26. What is the ideal speed to take a 100 m radius curve banked at a 20.0° angle?
26. What is the ideal speed to take a 100 m radius curve banked at a 20.0° angle?
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![**Question 26:** What is the ideal speed to take a 100 m radius curve banked at a 20.0° angle?
This question involves calculating the ideal speed for navigating a banked curve. When a curve is banked, the angle allows a vehicle to negotiate the curve without relying solely on friction. This principle is important in road design for both safety and efficiency.
### Explanation:
To find the ideal speed (\(v\)) for a banked curve, use the following formula derived from the forces acting on the vehicle, including gravitational and centripetal forces:
\[ v = \sqrt{r \cdot g \cdot \tan(\theta)} \]
Where:
- \(v\) is the ideal speed,
- \(r\) is the radius of the curve (100 m in this case),
- \(g\) is the acceleration due to gravity (approximately 9.81 m/s²),
- \(\theta\) is the banking angle (20.0°).
By inputting these values into the formula, you can determine the speed at which a vehicle can safely and efficiently travel around this banked curve without additional frictional forces.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F18744455-e31e-4554-a26b-e7638996cbb9%2F17b2d9bd-f748-47d0-a529-feb4e0dd6038%2Faywfuji_processed.png&w=3840&q=75)
Transcribed Image Text:**Question 26:** What is the ideal speed to take a 100 m radius curve banked at a 20.0° angle?
This question involves calculating the ideal speed for navigating a banked curve. When a curve is banked, the angle allows a vehicle to negotiate the curve without relying solely on friction. This principle is important in road design for both safety and efficiency.
### Explanation:
To find the ideal speed (\(v\)) for a banked curve, use the following formula derived from the forces acting on the vehicle, including gravitational and centripetal forces:
\[ v = \sqrt{r \cdot g \cdot \tan(\theta)} \]
Where:
- \(v\) is the ideal speed,
- \(r\) is the radius of the curve (100 m in this case),
- \(g\) is the acceleration due to gravity (approximately 9.81 m/s²),
- \(\theta\) is the banking angle (20.0°).
By inputting these values into the formula, you can determine the speed at which a vehicle can safely and efficiently travel around this banked curve without additional frictional forces.
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