A roller coaster is designed such that riders experience 'weightlessness' as they go round the top o

Question

A roller coaster is designed such that riders experience 'weightlessness' as they go round the top of a hill whose radius of curvature is 90 m. The speed of the car at the top of the hill is (Take $g=10 \mathrm{~m/s}^2$)

Professor PC Thomas Classes · Answer

For weightlessness at the top of the hill, the required centripetal force is entirely provided by gravity, so normal force $N = 0$. $mg = \frac{mv^2}{R} \implies v = \sqrt{Rg}$. Substituting $R = 90 \mathrm{~m}$, $v = \sqrt{90 	imes 10} = 30 \mathrm{~m/s}$.