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A car has to move on a level turn of rad...

A car has to move on a level turn of radius 45 m. If the coefficient of static friction between the tyre and the road is `mu_s=2.0,` find the maximum speed the car can take without skidding.

Text Solution

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Let the mass of the casr be M. The forces on the car are
a. Weight Mg downward
b. normal force N by the road upward
c. friction `f_s` by the road towards the centre.
The car is going on a horizontla circle of radius R, so it is accelerating. THe acceleration is towards the centre nd its magnitude is `v^2/R`, where v is the speed. For vertical direction, wcceleration =0. Resolving the forces in vertical and horizontal directions and aspplying Newton's laws we have
`N=mg
and `f_s=Mv^2/R`
As we arelooking for the for the maximum speed for no skidding, it is a case of limiting friction and hence `f_s=mu_sN=mu_sMg`
So, we have
`mu_sMg=Mv^2/R`
or `v^2=mu_sgR`.
Putting the values `v=sqrt(2xx10 m/s^2xx45m)`
`=30 m/s=108 km/hr`
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