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!

Dynamics Question: What is the velocity of a car traveling on a known curvature

  1. Mar 1, 2012 #1
    Hi all,

    I'm trying to write a Matlab simulation that determines the velocity of a car of known mass and moment of inertia which travels on a track whose curvature is also known.

    To say the least, I'm at a loss as to what approach I should take to create my simulation. I'm finding it somewhat difficult to grasp the physics of the situation. The free body diagram is easy enough, but I can't recall how to couple this information with the constraint that the cart is confined to roll on the path.

    If someone could provide some hints or a resource that I can read, I'd really appreciate it.


    Thanks,

    -PN
     
  2. jcsd
  3. Mar 2, 2012 #2
    I've given this some thought, was wondering if some higher up could check my reasoning/math:

    Coordinate system: x,y conventional.

    Say we have a ramp given by the cubic function: [itex]y(x)[/itex] = a[itex]x^{3}[/itex] + b[itex]x^{2}[/itex] + [itex]cx[/itex] + d

    If we start the cart at x = 0 and y = [itex]y_{0}[/itex], where [itex]y_{0}[/itex], is a maximum, the kinetic energy at any point is

    Kinetic Energy T = [itex]\frac{1}{2}[/itex]M[itex]v_{x}(t)^{2}[/itex] + [itex]\frac{1}{2}[/itex]I[itex]ω^{2}[/itex] = mg([itex]y_{0}[/itex] - [itex]y(t)[/itex])

    Assuming roll without slip condition: ω = [itex]\frac{v_{x}}{R}[/itex] and some simplification we get:
    T = C[itex]v_{x}(t)^{2}[/itex] = mg([itex]y_{0}[/itex] - [itex]y(t)[/itex]) where C is some constant.

    In order to get the equation solely in terms of [itex]x(t)[/itex] and [itex]v_{x}(t)[/itex], we can substitute [itex]y(t)[/itex] for the cubic function [itex]y(x)[/itex], which is implicitly a function of time through x.

    By integrating both sides of the equation now, we can get a function for [itex]x(t)[/itex], which we can plug back into [itex]y(x)[/itex] to get [itex]y(t)[/itex].


    Alright, how far off am I?



    Thanks in advance,

    -AN
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Dynamics Question: What is the velocity of a car traveling on a known curvature
  1. Car Velocity question (Replies: 2)

Loading...