Physics for Scientists and Engineers, Technology Update (No access codes included)
Physics for Scientists and Engineers, Technology Update (No access codes included)
9th Edition
ISBN: 9781305116399
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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### Physics Problem on Acceleration

**(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_

\[ a = \_\_\_\_ \, \text{m/s}^2 \]

### Notes:
- Ensure accuracy by maintaining three significant figures in your calculations.
- Apply Newton's second law and consider any forces acting on the object, such as friction when answering part (b).
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Transcribed Image Text:### Physics Problem on Acceleration **(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_ \[ a = \_\_\_\_ \, \text{m/s}^2 \] ### Notes: - Ensure accuracy by maintaining three significant figures in your calculations. - Apply Newton's second law and consider any forces acting on the object, such as friction when answering part (b).
## Educational Content: Free Body Diagram and Forces

### Free Body Diagram Explanation

1. **Diagram Instructions:**
   - Construct the free-body 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.

2. **Diagram Details:**
   - The diagram is a vector representation centered around a box, symbolizing the mass. 
   - Key Forces:
     - **N** (Normal Force): Points upwards at 90°.
     - **\(F_L\)** (Force to the Left): Arrows point left with an angle of 179.87° from the right.
     - **\(F_R\)** (Force to the Right): Arrows point right at a slight angle of 0.04°.
     - **\(mg\)** (Gravitational Force): Points directly downward at 270°.
     - **f** (Friction): Not depicted separately but should be considered in force calculations.

### Problem Context and Analysis

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

1. **Direction of Forces:**
   - The forces applied by the two children are in opposition. 
   - Consider how friction acts in the context of the motion.
  
2. **Net Force Analysis:**
   - Determine if friction acts to add to or subtract from the total net force.
   - Analyze the resultant motion based on force interactions.

This explanation will help you understand the balance of forces and how vector components influence physical systems.
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Transcribed Image Text:## Educational Content: Free Body Diagram and Forces ### Free Body Diagram Explanation 1. **Diagram Instructions:** - Construct the free-body 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. 2. **Diagram Details:** - The diagram is a vector representation centered around a box, symbolizing the mass. - Key Forces: - **N** (Normal Force): Points upwards at 90°. - **\(F_L\)** (Force to the Left): Arrows point left with an angle of 179.87° from the right. - **\(F_R\)** (Force to the Right): Arrows point right at a slight angle of 0.04°. - **\(mg\)** (Gravitational Force): Points directly downward at 270°. - **f** (Friction): Not depicted separately but should be considered in force calculations. ### Problem Context and Analysis 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 1. **Direction of Forces:** - The forces applied by the two children are in opposition. - Consider how friction acts in the context of the motion. 2. **Net Force Analysis:** - Determine if friction acts to add to or subtract from the total net force. - Analyze the resultant motion based on force interactions. This explanation will help you understand the balance of forces and how vector components influence physical systems.
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