1. Not finding help here? Sign up for a free 30min 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!

Car accelerated by repulsion of two point charges

  1. Oct 13, 2015 #1
    At the outset, I want to explain that this is a problem I came up with myself. It's not actually homework, and I suspect it is deeply conceptually flawed in some manner that I have yet to determine.

    1. Two point charges of like polarity, ## q_1 = q_2 = 1C ##, start out separated by distance ## x = 1m ##. ##q_2## is attached to a car of mass ##m=1000kg##. When released, the car is accelerated by the force repelling the two charges. Find a function ## v(t) ## which gives the speed at time t.



    2. Relevant equations

    $$ F = k \frac{q_1 q_2}{x^2} $$

    $$ a = \frac{F}{m} $$

    $$ v = a t $$

    Potential Energy

    $$ U = k \frac{q_1 q_2}{x} $$

    Kinetic Energy

    $$ K = \frac{1}{2} m v^2 $$



    3. The attempt at a solution

    This has been giving me fits. I keep ending up in circular definitions. Firstly, I approach from the perspective of energy, ## U_0 = K_f ##. The end result of that was that the final speed should be ## 3.16*10^3 \frac{m}{s} ##.

    ## F ## becomes: $$ F = \frac{k}{x^2} $$

    Inserting into Newton's second law I get:

    $$ a = \frac{k}{m x^2} $$


    Then:

    $$ v = \frac{k}{m x^2} t $$

    You'll notice my problem. Through some means, I have to express ## x ## in terms of ## t ##, but every idea I've had relies, ultimately, on ## x ##. Truthfully, to list the approaches I've tried in detail here would require quite some typing. I feel intuitively that there ought to be some way to solve this, but frankly I'm at a loss. Any assistance you can provide in pointing me in the right direction would be greatly appreciated.
     
  2. jcsd
  3. Oct 13, 2015 #2

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    Ok.
    Not ok.
    x is a variable. You cannot integrate x-2 by simply multiplying by t.

    You can use energy conservation to find the velocity as a function of position, but getting it as a function of time is quite tricky.
     
  4. Oct 15, 2015 #3
    Thanks! Your help is greatly appreciated.

    I've been wondering if perhaps this would be a good application of the laplace transform?
     
  5. Oct 15, 2015 #4

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

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

Have something to add?
Draft saved Draft deleted



Similar Discussions: Car accelerated by repulsion of two point charges
  1. Two point charges (Replies: 7)

Loading...