Aflat (unbanked) curve on a highway has a radius of 170.0 m. a car rounds the curve at a speed of 25.0 m> s. (a) what is the minimum coefficient of static friction that will prevent sliding? (b) suppose that the highway is icy and the coefficient of static friction between the tires and pavement is only one-third of what you found in part (a). what should be the maximum speed of the car so that it can round the curve safely?

When a vehicle is moving on rough unbanked road then the centripetal force on the vehicle is provided by friction force to take a safe turn

now we can write

here

v = 25 m/s

R = 170 m/s

now we can find the friction coefficient by above equation

so minimum friction coefficient needed is 0.375

Part b)

now again if we have friction coefficient is half of this what we calculated above

then we can find the safe speed by same equation

so here maximum safe speed is 17.67 m/s

Explanation:

Radius of the curve, r = 170 m

Speed of the car, v = 25 m/s

(a) Let is the coefficient of static friction that will prevent sliding. The centripetal force is balanced by the force of static friction as :

(b) Let v' is the maximum speed of the car so that it can round the curve safely if the coefficient of static friction between the tires and pavement is only one-third of what you found in part (a).

It is calculated as :

v' = 14.43 m/s

Hence, this is the required solution.

it is the second option.

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