Question

If the vehiche has a speed of 24.0 m/s at point a what is the force of the track on the vehicle at this point?

Answer 1

Question:

A roller-coaster vehicle has a mass of 500 kg when fully loaded with passengers.  If the vehicle has a speed of 20.0 m/s at point A, what is the force exerted by the track on the vehicle at this point?

See attachment

Answer:

33700 Newton

Explanation:

Given

$m = 500kg\\v = 24.0m/s\\r=10m$

First, we determine the forces acting on mass m.

They are: the force exerted by the track (Fn) and the weight of the vehicle (W)

So, the net force is:

$F_{net} = F_n - W$

$W=mg$

So:

$F_{net} = F_n - mg$

Make Fn the subject

$F_n = F_{net} + mg$

Fnet is calculated as:

$F_{net} = F_c = \frac{mv^2}{r}$ --- i.e. the centripetal force

So:

$F_n = F_{net} + mg$

$F_n = \frac{mv^2}{r} + mg$

$F_n = \frac{500 * 24^2}{10} + 500 * 9.8$

$F_n = 28800 + 4900$

$F_n = 33700N$