The system shown in the figure below is used to lift an object of mass m = 12.5 kg. A constant downward force of magnitude F is applied to the loose end of the rope such that the hanging object moves upward at constant speed. Neglecting the masses of the rope and pulleys, find the following. T T2 (a) Find the required value of F. (b) Find the tensions 7,, T2, and 73. (7, indicates the tension in the rope which attaches the pulley to the ceiling.) N 2 = N T3 N (c) Find the work done by the applied force in raising the object a distance of 2.10 m. kJ

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### Lifting an Object with a Pulley System

The system shown in the figure below is used to lift an object of mass \( m = 12.5 \, \text{kg} \). A constant downward force of magnitude \( F \) is applied to the loose end of the rope such that the hanging object moves upward at constant speed. Neglecting the masses of the rope and pulleys, find the following:

![Pulley System](path_to_image)

#### Given:
- Mass of the object, \( m = 12.5 \, \text{kg} \)

(a) **Find the required value of \( F \)**.

\[ F = \boxed{} \, \text{N} \]

(b) **Find the tensions \( T_1 \), \( T_2 \), and \( T_3 \). ( \( T_3 \) indicates the tension in the rope which attaches the pulley to the ceiling.)**

\[ T_1 = \boxed{} \, \text{N} \]
\[ T_2 = \boxed{} \, \text{N} \]
\[ T_3 = \boxed{} \, \text{N} \]

(c) **Find the work done by the applied force in raising the object a distance of \( 2.10 \, \text{m} \).**

\[ \text{Work} = \boxed{} \, \text{kJ} \]

#### Diagram Explanation

The figure includes a pulley system setup:

- **Pulley 1**: Positioned on the left side with the rope passing through it vertically downward.
- **Pulley 2**: Positioned on the right side with the rope passing over it and then leading to the hand applying force \( F \).
- **Force \( F \)**: A downward force applied by the hand.
- **\( T_1 \)**: Tension in the vertical section of the rope holding the mass \( m \).
- **\( T_2 \)**: Another section of tension in the rope as it passes through Pulley 2.
- **\( T_3 \)**: Tension in the rope segment that attaches Pulley 2 to the ceiling.

The system achieves equilibrium and moves the hanging mass \( m \) upward at a constant speed when force \( F \) is applied.

**Notes:**
- Since the mass is moving at constant speed, the acceleration is
Transcribed Image Text:### Lifting an Object with a Pulley System The system shown in the figure below is used to lift an object of mass \( m = 12.5 \, \text{kg} \). A constant downward force of magnitude \( F \) is applied to the loose end of the rope such that the hanging object moves upward at constant speed. Neglecting the masses of the rope and pulleys, find the following: ![Pulley System](path_to_image) #### Given: - Mass of the object, \( m = 12.5 \, \text{kg} \) (a) **Find the required value of \( F \)**. \[ F = \boxed{} \, \text{N} \] (b) **Find the tensions \( T_1 \), \( T_2 \), and \( T_3 \). ( \( T_3 \) indicates the tension in the rope which attaches the pulley to the ceiling.)** \[ T_1 = \boxed{} \, \text{N} \] \[ T_2 = \boxed{} \, \text{N} \] \[ T_3 = \boxed{} \, \text{N} \] (c) **Find the work done by the applied force in raising the object a distance of \( 2.10 \, \text{m} \).** \[ \text{Work} = \boxed{} \, \text{kJ} \] #### Diagram Explanation The figure includes a pulley system setup: - **Pulley 1**: Positioned on the left side with the rope passing through it vertically downward. - **Pulley 2**: Positioned on the right side with the rope passing over it and then leading to the hand applying force \( F \). - **Force \( F \)**: A downward force applied by the hand. - **\( T_1 \)**: Tension in the vertical section of the rope holding the mass \( m \). - **\( T_2 \)**: Another section of tension in the rope as it passes through Pulley 2. - **\( T_3 \)**: Tension in the rope segment that attaches Pulley 2 to the ceiling. The system achieves equilibrium and moves the hanging mass \( m \) upward at a constant speed when force \( F \) is applied. **Notes:** - Since the mass is moving at constant speed, the acceleration is
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