A highway is being constructed to accommodate traffic for speeds of 12.2 m/s. If the angle of the bank is 7.97° and there is no friction force, what is the highway's curve radius? 1.06×103 m 8.89 m 15.3 m 108 m
Question
A highway is being constructed to accommodate traffic for speeds of 12.2 m/s. If the angle of the bank is 7.97° and there is no friction force, what is the highway's curve radius? 1.06×103 m 8.89 m 15.3 m 108 m
Solution 1
The radius of the curve of the highway can be calculated using the formula for the banking of roads without friction, which is:
r = v² / g * tan θ
where:
- r is the radius of the curve,
- v is the speed of the vehicles,
- g is the acceleration due to gravity (approximately 9.81 m/s²), and
- θ is the angle of the bank.
Substituting the given values into the formula:
r = (12.2 m/s)² / (9.81 m/s² * tan(7.97°))
After calculating the above expression, you will get the radius of the curve of the highway.
Solution 2
The radius of the curve of the highway can be calculated using the formula for the banking of roads without friction, which is:
r = v² / g * tan θ
where:
- r is the radius of the curve,
- v is the speed of the vehicles,
- g is the acceleration due to gravity (approximately 9.81 m/s²), and
- θ is the angle of the bank.
Substituting the given values into the formula:
r = (12.2 m/s)² / (9.81 m/s² * tan(7.97°))
After calculating the above expression, you will get the radius of the curve of the highway.
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