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Math Help - Inelastic collision of right angled bodies

  1. #1
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    Inelastic collision of right angled bodies

    1. The problem statement, all variables and given/known data
    Hi
    Can someone help with this problem.
    2 particles of mass 30g and 40g respectively both travel at a speed of 35m/s in directions at right angles. The 2 particles collide and stick together. Calculate their speed after impact.

    2. Relevant equations
    MaVa + MbVb =(Ma + Mb)v
    v= common velocity

    3. The attempt at a solution
    I am not sure how to start. Solving the total momentum before and total momentum after gives the original speed. I then resolved the respective velocities. But that means I got my final value without consideration of the masses! Finally, I resolved the masses into forces, but still didnt get anywhere. Where I am going wrong? Please advice
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by gbenguse78 View Post
    1. The problem statement, all variables and given/known data
    Hi
    Can someone help with this problem.
    2 particles of mass 30g and 40g respectively both travel at a speed of 35m/s in directions at right angles. The 2 particles collide and stick together. Calculate their speed after impact.

    2. Relevant equations
    MaVa + MbVb =(Ma + Mb)v
    v= common velocity

    3. The attempt at a solution
    I am not sure how to start. Solving the total momentum before and total momentum after gives the original speed. I then resolved the respective velocities. But that means I got my final value without consideration of the masses! Finally, I resolved the masses into forces, but still didnt get anywhere. Where I am going wrong? Please advice
    Since we are dealing with a two dimensional collision, we need to use the following formulas:

    \begin{aligned}m_1v_{1x_i}+m_2v_{2x_i}&=(m_1+m_2)v  _x\\m_1v_{1y_i}+m_2v_{2y_i}&=(m_1+m_2)v_y\end{alig  ned}

    Without loss of generality, I'm going to assume the following:

    * Each mass moves in the positive axis directions -- m_1=.03\,kg in the positive x direction, and m_2=.04\,kg in the positive y direction.

    So, with this information, we have the following:

    \begin{aligned}<br />
   (.03\,kg)(35\,m/s) &= (.03\,kg+.04\,kg)v_x\\ (.04\,kg)(35\,m/s) &= (.03\,kg+.04\,kg)v_y<br />
\end{aligned}

    With this, you should be able to find the x and y components of your velocity.

    Finally, your answer will be v=\sqrt{v_x^2+v_y^2}.

    Does this make sense? Can you finish this off?
    Last edited by Chris L T521; January 14th 2011 at 09:32 PM. Reason: inserted wrong mass values when I plugged everything in! :/
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  3. #3
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    Yes! Thanks.
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