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What is the need for banking of tracks? ...

What is the need for banking of tracks? Draw free body diagram of a car negotiating a banked track [ Take friction into account]. Write the expression for maximum velocity to negotiate the curve safely.

Text Solution

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A vehicle moving along a curved path needs some centripetal force. If the path is banked. i.e., inclined with the horizontal , then the horizontal components of friction and normal reaction help to provide this centripetal force. The vehicle may attain a velocity greater than that if the path would have been horizontal along the curve.
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Knowledge Check

  • A car of mass 800 kg moves on a circular track of radius 40m . If the coefficient of friction is 0.5. then maximum velocity with which the car can move is

    A
    7 m/s
    B
    14 m/s
    C
    8 m/s
    D
    12 m/s

  • A car of mass 1000 kg negotiates a banked curve of radius 90 m on a frictionless road. If the banking angle is 45^@ , the speed of the car is

    A
    `30 mS^-1`
    B
    `5 mS^-1`
    C
    `10 mS^-1`
    D
    `20 mS^-1`

  • A car of mass 1000 kg negotiates a banked curve of radius 90 m on a frictionless road. If the banking angle is 45^@ the speed of the car is

    A
    `20 ms^(-1)`
    B
    `30 ms^(-1)`
    C
    `5 ms^(-1)`
    D
    `10 ms^(-1)`

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    This question has statement-I and statement-II of the four choices given after the statement.Choose the one that best describes the two statements Statement-I is true Statement-II is true Statement-II is a correct explanation of statement-I Statement-I is true Statement-II is true Statement-II is not a correct explanation of statement-I Statement--I is true , Statement-II is false Statement-I is false statement-II is true Both statement-I and statement-II are false Statement - I : As the frictional force increases, the safe velocity limit for taking a turn on an unbanked road also increases. Statement- II : banking of roads will increase the value of limiting velocity.

    Why are circular roads banked? Deduce an expression for maximum speed of a vehicle which can be achieved while taking a turn on the banked curved road neglecting friction.

    A road curve is banked so that there is no side thrust on the passengers in a car which negotiate the curve at 72 km/hr speed . Find the angle of banking for a circular curve making a 90^(@) turn in a distance of 157 m along the road.

    A circular race track of radiu 400 m is banked at an angle of 10^(@) . If the coefficient of friction between the wheels of a race car and the road is 0.2, what is the (i) optimum speed of the race car to avoid wear and tear on its tyres? maximum permissible speed to avoid slipping?

    A circular racetrack of radius 300 m is banked at an angle of 15^@ . If the coefficient of friction between the wheels of a race-car and the road is 0.2, what is the (a) optimum speed of the race- car to avoid wear and tear on its tyres, and (b) maximum permissible speed to avoid slipping ?

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