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!

Simple particle on slope confusion

  1. Jun 5, 2015 #1
    1. The problem statement, all variables and given/known data
    a particle on a slope with angle theta with no friction. v(0) = 0, x(0) = 0, with coordinates i down the slope and j normal to it.

    I am confused about why with the constant velocity forumla I get a different answer to my attempted method.. I cant see whats wrong..


    I need to find the velocity at "l"
    x is the top of the slope of a particle on a smooth surface, with no friction,
    v(0) = 0, x(0) = 0

    along i direction I am starting with:

    mgsin(theta) == ma

    gsin(theta) == a

    using constant acceleration formula

    v^2 = v0^2 + 2a0(x-x0)
    v^2 = 0 + 2gsin(theta)(x-0)
    v = sqrt( 2gl*sin(theta) )

    My original attempt below is wrong, but I cant see why. I want to know what it doesn't work the same.

    so from
    gsin(theta) == a

    Integrating wrt t

    gsin(theta)t == v + c

    Integrating wrt t again

    1/2*gsin(theta)t^2 == x + ct + d

    with v(0) == 0 and x(0) == 0

    0 = c and d = 0

    so if I now plugged in 'l' to the equation for position

    1/2*gsin(theta)t^2 == l

    and solve for t I get,

    t = sqrt[ (2l)/(gsin(theta)) ]

    so this is the time at which position == l ?

    If I then plug this time into the equation for velocity,

    gsin(theta)t == v

    gsin(theta)*sqrt[ (2l)/(gsin(theta)) ] = v

    not the same as with the constant velocity forumla..
    why ? what is wrong with this method

    Thanks for any help
     
  2. jcsd
  3. Jun 5, 2015 #2

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

     
  4. Jun 5, 2015 #3
    If I plug in numbers I get a different answer for both??
     
  5. Jun 5, 2015 #4

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    Example ... ?
     
  6. Jun 5, 2015 #5
    Looks like I did something wrong when I checked it. I was so sure that my formula must be wrong (as it was a different way to the book and done by me) I didn't check twice.

    You are right, and with some simple rearranging it comes out the same... thank you for your help.
     
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: Simple particle on slope confusion
Loading...