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A road is designed in such a manner that the speed on a horizontal curve with an elevation of 8% is 110 km/hr. The minimum radius of the curve (in m) that is required for a vehicle to move safely, if the coefficient of friction is 0.10, is (Answer up to one decimal place)
Correct answer is '529.3'. Can you explain this answer?
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A road is designed in such a manner that the speed on a horizontal cu...
Given:
Speed on the curve (V) = 110 km/hr
Elevation of the curve (h) = 8%
Coefficient of friction (μ) = 0.10
To find:
Minimum radius of the curve (R) required for a vehicle to move safely
Assumption:
The vehicle is moving in a circular path with a constant speed. Thus, the horizontal force acting on the vehicle is responsible for providing the necessary centripetal force.
Formula:
The centripetal force (Fc) acting on the vehicle can be calculated using the formula:
Fc = m * g * R
The maximum frictional force (Ff) that can be provided by the friction between the tires and the road can be calculated using the formula:
Ff = μ * m * g
Derivation:
Step 1: Convert the speed from km/hr to m/s.
Speed on the curve (V) = 110 km/hr = 110 * (1000/3600) m/s = 30.56 m/s
Step 2: Calculate the acceleration (a) of the vehicle on the curve using the formula:
a = V^2 / R
Step 3: Calculate the gravitational force (mg) acting on the vehicle using the formula:
mg = m * g
Step 4: Equate the centripetal force (m * g * R) and the maximum frictional force (μ * m * g) to find the minimum radius (R) required:
m * g * R = μ * m * g
R = μ * g / a
Step 5: Substitute the given values into the formula to calculate the minimum radius:
R = (0.10 * 9.8) / (30.56^2 / R)
R = 0.98 / (939.04 / R)
R^2 = 0.98 * R / 939.04
R^2 = 0.001042
R = √0.001042
R = 0.0323 m (rounded to one decimal place)
R = 32.3 m
The minimum radius of the curve required for the vehicle to move safely is 32.3 m. However, the answer provided as '529.3' does not match the calculated value.
Speed on the curve (V) = 110 km/hr
Elevation of the curve (h) = 8%
Coefficient of friction (μ) = 0.10
To find:
Minimum radius of the curve (R) required for a vehicle to move safely
Assumption:
The vehicle is moving in a circular path with a constant speed. Thus, the horizontal force acting on the vehicle is responsible for providing the necessary centripetal force.
Formula:
The centripetal force (Fc) acting on the vehicle can be calculated using the formula:
Fc = m * g * R
The maximum frictional force (Ff) that can be provided by the friction between the tires and the road can be calculated using the formula:
Ff = μ * m * g
Derivation:
Step 1: Convert the speed from km/hr to m/s.
Speed on the curve (V) = 110 km/hr = 110 * (1000/3600) m/s = 30.56 m/s
Step 2: Calculate the acceleration (a) of the vehicle on the curve using the formula:
a = V^2 / R
Step 3: Calculate the gravitational force (mg) acting on the vehicle using the formula:
mg = m * g
Step 4: Equate the centripetal force (m * g * R) and the maximum frictional force (μ * m * g) to find the minimum radius (R) required:
m * g * R = μ * m * g
R = μ * g / a
Step 5: Substitute the given values into the formula to calculate the minimum radius:
R = (0.10 * 9.8) / (30.56^2 / R)
R = 0.98 / (939.04 / R)
R^2 = 0.98 * R / 939.04
R^2 = 0.001042
R = √0.001042
R = 0.0323 m (rounded to one decimal place)
R = 32.3 m
The minimum radius of the curve required for the vehicle to move safely is 32.3 m. However, the answer provided as '529.3' does not match the calculated value.
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Community Answer
A road is designed in such a manner that the speed on a horizontal cu...
The minimum radius of the curve required for safe vehicular movement is the ruling gradient.
The expression for the ruling gradient is:
Substitute the values in the above expression:
= 529.3 m
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A road is designed in such a manner that the speed on a horizontal curve with an elevation of 8% is 110 km/hr. The minimum radius of the curve (in m) that is required for a vehicle to move safely, if the coefficient of friction is 0.10, is (Answer up to one decimal place)Correct answer is '529.3'. Can you explain this answer?
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A road is designed in such a manner that the speed on a horizontal curve with an elevation of 8% is 110 km/hr. The minimum radius of the curve (in m) that is required for a vehicle to move safely, if the coefficient of friction is 0.10, is (Answer up to one decimal place)Correct answer is '529.3'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A road is designed in such a manner that the speed on a horizontal curve with an elevation of 8% is 110 km/hr. The minimum radius of the curve (in m) that is required for a vehicle to move safely, if the coefficient of friction is 0.10, is (Answer up to one decimal place)Correct answer is '529.3'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A road is designed in such a manner that the speed on a horizontal curve with an elevation of 8% is 110 km/hr. The minimum radius of the curve (in m) that is required for a vehicle to move safely, if the coefficient of friction is 0.10, is (Answer up to one decimal place)Correct answer is '529.3'. Can you explain this answer?.
A road is designed in such a manner that the speed on a horizontal curve with an elevation of 8% is 110 km/hr. The minimum radius of the curve (in m) that is required for a vehicle to move safely, if the coefficient of friction is 0.10, is (Answer up to one decimal place)Correct answer is '529.3'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A road is designed in such a manner that the speed on a horizontal curve with an elevation of 8% is 110 km/hr. The minimum radius of the curve (in m) that is required for a vehicle to move safely, if the coefficient of friction is 0.10, is (Answer up to one decimal place)Correct answer is '529.3'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A road is designed in such a manner that the speed on a horizontal curve with an elevation of 8% is 110 km/hr. The minimum radius of the curve (in m) that is required for a vehicle to move safely, if the coefficient of friction is 0.10, is (Answer up to one decimal place)Correct answer is '529.3'. Can you explain this answer?.
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