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The coefficient of friction between the rubber tyres and the road way is 0.25. The maximum speed with which a car can be driven round a curve of radius 20 m without skidding is (g = 9.8 m/s2)
- a)5 m/s
- b)7 m/s
- c)10 m/s
- d)14 m/s
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
The coefficient of friction between the rubber tyres and the road way ...
μ mg = mv2 / r or v = 
or v =
= 7 m / s
or v =
= 7 m / sMost Upvoted Answer
The coefficient of friction between the rubber tyres and the road way ...
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 compare it to the maximum frictional force that can be provided by the tires.
1. Centripetal Force:
The centripetal force required to keep the car moving in a circular path is given by the equation:
F = m * v^2 / r
where F is the centripetal force, m is the mass of the car, v is its velocity, and r is the radius of the curve.
2. Frictional Force:
The maximum frictional force that can be provided by the tires is given by:
F_friction = μ * N
where F_friction is the frictional force, μ is the coefficient of friction, and N is the normal force acting on the car.
3. Equating Forces:
To find the maximum speed without skidding, we equate the centripetal force with the frictional force:
m * v^2 / r = μ * N
4. Normal Force:
The normal force can be calculated as:
N = m * g
where g is the acceleration due to gravity.
5. Substituting Values:
Substituting the values given in the problem, we have:
m * v^2 / r = μ * m * g
6. Simplifying and Solving:
Canceling the mass term on both sides, we get:
v^2 / r = μ * g
v^2 = μ * g * r
v = √(μ * g * r)
Substituting the given values, we have:
v = √(0.25 * 9.8 * 20) ≈ 7 m/s
Therefore, the maximum speed at which the car can be driven around the curve without skidding is approximately 7 m/s. Hence, option B is the correct answer.
1. Centripetal Force:
The centripetal force required to keep the car moving in a circular path is given by the equation:
F = m * v^2 / r
where F is the centripetal force, m is the mass of the car, v is its velocity, and r is the radius of the curve.
2. Frictional Force:
The maximum frictional force that can be provided by the tires is given by:
F_friction = μ * N
where F_friction is the frictional force, μ is the coefficient of friction, and N is the normal force acting on the car.
3. Equating Forces:
To find the maximum speed without skidding, we equate the centripetal force with the frictional force:
m * v^2 / r = μ * N
4. Normal Force:
The normal force can be calculated as:
N = m * g
where g is the acceleration due to gravity.
5. Substituting Values:
Substituting the values given in the problem, we have:
m * v^2 / r = μ * m * g
6. Simplifying and Solving:
Canceling the mass term on both sides, we get:
v^2 / r = μ * g
v^2 = μ * g * r
v = √(μ * g * r)
Substituting the given values, we have:
v = √(0.25 * 9.8 * 20) ≈ 7 m/s
Therefore, the maximum speed at which the car can be driven around the curve without skidding is approximately 7 m/s. Hence, option B is the correct answer.
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The coefficient of friction between the rubber tyres and the road way ...
Answer ( B ) 7m/s
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The coefficient of friction between the rubber tyres and the road way is 0.25. The maximum speed with which a car can be driven round a curve of radius 20 m without skidding is (g = 9.8 m/s2)a)5 m/sb)7 m/sc)10 m/sd)14 m/sCorrect answer is option 'B'. Can you explain this answer?
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