Question

A roller coaster is designed so that at the very top of a particular hill, the riders need the seat belt to keep them from flying out of their seats. In fact, the seatbelts have to pull down on the riders with a force equal to half the weight of the riders.
How fast is the coaster moving at the top of this hill if its circular radius is $25.0m$ (Radius measured from center of circular hill to the seat of the coaster.)?

• A. $2.55m/s$
• B. $19.2m/s$
• C. $17.2m/s$
• D. $15.7m/s$
• E. $245m/s$

Answer 1

The correct option is B $19.2m/s$

Given : $T=\frac{1}{2}mg$ $g=9.8m/s^2$ $r=25.0$ m

From figure, $\frac{m{v}^2}{r}=T+mg$

OR $\frac{m{v}^2}{r}=\frac{mg}{2}+mg$ $⟹v=\sqrt{\frac{3}{2}gr}$

$\therefore$ $v=\sqrt{\frac{3}{2}\times 9.8\times 25.0}=19.2$ $m/s$