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The outer side of a circular track of radius 200 m is raised to make an angle of 150 with the horizontal. a) Which force provides the necessary centric petal force for a car taking the circular track? b) Name the process by which the outer side of a curved track is raised a little above the inner side. c) Using the data provided in this case, determine the maximum permissible speed to avoid skidding (given s = 0.25 ).?
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The outer side of a circular track of radius 200 m is raised to make a...
B) Name the process by which the outer side of a curved track is raised a little above the inner side.
The process by which the outer side of a curved track is raised a little above the inner side is called banking or superelevation.
c) Determining the maximum permissible speed to avoid skidding:
To determine the maximum permissible speed to avoid skidding, we need to consider the centripetal force acting on the car as it goes around the curved track. The centripetal force is responsible for keeping the car moving in a circular path.
The centripetal force is provided by the friction between the car's tires and the track. The maximum friction force that can be exerted before the car starts skidding is given by the equation:
F_friction = μ_s * m * g
Where:
F_friction is the maximum friction force,
μ_s is the coefficient of static friction between the tires and the track,
m is the mass of the car, and
g is the acceleration due to gravity.
In this case, the angle of banking (θ) is given as 150 degrees. The vertical component of the normal force (N) acting on the car is given by:
N = m * g * cos(θ)
The horizontal component of the normal force provides the necessary centripetal force for the car to move in a circular path. It is given by:
F_centrifugal = m * v^2 / R
Where:
F_centrifugal is the centripetal force,
v is the velocity of the car, and
R is the radius of the circular track.
To avoid skidding, the maximum friction force (F_friction) should be greater than or equal to the centripetal force (F_centrifugal).
Setting F_friction = F_centrifugal, we have:
μ_s * m * g = m * v^2 / R
Simplifying the equation, we can solve for the maximum permissible speed (v):
v = √(μ_s * g * R)
Substituting the given values into the equation:
μ_s = 0.25 (given)
g = 9.8 m/s^2 (acceleration due to gravity)
R = 200 m (radius of the circular track)
v = √(0.25 * 9.8 * 200)
v = √490
v ≈ 22.14 m/s
Therefore, the maximum permissible speed to avoid skidding on this circular track is approximately 22.14 m/s.
The process by which the outer side of a curved track is raised a little above the inner side is called banking or superelevation.
c) Determining the maximum permissible speed to avoid skidding:
To determine the maximum permissible speed to avoid skidding, we need to consider the centripetal force acting on the car as it goes around the curved track. The centripetal force is responsible for keeping the car moving in a circular path.
The centripetal force is provided by the friction between the car's tires and the track. The maximum friction force that can be exerted before the car starts skidding is given by the equation:
F_friction = μ_s * m * g
Where:
F_friction is the maximum friction force,
μ_s is the coefficient of static friction between the tires and the track,
m is the mass of the car, and
g is the acceleration due to gravity.
In this case, the angle of banking (θ) is given as 150 degrees. The vertical component of the normal force (N) acting on the car is given by:
N = m * g * cos(θ)
The horizontal component of the normal force provides the necessary centripetal force for the car to move in a circular path. It is given by:
F_centrifugal = m * v^2 / R
Where:
F_centrifugal is the centripetal force,
v is the velocity of the car, and
R is the radius of the circular track.
To avoid skidding, the maximum friction force (F_friction) should be greater than or equal to the centripetal force (F_centrifugal).
Setting F_friction = F_centrifugal, we have:
μ_s * m * g = m * v^2 / R
Simplifying the equation, we can solve for the maximum permissible speed (v):
v = √(μ_s * g * R)
Substituting the given values into the equation:
μ_s = 0.25 (given)
g = 9.8 m/s^2 (acceleration due to gravity)
R = 200 m (radius of the circular track)
v = √(0.25 * 9.8 * 200)
v = √490
v ≈ 22.14 m/s
Therefore, the maximum permissible speed to avoid skidding on this circular track is approximately 22.14 m/s.
Community Answer
The outer side of a circular track of radius 200 m is raised to make a...
A) a component of the normal reaction provides the necessary centripetal force.
B) banking of a curve.
c) v=(mu ×r×g)^1/2
=10√5 m/s....
B) banking of a curve.
c) v=(mu ×r×g)^1/2
=10√5 m/s....
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The outer side of a circular track of radius 200 m is raised to make an angle of 150 with the horizontal. a) Which force provides the necessary centric petal force for a car taking the circular track? b) Name the process by which the outer side of a curved track is raised a little above the inner side. c) Using the data provided in this case, determine the maximum permissible speed to avoid skidding (given s = 0.25 ).?
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The outer side of a circular track of radius 200 m is raised to make an angle of 150 with the horizontal. a) Which force provides the necessary centric petal force for a car taking the circular track? b) Name the process by which the outer side of a curved track is raised a little above the inner side. c) Using the data provided in this case, determine the maximum permissible speed to avoid skidding (given s = 0.25 ).? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The outer side of a circular track of radius 200 m is raised to make an angle of 150 with the horizontal. a) Which force provides the necessary centric petal force for a car taking the circular track? b) Name the process by which the outer side of a curved track is raised a little above the inner side. c) Using the data provided in this case, determine the maximum permissible speed to avoid skidding (given s = 0.25 ).? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The outer side of a circular track of radius 200 m is raised to make an angle of 150 with the horizontal. a) Which force provides the necessary centric petal force for a car taking the circular track? b) Name the process by which the outer side of a curved track is raised a little above the inner side. c) Using the data provided in this case, determine the maximum permissible speed to avoid skidding (given s = 0.25 ).?.
The outer side of a circular track of radius 200 m is raised to make an angle of 150 with the horizontal. a) Which force provides the necessary centric petal force for a car taking the circular track? b) Name the process by which the outer side of a curved track is raised a little above the inner side. c) Using the data provided in this case, determine the maximum permissible speed to avoid skidding (given s = 0.25 ).? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The outer side of a circular track of radius 200 m is raised to make an angle of 150 with the horizontal. a) Which force provides the necessary centric petal force for a car taking the circular track? b) Name the process by which the outer side of a curved track is raised a little above the inner side. c) Using the data provided in this case, determine the maximum permissible speed to avoid skidding (given s = 0.25 ).? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The outer side of a circular track of radius 200 m is raised to make an angle of 150 with the horizontal. a) Which force provides the necessary centric petal force for a car taking the circular track? b) Name the process by which the outer side of a curved track is raised a little above the inner side. c) Using the data provided in this case, determine the maximum permissible speed to avoid skidding (given s = 0.25 ).?.
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