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Simple Dynamics Problem Requiring Explanation

  1. Feb 28, 2016 #1
    1. The problem statement, all variables and given/known data

    Boxes are placed on a slope at uniform intervals of time trelease and slide down the slope with uniform acceleration. Knowing that as a box B is released, the preceding box A has slid 6 meters down the slope and that 1 second later they are 10 meters apart, determine the following:

    (a) The value of trelease

    (b) The acceleration of the boxes.

    2. Relevant equations
    ΔV = a⋅Δt
    Δx=Vi⋅t+½⋅a⋅t2
    2⋅a⋅Δx=Vf2-Vi2

    3. The attempt at a solution
    This problem isn't actually homework, I'm just studying. I'm posting the solution to the problem because I simply don't understand how exactly they arrive at the equations that they do. Here it is:

    http://i.imgur.com/oSyIFsm.png

    For example, equation (2) doesn't make sense to me as t = tr + 1, yet in the problem t = 1. Also, how come in eqn. (3) they don't employ the 10 m @ t=tr+1? Why is Δx simply xA@tr+1?
     
  2. jcsd
  3. Feb 28, 2016 #2
    When using the equations of motion listed you need to put the time interval that the particle has been under that constant acceleration.
    When Box B is released: Box A has already been travelling for "tr" time. Box B has travelled for "Zero" time.
    After 1 second of releasing Box B: Box A has travelled for "tr time PLUS One extra second". Box B has only travelled for "1 second".

    Coming to Eq. 3:
    Notice that the diagram isn't drawn properly. After 1 second both the boxes would have travelled a certain distance from their initial position. The distance between them is given to be 10m. So you need to use (xb - xa) = 10 @t=tr+1.
     
  4. Feb 28, 2016 #3
    That really clears it up. Thank you, I appreciate that.
     
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