A car rounds a curve with a circular radius of 20 m at a steady 20 km/h. If a second car of the same mass rounds the curve at twice the speed, how will the second car's centripetal acceleration be different than the first car's? It will be 1/2 the magnitude of the first car's It will be 4 times larger than the first car's It will be 1/4 the magnitude of the first car's It will be 2 times larger than the first car's
A car rounds a curve with a circular radius of 20 m at a steady 20 km/h. If a second car of the same mass rounds the curve at twice the speed, how will the second car's centripetal acceleration be different than the first car's? It will be 1/2 the magnitude of the first car's It will be 4 times larger than the first car's It will be 1/4 the magnitude of the first car's It will be 2 times larger than the first car's
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![### Centripetal Force and Acceleration Comparison Activity
#### Question:
A car rounds a curve with a circular radius of 20 m at a steady 20 km/h. If a second car of the same mass rounds the curve at twice the speed, how will the second car’s centripetal acceleration be different than the first car’s?
#### Answer Choices:
- **Option A:** It will be 1/2 the magnitude of the first car's
- **Option B:** It will be 4 times larger than the first car's
- **Option C:** It will be 1/4 the magnitude of the first car's
- **Option D:** It will be 2 times larger than the first car's
### Explanation:
When examining centripetal acceleration, it is important to recognize that it is dependent on both the speed of the moving object and the radius of the circular path, following the formula:
\[ a_c = \frac{v^2}{r} \]
where \(a_c\) is the centripetal acceleration, \(v\) is the velocity, and \(r\) is the radius of the circle.
1. **First Car's Centripetal Acceleration:**
- Radius (\(r\)): 20 m
- Velocity (\(v\)): 20 km/h (which needs to be converted to meters per second)
- \( v \) in m/s: \( 20 \times \frac{1000}{3600} \approx 5.56 \, \text{m/s} \)
- Using the formula:
\[ a_{c1} = \frac{(5.56 \, \text{m/s})^2}{20 \, \text{m}} \]
\[ a_{c1} \approx 1.54 \, \text{m/s}^2 \]
2. **Second Car's Centripetal Acceleration (going twice as fast):**
- Radius (\(r\)): 20 m
- Velocity (\(v\)): 40 km/h (also converted to m/s)
- \( v \) in m/s: \( 40 \times \frac{1000}{3600} \approx 11.11 \, \text{m/s} \)
- Using the formula:
\[ a_{c2} =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffbc1cd9d-8d4f-40e4-add2-a376f2364edb%2F9adf0a79-97a4-478e-9609-db2d88df53b8%2Fwu53opo.png&w=3840&q=75)
Transcribed Image Text:### Centripetal Force and Acceleration Comparison Activity
#### Question:
A car rounds a curve with a circular radius of 20 m at a steady 20 km/h. If a second car of the same mass rounds the curve at twice the speed, how will the second car’s centripetal acceleration be different than the first car’s?
#### Answer Choices:
- **Option A:** It will be 1/2 the magnitude of the first car's
- **Option B:** It will be 4 times larger than the first car's
- **Option C:** It will be 1/4 the magnitude of the first car's
- **Option D:** It will be 2 times larger than the first car's
### Explanation:
When examining centripetal acceleration, it is important to recognize that it is dependent on both the speed of the moving object and the radius of the circular path, following the formula:
\[ a_c = \frac{v^2}{r} \]
where \(a_c\) is the centripetal acceleration, \(v\) is the velocity, and \(r\) is the radius of the circle.
1. **First Car's Centripetal Acceleration:**
- Radius (\(r\)): 20 m
- Velocity (\(v\)): 20 km/h (which needs to be converted to meters per second)
- \( v \) in m/s: \( 20 \times \frac{1000}{3600} \approx 5.56 \, \text{m/s} \)
- Using the formula:
\[ a_{c1} = \frac{(5.56 \, \text{m/s})^2}{20 \, \text{m}} \]
\[ a_{c1} \approx 1.54 \, \text{m/s}^2 \]
2. **Second Car's Centripetal Acceleration (going twice as fast):**
- Radius (\(r\)): 20 m
- Velocity (\(v\)): 40 km/h (also converted to m/s)
- \( v \) in m/s: \( 40 \times \frac{1000}{3600} \approx 11.11 \, \text{m/s} \)
- Using the formula:
\[ a_{c2} =
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