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The maximum speed with which a car can be driven round a curve of radius 18m without skidding (when g=10m/s^2 and the coefficient of friction between rubber tyres and roadway is 0.2) is ?
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The maximum speed with which a car can be driven round a curve of radi...
Max Speed on a Curve without Skidding
To determine the maximum speed at which a car can be driven around a curve without skidding, we need to consider the centripetal force acting on the car and the maximum friction force that can be exerted by the tires.
Centripetal Force
The centripetal force is the force that keeps an object moving in a curved path. It always acts towards the center of the curve and is given by the equation:
Fc = m * v^2 / r
Where:
Fc is the centripetal force
m is the mass of the car
v is the velocity of the car
r is the radius of the curve
Friction Force
The friction force between the car's tires and the road provides the centripetal force required to keep the car moving in a curve. The maximum friction force that can be exerted depends on the coefficient of friction between the tires and the road surface.
The friction force is given by the equation:
Ff = μ * N
Where:
Ff is the friction force
μ is the coefficient of friction
N is the normal force (equal to the weight of the car, mg)
Maximum Speed Calculation
To find the maximum speed, we need to equate the centripetal force to the maximum friction force:
Fc = Ff
Substituting the equations for centripetal force and friction force:
m * v^2 / r = μ * m * g
Simplifying the equation:
v^2 = μ * g * r
Taking the square root of both sides:
v = √(μ * g * r)
Calculating the Maximum Speed
Given:
Radius of the curve, r = 18m
Acceleration due to gravity, g = 10m/s^2
Coefficient of friction, μ = 0.2
Substituting the values into the equation:
v = √(0.2 * 10 * 18)
Simplifying the equation:
v = √(36)
v = 6 m/s
Conclusion
The maximum speed at which the car can be driven around the curve without skidding is 6 m/s. It is important to note that this calculation assumes ideal conditions and does not take into account other factors such as the condition of the tires, the road surface, and any external forces acting on the car. It is always recommended to drive at a safe and reasonable speed, considering all the factors that can affect the vehicle's stability and control.
To determine the maximum speed at which a car can be driven around a curve without skidding, we need to consider the centripetal force acting on the car and the maximum friction force that can be exerted by the tires.
Centripetal Force
The centripetal force is the force that keeps an object moving in a curved path. It always acts towards the center of the curve and is given by the equation:
Fc = m * v^2 / r
Where:
Fc is the centripetal force
m is the mass of the car
v is the velocity of the car
r is the radius of the curve
Friction Force
The friction force between the car's tires and the road provides the centripetal force required to keep the car moving in a curve. The maximum friction force that can be exerted depends on the coefficient of friction between the tires and the road surface.
The friction force is given by the equation:
Ff = μ * N
Where:
Ff is the friction force
μ is the coefficient of friction
N is the normal force (equal to the weight of the car, mg)
Maximum Speed Calculation
To find the maximum speed, we need to equate the centripetal force to the maximum friction force:
Fc = Ff
Substituting the equations for centripetal force and friction force:
m * v^2 / r = μ * m * g
Simplifying the equation:
v^2 = μ * g * r
Taking the square root of both sides:
v = √(μ * g * r)
Calculating the Maximum Speed
Given:
Radius of the curve, r = 18m
Acceleration due to gravity, g = 10m/s^2
Coefficient of friction, μ = 0.2
Substituting the values into the equation:
v = √(0.2 * 10 * 18)
Simplifying the equation:
v = √(36)
v = 6 m/s
Conclusion
The maximum speed at which the car can be driven around the curve without skidding is 6 m/s. It is important to note that this calculation assumes ideal conditions and does not take into account other factors such as the condition of the tires, the road surface, and any external forces acting on the car. It is always recommended to drive at a safe and reasonable speed, considering all the factors that can affect the vehicle's stability and control.
Community Answer
The maximum speed with which a car can be driven round a curve of radi...
V=(coeff.of friction×r×g)^1/2
v=(.2×18×10)^1/2
v=6 m/s
v=(.2×18×10)^1/2
v=6 m/s
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The maximum speed with which a car can be driven round a curve of radius 18m without skidding (when g=10m/s^2 and the coefficient of friction between rubber tyres and roadway is 0.2) is ?
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The maximum speed with which a car can be driven round a curve of radius 18m without skidding (when g=10m/s^2 and the coefficient of friction between rubber tyres and roadway is 0.2) is ? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about The maximum speed with which a car can be driven round a curve of radius 18m without skidding (when g=10m/s^2 and the coefficient of friction between rubber tyres and roadway is 0.2) is ? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The maximum speed with which a car can be driven round a curve of radius 18m without skidding (when g=10m/s^2 and the coefficient of friction between rubber tyres and roadway is 0.2) is ?.
The maximum speed with which a car can be driven round a curve of radius 18m without skidding (when g=10m/s^2 and the coefficient of friction between rubber tyres and roadway is 0.2) is ? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about The maximum speed with which a car can be driven round a curve of radius 18m without skidding (when g=10m/s^2 and the coefficient of friction between rubber tyres and roadway is 0.2) is ? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The maximum speed with which a car can be driven round a curve of radius 18m without skidding (when g=10m/s^2 and the coefficient of friction between rubber tyres and roadway is 0.2) is ?.
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