# Riders on the Behemoth roller coaster pass through a hammerhead turn at a speed of 122.4km/hr and experience a centripetal acceleration of 37.2m/s². How much force would a person that weighs 539N feel on this turn?

Nov 8, 2015

$1507 \text{N}$

#### Explanation:

I am assuming that this is a vertical loop.

To get the mass of the person we divide the weight by$\text{g} :$

$m = \frac{539}{9.8} = 55 \text{kg}$

At the top.of the ride the net force that the person feels will be the difference between the centripetal force and the weight:

$F = \frac{m {v}^{2}}{r} - m g$

We are told that the centripetal acceleration $= 37.2 {\text{m/s}}^{2}$

So ${v}^{2} / r = 37.2 {\text{m/s}}^{2}$

$\therefore F = \left(55 \times 37.2\right) - 539 = 1507 \text{N}$