direction.

The expression  for the vertical force in the block is given as:

ma=mg-TT=mg-a.....(1)

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