Driving in your car with a constant speed of 12 m/s, you encounter a bump in the

Question

Driving in your car with a constant speed of 12 m/s, you encounter a bump in the road that has a circular cross section, as shown below. If the radius of curvature of the bump is r = 39 m,

a.) find the apparent weight of a 78 kg person in your car as you pass over the top of the bump.
___ N

b.) What is the maximum speed at which you can go over this bump, where your car will not lose contact with the road and fly off the bump? ___ m/s

Driving in your car with a constant speed of 12 m/s, you encounter a bump in the road that has a circular cross section, as shown below. If the radius of curvature of the bump is r = 39 m, a.) find the apparent weight of a 78 kg person in your car as you pass over the top of the bump. ___ N b.) What is the maximum speed at which you can go over this bump, where your car will not lose contact with the road and fly off the bump? ___ m/s

Explanation / Answer

A. Fc = 78*12^2/39 = 288 N
Weight of person = 78 * 9.8 = 764.4
Apparent weight = 764.4 - 288 = 476.4 N

B. For people to feel weightless, Fn = 0
Substituting Fn = 0
M(g - v^2/r) = Fn = 0
g = v^2/r
v^2 = gr
v = sqrt(gr)
v = sqrt(9.8 * 39)
v = 19.54 m/s

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