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(a) Find the maximum speed at which a ve...

(a) Find the maximum speed at which a vehicle can turn round a curve of `20m` radius on a level road, `mu_(s)=0.5`.
(b) A circular track of radius `100 m` is to be designed for vehicles at an average speed of `72km//h`. Find the angle of banking of the track.

Text Solution

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(a) Maximum speed for no slipping or skidding
`v_(max)=sqrt(mu_(s)Rg)`
`=sqrt(0.5xx20xx10)`
`=10m//s`
(b) `tan theta=(v^(2))/(Rg),v=72km//h=72xx(5)/(18)=20m//s`
`=(20xx20)/(100xx10)=(2)/(5)=0.4`
`theta=tan^(-1)(0.4)`
where `theta` is the angle of banking.
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Knowledge Check

  • A circular track of radius 600 m is tio be designed for cars at an average speed of 180 km/hr. What should be the angle of banking of the track?

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    D
    `tan^-1 (5/2)`

  • A circular track of radius 600 m is to be designed for vehicles passing at an average speed of 54 km/hr. The required angle of banking is :

    A
    `tan^(-1)(3/40)`
    B
    `tan _(1) (3/20)`
    C
    `tan^(-1)(3/16)`
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    `theta=tan^(-1)((1)/(8))`
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