Consider a 1112 kg automobile as it passes over a hill on a road that follows th

Question

Consider a 1112 kg automobile as it passes over a hill on a road that follows the arc of a vertical circle of radius 48 m near its top. a) Show the forces acting on the car at the top of the hill. b) Find the normal force acting on the car when the car is at rest. c) Find the normal force acting on this car when it travels over the hill at 12 m/s. d) Find the maximum speed at which this car can pass over the hill without leaving contact with the road. Hint: it leaves the road when the normal force between it and the car is reduced to zero. e) Would a more massive vehicle lose contact with the road at a i) greater, ii) lesser, or iii) the same speed?Explain.

Explanation / Answer

a) normal up mg down

b) when at rest N - mg = 0

N = mg = 1112*9.81 = 10908 N

c) mg - N = mv^2/r

N = mg - mv^2/r = 1112*(9.81 - 12^2/48)=7573 N

d) leaves road when N = 0

so mg = mv^2/r

v = sqrt(gr) = sqrt(9.81*48)=21.7 m/s

e) mass canceled so iii same speed

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