Spring scale A is attached to the floor and a rope runs vertically upward, loops over an ideal pulley, and runs down on the other side to a 255-N weight. Scale B is attached to the ceiling and the pulley is hung below it. Ignore the weights of the rope, pulley, and scales. Pulley A B PN

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a. What is the reading of spring scale A? answer in N

b. What is the reading of spring scale B? answer in N

### Understanding the Spring Scale and Pulley System

**Description:**

In this setup, we have a spring scale (Scale A) attached to the floor. A rope extends upward from this scale, loops over an ideal pulley, and then runs down on the other side to support a 255-N weight. Another spring scale (Scale B) is attached to the ceiling, with the pulley suspended below it. For the sake of simplicity, the weights of the rope, pulley, and scales are ignored in this scenario.

**Diagram Explanation:**
1. **Spring Scale A** is secured to the floor.
2. The **Rope** extends vertically from Scale A, passing over an **Ideal Pulley** (labelled simply as "Pulley" in the diagram).
3. After looping over the pulley, the rope descends on the opposite side, leading to the attachment of a **Weight** marked "PN". 
4. **Spring Scale B** is affixed to the ceiling, supporting the pulley from above.
5. The **Weight (P = 255 N)** is suspended on the free end of the rope.

**Key Points of the System:**
1. **Scale A** measures the tension in the rope extending to the weight.
2. **Scale B** measures the total force exerted on the pulley and hence the ceiling attachment.
3. Using an **Ideal Pulley** implies frictionless and weightless pulley, which only redirects the force.

**Forces in Play:**
- The weight of 255 N creates tension in the rope.
- Scale A experiences tension due to the weight.
- Scale B experiences tension due to the combined effect of the rope and the weight pulling downwards through the pulley.

This setup is commonly used to demonstrate principles of mechanics such as tension, Newton’s laws, and the mechanical advantage provided by pulleys. By analyzing this system, students can better understand how forces are distributed and transmitted in simple mechanical systems.
Transcribed Image Text:### Understanding the Spring Scale and Pulley System **Description:** In this setup, we have a spring scale (Scale A) attached to the floor. A rope extends upward from this scale, loops over an ideal pulley, and then runs down on the other side to support a 255-N weight. Another spring scale (Scale B) is attached to the ceiling, with the pulley suspended below it. For the sake of simplicity, the weights of the rope, pulley, and scales are ignored in this scenario. **Diagram Explanation:** 1. **Spring Scale A** is secured to the floor. 2. The **Rope** extends vertically from Scale A, passing over an **Ideal Pulley** (labelled simply as "Pulley" in the diagram). 3. After looping over the pulley, the rope descends on the opposite side, leading to the attachment of a **Weight** marked "PN". 4. **Spring Scale B** is affixed to the ceiling, supporting the pulley from above. 5. The **Weight (P = 255 N)** is suspended on the free end of the rope. **Key Points of the System:** 1. **Scale A** measures the tension in the rope extending to the weight. 2. **Scale B** measures the total force exerted on the pulley and hence the ceiling attachment. 3. Using an **Ideal Pulley** implies frictionless and weightless pulley, which only redirects the force. **Forces in Play:** - The weight of 255 N creates tension in the rope. - Scale A experiences tension due to the weight. - Scale B experiences tension due to the combined effect of the rope and the weight pulling downwards through the pulley. This setup is commonly used to demonstrate principles of mechanics such as tension, Newton’s laws, and the mechanical advantage provided by pulleys. By analyzing this system, students can better understand how forces are distributed and transmitted in simple mechanical systems.
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