Question

while driving to work you pass over a "crest" or a "bump" in the road that has a radius of 30 meters. How fast would you need to be traveling to experience apparent weightlessness while passing over the crest?

Answer 1

Using force balance on the top of crest in vertical direction:

Fc = W - N

Fc = Centripetal force = m*V^2/R

W = Weight = m*g

m*V^2/R = m*g - N

Now given that we need speed for which you experience weightlessness while passing over the crest, So that means over the crest

N = 0, Which gives

m*V^2/R = m*g - 0

V^2/R = g

V^2 = g*R

V = sqrt (g*R)

given that radius of crest = R = 30 m

So,

V = sqrt (9.8*30)

V = Speed required for weightlessness = 17.146 m/s

V = 17.2 m/s

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