Physics Speed Question

Question

A car is going over a rounded hill with a radius of 50 meters. At what speed would the car’s occupants weigh ½ of their regular weight?

Answer 1

1st step is to draw a free body diagram of the car. At the top of the hill there are only two forces vertically, the Normal force N pointing up and weight mg pointing down.

Using Newton's 2nd law F_net = ma, we get F_net = mg-N = ma_c (taking down to be positive). The net force is non zero because we have acceleration in the form of centripetal acceleration a_c = v²/r pointing toward the center of the circle defined by the curvature of the road.

Weight of the car is half means N=(mg)/2. Substituting into the 2nd law and solving for v we get:

mg-(mg)/2 = m(v²/r)

(mg)/2 = m(v²/r)

g/2 = v²/r

v = sqrt(rg/2) = sqrt[(50m)(9.8m/s²)/2] = 15.7m/s