- #1

jaumzaum

- 434

- 33

We can calculate the velcity V if we have alpha, the angle that the car is in the rollercoaster

acceleration in alpha = g.sen alpha - acceleration by atrictFc=N+g.cos alpha[itex]A(\alpha ) = g.sen\alpha - (v²/R + g.cos \alpha)u [/itex]and

[itex]V = \sqrt{Vo² + \int a.ds} [/itex]

The problem is now, I don't know how to solve the equation. I've tried to to this, but I don't know if it's right.

[itex]A(\alpha ) = g. (sen\alpha +cos \alpha u) -(v²/R) U [/itex]

[itex]A(\alpha ) = g. (sen\alpha +cos \alpha u) -(v²/R) u [/itex]

[itex] v² = g. (sen\alpha +cos \alpha u) - A (\alpha) .u/R [/itex]

[itex] Vo² + \int a.ds =( g. (sen\alpha +cos \alpha u) - A (\alpha)) .u/R [/itex][itex] a.ds = d(Vo²)- d(g. (sen\alpha +cos \alpha u)) .u/R - d(A (\alpha) .u/R [/itex]

[itex] a.ds = d(Vo²)- d(g. (sen\alpha +cos \alpha u)) .u/R - d(A (\alpha) .u/R) [/itex]Now we have a equation with da and ds, alpha = S/R so alpha depends on dS and da depends on a, ok, how do we integrate this?