Answer to Question #145004 in Physics for Jamie

Question

If you’ve been a passenger in a car travelling quickly over a hill you may have experienced a moment of weightlessness at the top.  A 1750-kg car drives over the top of a circular hill with a 28-meter radius of curvature. 

1. Calculate the magnitude of the normal force when the car is travelling 55 km/h.
2. How fast (in km/h) must the car be travelling for the occupants to feel weightless at the top of the hill.

Answer 1

The magnitude of the normal force when the car is travelling 55 km/h is

$$N=mg-ma_c=m\bigg(g-\frac{v^2}{R}\bigg)=2561\text{ N}.$$

To feel weightless (i.e. when N=0), they must acquire a speed of

$$v=\sqrt{gR}=16.57\text{ m/s},$$

or 59.6 km/h.