Question A car travels at a constant speed of 30.0 mi/h (13.4 m/s) on a level ci

Question

Question A car travels at a constant speed of 30.0 mi/h (13.4 m/s) on a level circular turn of radius 50.0 m, as shown in the bird's eye view diagram in Figure a. (a) What minimum coefficient of static friction, between the tires and roadway will allow the car to make the circular turn without sliding? Hint: Draw a free body diagram of the car as viewed from behind, using Newton's second law to determine the net force in the radial and perpendicular directions, as shown in Figure b. (b) Suppose that the road is wet and the coefficient of static perpendicular friction is reduced to a value of 0.230. At what maximum speed can the car negotiate the turn without sliding out of control? ty radial

Explanation / Answer

Here ,

a) let the minimum coefficient of static friction is us

Now, Using second law of motion

us * m * g = m * v^2/r

us * 9.8 = 13.4^2/50

solving for us

us = 0.37

the minimum static friction needed is 0.37

b)

let the maximum speed is v

Now, Using second law of motion

us * m * g = m * v^2/r

0.230 * 9.8 = v^2/50

solving for v

v = 10.6 m/s

the maximum speed of the car is 10.6 m/s

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