7) Suppose you use an ideal pulley of the type shown in the figure below and find it necessary to exert a force of 240 N to support a load. MA-3 (a) What is the load's mass (in kg)? kg (b)What force (in N) is exerted on the ceiling? Neglect the pulley system's mass. N (upward)

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**Understanding Ideal Pulley Systems**

To explore mechanical advantage (MA) through an ideal pulley system, let’s analyze the example below.

**Problem Statement:**
Suppose you use an ideal pulley, as illustrated, and find it necessary to exert a force of **240 N** to support a load.

**Diagram Analysis:**
- The diagram features a pulley system with a mechanical advantage (MA) of 3. 
- The force \( T \) is exerted through different sections of the rope and distributed across the pulleys.
- The weight \( w \) is illustrated at the bottom, being supported by the pulley system.

**Questions:**
(a) **What is the load's mass (in kg)?**
\[ \_\_\_\_ \text{ kg} \]

(b) **What force (in N) is exerted on the ceiling? Neglect the pulley's mass.**
\[ \_\_\_\_ \text{ N (upward)} \]

### Detailed Explanation:

**Diagram Components:**
- **Pulleys**: The system consists of multiple pulleys to distribute the weight, reducing the force required to lift the load.
- **Tension (T)**: The diagram indicates \( T \) multiple times, showcasing the rope segments exerting tension.
- **Mechanical Advantage (MA = 3)**: This suggests that the force exerted is magnified three times, allowing a lighter force to lift a heavier load.

### Part (a) - Load's Mass Calculation:
Given that the mechanical advantage (MA) is 3,
\[  F_{\text{effort}} = 240 \text{ N} \]
\[ MA = \frac{ \text{Load Force (F}_{\text{load}} \text{)}}{ \text{Effort force (F}_{\text{effort}} \text{)}} \]
\[ 3 = \frac{ \text{Load Force}}{240 \text{ N}} \]
\[ \text{Load Force} = 3 \times 240 \text{ N} \]
\[ \text{Load Force} = 720 \text{ N} \]

The load's weight is defined by:
\[ w = mg \Rightarrow 720 \text{ N} = m \times 9.8 \text{ m/s}^2 \]
\[ m = \frac{720 \text{ N}}{9.8 \
Transcribed Image Text:**Understanding Ideal Pulley Systems** To explore mechanical advantage (MA) through an ideal pulley system, let’s analyze the example below. **Problem Statement:** Suppose you use an ideal pulley, as illustrated, and find it necessary to exert a force of **240 N** to support a load. **Diagram Analysis:** - The diagram features a pulley system with a mechanical advantage (MA) of 3. - The force \( T \) is exerted through different sections of the rope and distributed across the pulleys. - The weight \( w \) is illustrated at the bottom, being supported by the pulley system. **Questions:** (a) **What is the load's mass (in kg)?** \[ \_\_\_\_ \text{ kg} \] (b) **What force (in N) is exerted on the ceiling? Neglect the pulley's mass.** \[ \_\_\_\_ \text{ N (upward)} \] ### Detailed Explanation: **Diagram Components:** - **Pulleys**: The system consists of multiple pulleys to distribute the weight, reducing the force required to lift the load. - **Tension (T)**: The diagram indicates \( T \) multiple times, showcasing the rope segments exerting tension. - **Mechanical Advantage (MA = 3)**: This suggests that the force exerted is magnified three times, allowing a lighter force to lift a heavier load. ### Part (a) - Load's Mass Calculation: Given that the mechanical advantage (MA) is 3, \[ F_{\text{effort}} = 240 \text{ N} \] \[ MA = \frac{ \text{Load Force (F}_{\text{load}} \text{)}}{ \text{Effort force (F}_{\text{effort}} \text{)}} \] \[ 3 = \frac{ \text{Load Force}}{240 \text{ N}} \] \[ \text{Load Force} = 3 \times 240 \text{ N} \] \[ \text{Load Force} = 720 \text{ N} \] The load's weight is defined by: \[ w = mg \Rightarrow 720 \text{ N} = m \times 9.8 \text{ m/s}^2 \] \[ m = \frac{720 \text{ N}}{9.8 \
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