**Problem Statement: Analyzing Forces on a Backpack**You hang a backpack on a spring scale and place the bag on a platform scale so that the platform scale reads 25.7 N and the spring scale reads 17.6 N. Draw a force diagram for the backpack and explain how you would use it to determine the magnitude of the force that Earth exerts on the bag.**Explanation: Force Diagram and Analysis**To analyze the forces acting on the backpack, we need to understand the roles of the platform and spring scales:1. **Platform Scale (25.7 N):** - This scale measures the normal force exerted by the platform on the backpack. It indicates the force the platform applies upward to support the backpack.2. **Spring Scale (17.6 N):** - This scale measures the tension in the rope or strap used to hang the backpack. It represents the upward force exerted by the spring mechanism.3. **Gravitational Force (Weight):** - The force of gravity acting on the backpack, directed downward toward the center of the Earth.**Force Diagram:**- **Gravitational Force (Fg):** This is the force exerted by Earth on the backpack. It acts downward.- **Normal Force (Fn):** This is exerted by the platform, acting upward, measured by the platform scale.- **Tension Force (Ft):** This is measured by the spring scale, acting upward.**Finding the Gravitational Force (Weight):**To determine the gravitational force or weight (Fg) of the backpack, apply the principle of equilibrium where the sum of the forces acting on the backpack is zero:- The sum of the upward forces (normal and tension) equals the downward gravitational force.\[ Fg = Fn + Ft \]\[ Fg = 25.7 \, \text{N} + 17.6 \, \text{N} \]\[ Fg = 43.3 \, \text{N} \]Thus, the magnitude of the force that Earth exerts on the bag, or the backpack's weight, is 43.3 N.

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You hang a backpack on a spring scale and place the bag on a platform scale so that the platform scale reads 25.7 N and the spring scale reads 17.6 N. Draw a force diagram for the backpack and explain how you would use it to determine the magnitude of the force that Earth exerts on the bag.

You hang a backpack on a spring scale and place the bag on a platform scale so that the platform scale reads 25.7 N and the spring scale reads 17.6 N. Draw a force diagram for the backpack and explain how you would use it to determine the magnitude of the force that Earth exerts on the bag.

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ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

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**Problem Statement: Analyzing Forces on a Backpack**

You hang a backpack on a spring scale and place the bag on a platform scale so that the platform scale reads 25.7 N and the spring scale reads 17.6 N. Draw a force diagram for the backpack and explain how you would use it to determine the magnitude of the force that Earth exerts on the bag.

**Explanation: Force Diagram and Analysis**

To analyze the forces acting on the backpack, we need to understand the roles of the platform and spring scales:

1. **Platform Scale (25.7 N):**
- This scale measures the normal force exerted by the platform on the backpack. It indicates the force the platform applies upward to support the backpack.

2. **Spring Scale (17.6 N):**
- This scale measures the tension in the rope or strap used to hang the backpack. It represents the upward force exerted by the spring mechanism.

3. **Gravitational Force (Weight):**
- The force of gravity acting on the backpack, directed downward toward the center of the Earth.

**Force Diagram:**

- **Gravitational Force (Fg):** This is the force exerted by Earth on the backpack. It acts downward.
- **Normal Force (Fn):** This is exerted by the platform, acting upward, measured by the platform scale.
- **Tension Force (Ft):** This is measured by the spring scale, acting upward.

**Finding the Gravitational Force (Weight):**

To determine the gravitational force or weight (Fg) of the backpack, apply the principle of equilibrium where the sum of the forces acting on the backpack is zero:

- The sum of the upward forces (normal and tension) equals the downward gravitational force.

\[ Fg = Fn + Ft \]

\[ Fg = 25.7 \, \text{N} + 17.6 \, \text{N} \]

\[ Fg = 43.3 \, \text{N} \]

Thus, the magnitude of the force that Earth exerts on the bag, or the backpack's weight, is 43.3 N.

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