You and your family take a road trip on a long holiday weekend. In a certain sec

Question

You and your family take a road trip on a long holiday weekend. In a certain section of the trip where the road is particularly uneven, the car goes over a bump that is curved downward with a radius of 20.0 m. See diagram below. The mass of the car and its passengers is 1450 kg.

(a)

When the car is at the highest point of the bump its speed is 6.75 m/s. Determine the magnitude, in N, and the direction of the force exerted by the road on the car at this highest point.

(b)

If the speed at the highest point is above a certain maximum value the car will lose contact with the road. Calculate this maximum speed in m/s.

m/s

Explanation / Answer

Given

radius of the curve is r = 20.0 m

mass is m = 1450 kg ,

speed at highest point of the bump is v = 6.75 m/s

a) the force the force exerted by the road on the car at this highest point is

N = mg - mv^2/r

N = 1450*9.8-1450*6.75^2/20 N

N = 10906.71875 N

b) the maximum speed is

mg = mv^2/r

v = sqrt(g*r)

v = sqrt(9.8*20) m/s

v = 14 m/s

if the speed of the car is greater than 14 m/s the car will lose contact with the road.

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