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!

Impulsive Tensions involving 3 particles

  1. Oct 2, 2015 #1
    1. The problem statement, all variables and given/known data
    Please help; I've been attempting this question for days now and cannot get very far.... Im desperate now

    Three identical particles X, Y, and Z of mass m are placed on a smooth horizontal
    table. X is joined to Y and Z by light (can be thought of as massless) inextensible
    strings XY and XZ. The angle XYZ is 60. An impulse I is applied to X in the
    direction YX. The strings act as constraints so that the initial motions of Y
    and Z must be the same as the components of the initial motion of X along YX
    and ZX, respectively. Determine the initial velocities of the particles.

    2. Relevant equations
    So I managed to get

    Vxcos(alpha)= Vy where alpha is the angle made by the horizontal and velocity of x
    Vxsin(alpha)= Vzsin(theta)
    I=2mVy+ mVzcos(theta)
    Vxcos(theta + alpha) = Vz
    3. The attempt at a solution
     
  2. jcsd
  3. Oct 2, 2015 #2

    TSny

    User Avatar
    Homework Helper
    Gold Member

    I suspect that your equations are correct. But, you didn't specify the meaning of the angle theta in your equations. It would have been helpful if you had stated that you are taking the string between X and Y to be horizontal.
     
  4. Oct 2, 2015 #3
    Oops- I forgot to mention that. Changing the orientation of it just makes the maths a bit easier I find. Do you have any advice as to where to go from here?
     
  5. Oct 2, 2015 #4
    I would write out the 2nd law equations as if there were a time-dependent force F(t) acting on X , rather than an impulsive force. Then I would integrate as if the force F were very large and imposed for a very short time.

    Chet
     
  6. Oct 2, 2015 #5

    TSny

    User Avatar
    Homework Helper
    Gold Member

    OK, your equations look correct. You have four equations for four unknowns. So now it's algebra.
    You might consider writing the equations in terms of the horizontal and vertical components of the velocity of X rather than the magnitude and direction of the velocity of X.
     
  7. Oct 2, 2015 #6

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    Did you mean YXZ?
     
  8. Oct 3, 2015 #7
    No it's the angle xyz. If it were yxz I could do it :/
     
  9. Oct 3, 2015 #8

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    If the only known angle is XYZ then you do not have enough information. Consider the case where XZ is extremely long. The angle YXZ could be obtuse, meaning that Z will not immediately move (the string XZ will go slack). Conversely, if XZ=XY then Y and Z could be at the same point.
     
  10. Oct 3, 2015 #9
    Yeah. The XYZ must be a typo.

    Physgeek64: Let's see what you come up with if you solve it with YXZ. Now that's an interesting (and challenging) problem.

    Chet
     
  11. Oct 3, 2015 #10
    I've solved it if I let yxz be 60 degrees. My big problem is if xyz is 60 because, as you've said, resolving momentum in the Xz direction is near impossible
     
  12. Oct 3, 2015 #11

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    If the given angle is XYZ then, as I have shown, solving the question is not near impossible - it is completely impossible. It has to be a typo.
    With YXZ as 60, you get fractions like 4/9 in the answer, yes?
     
  13. Oct 3, 2015 #12
    I got answers such as 7/15
     
  14. Oct 3, 2015 #13
    Can you please tell us what your results were for the x and y components of the three particle velocities. We would like to compare them with our results. Thanks.
     
  15. Oct 3, 2015 #14
    I get 7/15 also.
     
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: Impulsive Tensions involving 3 particles
  1. Impulsive Tensions (Replies: 1)

Loading...