42)A net force of 90 N accelerates a bike and rider at 2 m/s². What is the mass of the bike and rider together? Drawing FBD Components Adding Forces Solve for Variable CheckUnits the ava

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Chapter1: Units, Trigonometry. And Vectors
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Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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### Problem Statement:
A net force of \( 90 \, \text{N} \) accelerates a bike and rider at \( 2 \, \text{m/s}^2 \). What is the mass of the bike and rider together?

### Solution Checklist:
1. **Drawing:**
   - No drawing needed for this problem.

2. **Free Body Diagram (FBD):**
   - Illustrate the forces acting on the bike and rider. 
   - Label the net force (\( F_{\text{net}} = 90 \, \text{N} \)) and the acceleration (\( a = 2 \, \text{m/s}^2 \)).

3. **Components:**
   - Ensure that you are considering all components of the forces involved. Since this problem is straightforward and deals with net force and acceleration, additional components might not be required.

4. **Adding Forces:**
   - Not applicable in this simple context as a net force is already provided.

5. **Solve for Variable:**
   - Use Newton's Second Law: \( F = ma \)
   - Given \( F = 90 \, \text{N} \) and \( a = 2 \, \text{m/s}^2 \):
     \[
     m = \frac{F}{a} = \frac{90 \, \text{N}}{2 \, \text{m/s}^2} = 45 \, \text{kg}
     \]

6. **Check Units:**
   - Ensure the units of force are Newtons (N), mass are kilograms (kg), and acceleration are meters per second squared (\(\text{m/s}^2\)). The units correctly resolve as:
     \[
     1 \, \text{N} = 1 \, \text{kg} \cdot \text{m/s}^2
     \]

### Final Answer:
The mass of the bike and rider together is \( 45 \, \text{kg} \).
Transcribed Image Text:### Problem Statement: A net force of \( 90 \, \text{N} \) accelerates a bike and rider at \( 2 \, \text{m/s}^2 \). What is the mass of the bike and rider together? ### Solution Checklist: 1. **Drawing:** - No drawing needed for this problem. 2. **Free Body Diagram (FBD):** - Illustrate the forces acting on the bike and rider. - Label the net force (\( F_{\text{net}} = 90 \, \text{N} \)) and the acceleration (\( a = 2 \, \text{m/s}^2 \)). 3. **Components:** - Ensure that you are considering all components of the forces involved. Since this problem is straightforward and deals with net force and acceleration, additional components might not be required. 4. **Adding Forces:** - Not applicable in this simple context as a net force is already provided. 5. **Solve for Variable:** - Use Newton's Second Law: \( F = ma \) - Given \( F = 90 \, \text{N} \) and \( a = 2 \, \text{m/s}^2 \): \[ m = \frac{F}{a} = \frac{90 \, \text{N}}{2 \, \text{m/s}^2} = 45 \, \text{kg} \] 6. **Check Units:** - Ensure the units of force are Newtons (N), mass are kilograms (kg), and acceleration are meters per second squared (\(\text{m/s}^2\)). The units correctly resolve as: \[ 1 \, \text{N} = 1 \, \text{kg} \cdot \text{m/s}^2 \] ### Final Answer: The mass of the bike and rider together is \( 45 \, \text{kg} \).
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