1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Time to complete a loop

  1. Jul 4, 2011 #1
    Calculate the time t to complete a loop of a rollercoaster of radius R by a car that has initial velocity Vo, with friction u.

    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 atrict


    Fc=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?
     
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted



Loading...