A car is traveling at 30 m/s. The coefficient of kinetic friction between the ti

Question

A car is traveling at 30 m/s. The coefficient of kinetic friction between the tires and the road is ?k=0.8. What is the resulting deceleration of the car in the direction tangent to its path when the driver applies the brakes and the car’s wheels lock (a) when the car is at the top of a hill; (b) when the car is at the bottom of a depression curve? In both cases, the instantaneous radius of curvature of the car’s path is 200 m. (Hint: when the wheels lock in position, they are not able to rotate, the tires skid and the coefficient of kinetic frictions determines the braking force on the car.)

Explanation / Answer

a) when the car is at the top the hill

reaction force R = (mg + mv^2/ r)

friction force = uR

decelration = uR/m = (g+v^2/r)

decelration = 0.8*(9.8 + 30^2 / 200) = 11.44 m/s2

B) when the car is at the bottom of the curve

R = (mg - mv^2/r)    (R = reaction force)

friction force = uR

decelration = uR/m = (g-v^2/r)

decelration = 0.8*(9.8 - 30^2 / 200) = 4.24 m/s2

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