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Three blocks colliding

  1. Nov 3, 2009 #1

    1. The problem statement, all variables and given/known data

    Two blocks (m1 = 0.02 kg, m2 = 0.03 kg, v1 = 1.5 m/s, v2 = 0.5 m/s) are sliding without friction on a surface. They are approaching each other at angle θ = 60º. In what direction and with how much velocity do we have to push the third block (m3 = 0.05 kg) against the first two blocks, so that when they crash they will come to rest?

    2. Relevant equations


    p=mv

    3. The attempt at a solution


    First two blocks:

    G(x)= m(2)v(2)*(-sin θ)
    G(y)= m(1)v(1) + m(2)*cos θ

    Third block:


    G(3x)= sin θ

    G(3y)= m(1)v(1) – m(2)v(2)*cos θ

    For the direction of the third block:

    tan θ’= m(2)v(2)*sin θ / m(10v(1) + m(2)v(2)*cos θ → θ’= 19.1º

    For the velocity of the third block:


    G(3)= m(3)v(3) → v(3)= G3 / m(3)

    G3= sqrt(m(1)²v(1)² + m(2)²v(2)² +2m(1)v(1)m(2)v(2)*cos θ)= 0.039686

    v(3)= G3 / m(3)= 0.79372 m/s

    Are my calculations correct?
     
  2. jcsd
  3. Nov 3, 2009 #2

    Delphi51

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    Homework Helper

    I'm getting different answers. Did you get
    G(x)= m(2)v(2)*(-sin θ) = .013
    G(y)= m(1)v(1) - m(2)*cos θ = .0225
     
  4. Nov 4, 2009 #3
    I retraced my steps and found out that I messed up big.

    Here is how, I think, it is supposed to be:

    First two blocks:

    G(x)= m(1)v(1) + m(2)v(2) cos θ= 0.0375
    G(y)= m(2)v(2) (-sin θ)= 0.013

    Third block:

    G(3(x))= -G(x)= -(m(1)v(1) + m(2)v(2) cos θ)= -0.0375
    G(3(y))= -G(y)= m(2)v(2) sin θ= -0.013

    For the direction of the third block:

    tan θ’= m(2)v(2)*sin θ / m(10v(1) + m(2)v(2)*cos θ → θ’= 19.1º

    For the velocity of the third block:

    G(3)= m(3)v(3) → v(3)= G3 / m(3)

    G3= sqrt(m(1)²v(1)² + m(2)²v(2)² +2m(1)v(1)m(2)v(2)*cos θ)= 0.039686

    v(3)= G3 / m(3)= 0.79372 m/s

    Are now my calculations correct?
     
  5. Nov 4, 2009 #4

    Delphi51

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    There are several ways to look at this question! We'll have to agree on a diagram before we can understand each other. Show yours or use mine:
    threeblocks.jpg
     
  6. Nov 4, 2009 #5
    This is how I approached the problem graphically.
     

    Attached Files:

  7. Nov 4, 2009 #6

    Delphi51

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    It will be at least a few hours until your attachment is approved so I can see it.
    An alternative is to upload the image to a free photo site such as photobucket.com and put a link to it here. If you can save the image as a jpg instead of bmp, it will be much smaller and faster to load.
     
  8. Nov 4, 2009 #7
    Here we go:

    http://www.slide.com/s/QrlHnyTY6D_vkTXmDIP5GFj8tT_LIBU0?referrer=hlnk [Broken]
     
    Last edited by a moderator: May 4, 2017
  9. Nov 4, 2009 #8

    Delphi51

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    Homework Helper

    Ah, that makes sense and your calcs are correct!
     
  10. Nov 5, 2009 #9
    Thank you for helping and have a nice day!:smile:
     
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