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

Step-by-step 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 = (mv^2)/(r)` --- i.e. the centripetal force

So:

`F_n = F_(net) + mg`

`F_n = (mv^2)/(r) + mg`

`F_n = (500 * 24^2)/(10) + 500 * 9.8`

`F_n = 28800 + 4900`

`F_n = 33700N`