A roller -coaster car a mass of `500 kg` when fully loaded with passengers

a. If the vehicle has a speed of `20.0ms^(-1)` at point A what is the force exerted by the track on the car at this point ?
b. What is the maximum speed the vehicle can have at point B and still remain on the track?

Explanation

a. `v = 20.0ms^(-1), N_(A) = `force of track on roller conster and `R = 10 m`

`N_(A)= mg + (Mv^(2))/(R )`
`= (500 kg)(10 ms^(-2)) + ((500 kg)(20 m//s)^(2))/(10.0 m)`
`N_(A) = 500 N + 20.000 N = 2.50 xx 10^(4) N`
b. At` B` point
`Mg - N_(B) = (Mv^(2))/(R )`
For maximum velocity at `B, N_(B)` should be zero
`Mg = (Mv_(max)^(2))/(R )`
`v_(max) = sqrt(Rg) = sqrt(15.0 (10.0)) = 3 sqrt(6)ms^(-1)`