College Physics
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ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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![### Physics Problem: Calculating Net Force Using Newton's Second Law
**Problem Statement:**
A runner with a mass of 70 kg accelerates from 0 m/s to 8 m/s in 9 s. Find the magnitude of the net force (in newtons) on the runner using the alternate form of Newton's second law. Round your answer to the nearest whole number.
**Solution Guide:**
1. **Identify Given Information:**
- Mass (\( m \)) = 70 kg
- Initial velocity (\( u \)) = 0 m/s
- Final velocity (\( v \)) = 8 m/s
- Time (\( t \)) = 9 s
2. **Determine Acceleration:**
- Acceleration (\( a \)) can be calculated using the formula:
\[
a = \frac{v - u}{t}
\]
- Substitute the given values:
\[
a = \frac{8 \, \text{m/s} - 0 \, \text{m/s}}{9 \, \text{s}} = \frac{8}{9} \, \text{m/s}^2
\]
3. **Apply Newton's Second Law of Motion:**
- Newton's second law states that the net force (\( F \)) is the product of mass and acceleration:
\[
F = m \times a
\]
- Substitute the given values and calculated acceleration:
\[
F = 70 \, \text{kg} \times \frac{8}{9} \, \text{m/s}^2 = \frac{560}{9} \, \text{N} \approx 62.22 \, \text{N}
\]
4. **Round the Answer:**
- The magnitude of the net force, rounded to the nearest whole number, is:
\[
F \approx 62 \, \text{N}
\]
**Answer:**
The net force on the runner is approximately **62 newtons**.](https://content.bartleby.com/qna-images/question/f069b3c7-7f9d-47ba-a0ca-6a0fe29c2d54/5e20fda3-97b5-4468-b5f3-f07deec44c5c/nnpetor_processed.jpeg)
Transcribed Image Text:### Physics Problem: Calculating Net Force Using Newton's Second Law
**Problem Statement:**
A runner with a mass of 70 kg accelerates from 0 m/s to 8 m/s in 9 s. Find the magnitude of the net force (in newtons) on the runner using the alternate form of Newton's second law. Round your answer to the nearest whole number.
**Solution Guide:**
1. **Identify Given Information:**
- Mass (\( m \)) = 70 kg
- Initial velocity (\( u \)) = 0 m/s
- Final velocity (\( v \)) = 8 m/s
- Time (\( t \)) = 9 s
2. **Determine Acceleration:**
- Acceleration (\( a \)) can be calculated using the formula:
\[
a = \frac{v - u}{t}
\]
- Substitute the given values:
\[
a = \frac{8 \, \text{m/s} - 0 \, \text{m/s}}{9 \, \text{s}} = \frac{8}{9} \, \text{m/s}^2
\]
3. **Apply Newton's Second Law of Motion:**
- Newton's second law states that the net force (\( F \)) is the product of mass and acceleration:
\[
F = m \times a
\]
- Substitute the given values and calculated acceleration:
\[
F = 70 \, \text{kg} \times \frac{8}{9} \, \text{m/s}^2 = \frac{560}{9} \, \text{N} \approx 62.22 \, \text{N}
\]
4. **Round the Answer:**
- The magnitude of the net force, rounded to the nearest whole number, is:
\[
F \approx 62 \, \text{N}
\]
**Answer:**
The net force on the runner is approximately **62 newtons**.
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