Suppose two children push horizontally, but in exactly opposite directions, on a third child in a wagon. The first child exerts a force F₁ of 65.0 N, the second a force FR of 96.0 N, friction f is 13.0 N, and the mass of the third child plus wagon is 26.0 kg. Think & Prepare Consider the direction of the forces. The forces applied by the two children outside of the wagon are stated to be in opposition to one another. What about friction? With respect to the direction of motion, how does it act? Will its effect be additive or subtractive? (a) Calculate the acceleration. Enter to 3 significant figures a= m/s² (b) What would the acceleration be if friction were 31 N? Enter to 3 significant figures a= m/s²

College Physics
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Chapter1: Units, Trigonometry. And Vectors
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## Educational Content: Analyzing Forces and Acceleration

### Free Body Diagram
Your Free Body Diagram for Part 2 should appear as follows:

- **Instructions for Constructing the Diagram:**
  1. Place the tail of the vectors within the confines of the mass.
  2. Orient the vectors by dragging the heads in the proper direction.
  - Note: The angles may be within ±15°, the magnitudes are not considered, and the vectors do not need to be centered on the mass.

- **Diagram Description:**
  - The diagram shows several vectors:
    - **\(N\)**: A vertical vector pointing upwards at 90°.
    - **\(mg\)**: A vertical vector pointing downwards at 270° (denoting the mass and gravitational force).
    - **\(F_L\)**: A horizontal vector pointing to the left at 180°, labeled with a force of 65.0 N.
    - **\(F_R\)**: A horizontal vector pointing to the right at 0°, labeled with a force of 96.0 N.

### Problem Scenario
Suppose two children push horizontally, but in exactly opposite directions, on a third child in a wagon. The first child exerts a force \(F_L\) of 65.0 N, the second a force \(F_R\) of 96.0 N. Friction \(f\) is 13.0 N, and the mass of the third child plus the wagon is 26.0 kg.

### Think & Prepare
Consider the direction of the forces. The forces applied by the two children outside of the wagon are in opposition to one another. Consider how friction acts in relation to the direction of motion. Will its effect be additive or subtractive?

### Questions
(a) **Calculate the acceleration.**

Enter to 3 significant figures:
\[ a = \_\_\_\_ \, \text{m/s}^2 \]

(b) **What would the acceleration be if friction were 31 N?**

Enter to 3 significant figures:
\[ a = \_\_\_\_ \, \text{m/s}^2 \]

This exercise helps you understand the dynamics of forces in motion and calculate resulting accelerations under varying conditions.
Transcribed Image Text:## Educational Content: Analyzing Forces and Acceleration ### Free Body Diagram Your Free Body Diagram for Part 2 should appear as follows: - **Instructions for Constructing the Diagram:** 1. Place the tail of the vectors within the confines of the mass. 2. Orient the vectors by dragging the heads in the proper direction. - Note: The angles may be within ±15°, the magnitudes are not considered, and the vectors do not need to be centered on the mass. - **Diagram Description:** - The diagram shows several vectors: - **\(N\)**: A vertical vector pointing upwards at 90°. - **\(mg\)**: A vertical vector pointing downwards at 270° (denoting the mass and gravitational force). - **\(F_L\)**: A horizontal vector pointing to the left at 180°, labeled with a force of 65.0 N. - **\(F_R\)**: A horizontal vector pointing to the right at 0°, labeled with a force of 96.0 N. ### Problem Scenario Suppose two children push horizontally, but in exactly opposite directions, on a third child in a wagon. The first child exerts a force \(F_L\) of 65.0 N, the second a force \(F_R\) of 96.0 N. Friction \(f\) is 13.0 N, and the mass of the third child plus the wagon is 26.0 kg. ### Think & Prepare Consider the direction of the forces. The forces applied by the two children outside of the wagon are in opposition to one another. Consider how friction acts in relation to the direction of motion. Will its effect be additive or subtractive? ### Questions (a) **Calculate the acceleration.** Enter to 3 significant figures: \[ a = \_\_\_\_ \, \text{m/s}^2 \] (b) **What would the acceleration be if friction were 31 N?** Enter to 3 significant figures: \[ a = \_\_\_\_ \, \text{m/s}^2 \] This exercise helps you understand the dynamics of forces in motion and calculate resulting accelerations under varying conditions.
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