Question

A roller coaster loaded with passengers has a mass of 2000 kg; the radius of curvature of the track at the lowest point of the track is 24 m. If the vehicle has a tangential speed of 18 m/s at this point, what force is exerted on the vehicle by the track?

Answer 1

Answer:

The force is exerted on the vehicle by the track is 46600 N

Explanation:

It is given that,

Mass of the roller coaster, m = 2000 kg

Radius of the circular track, r = 24 m

Tangential speed of the vehicle, v = 18 m/s

Let W is the weight of the roller coaster, F is the force is exerted on the vehicle by the track and $F_c$ is the centripetal force. So,

$F-mg=\dfrac{mv^2}{r}$

$F=m(\dfrac{v^2}{r}+g)$

$F=2000\times (\dfrac{(18)^2}{24}+9.8)$

F = 46600 N

So, the net force exerted on the vehicle by the track is 46600 N. Hence, this is the required solution.