Side view 1 You are driving clockwise (CW) on a horizontal road with Top view: r

Question

Side view 1 You are driving clockwise (CW) on a horizontal road with Top view: radius of curvature R at a constant speed. a Find the maximum possible speed that you could negotiate the curve without slipping on the road. b Suppose the curve has radius of curvature of 100m. The coefficient of static friction between dry rubber and concrete is about 0.9 and between rubber and icy concrete about 0.1. Calculate the maximum speed (in km/hr) at which you can safely drive under these different conditions. Hint. You must draw the above pictures so that the situation is clear and you need a FBD. Try a FBD of the side view of the car. Be super clear on the car's direction of motion and turning and the direction of the acceleration, which is centripetal! Remarks: The friction is static because the tire is not sliding on the road To find the maximum speed, set the static friction to be its maximum, f,.one says that the car is "on the verge of slipping". If the car drove any faster then the tires would slide on the road. Only when f, , mE iS the static friction related to the normal force s u, F where , is the coefficient of static friction. The coefficient of static friction is generally larger than the coefficient of kinetic friction ' If t on the verge of slipping, then the force of static friction is not proportional to the normal force. he car is not

Explanation / Answer

a)

the frictional force provides the necessasry centripetal force to move in circle

hence

fs = m vmax2 /r

us mg = m vmax2 /r

vmax = sqrt(us rg)

b)

r = 100 m

us = 0.9

hence

vmax = sqrt(us rg) =  sqrt(0.9 x 100 x 9.8) = 29.7 m/s

in km/hr = 106.92 km/h

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