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Math Help - Collisions (physics problem)

  1. #1
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    Collisions (physics problem)

    In a game of marbles, a purple marble makes an off-center collision with a red marble of the same mass. Before the collision, the purple marble travels in the positive x direction and the red marble is at rest. After the collision, the purple marble's velocity of 0.0900 m/s makes a 35.0 degree angle above the positive x axis and the red marble's velocity makes an angle of negative 20.0 degrees with the axis. Find the initial speed of the purple marble.

    I think this is a completely elastic collision which means the kinetic energy is conserved. The momentum is also conserved. I'm a bit lost on how to do the problem because it doesn't tell me what is the red marble's final velocity (maybe I don't need it...).

    Thank you!
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  2. #2
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    I'm not entirely sure if this is correct, but if it's not, it's at least a step in the right direction.

    First, you shouldn't need the red marble's final velocity because you need conserve energy in both the x and y dimensions, which will allow you to set up a system of equations. This system will have 2 unknowns, so you can just express the red marble's velocity in terms of the purple's.

    First, you want to set it up so that the energy equation in the x direction is as follows (P.S. I factored out, and divided the 1/2*m factor because it is a like factor)

    \vec{V_{1}}^2=(\vec{V_{2}}\cos(35))^2+(\vec{V_{3}}  \cos(20))^2

    Doing the same for the y dimension, we get the following

    0=(\vec{V_{2}}\sin(35))^2-(\vec{V_{3}}\sin(20))^2

    Using the latter, we can express \vec{V_{3}} in terms of \vec{V_{2}} by solving for \vec{V_{3}}

    You should get \vec{V_{3}}=\vec{V_{2}}\frac{\sin(35)}{\sin(20)}

    When we replace the \vec{V_{3}} with the solution we just got, we get the equation \vec{V_{1}}^2=(\vec{V_{2}}\cos(35))^2+(\vec{V_2}\c  ot(20)\sin(35))^2

    or

    \vec{V_{1}}=\sqrt{(\vec{V_{2}}\cos(35))^2+(\vec{V_  2}\cot(20)\sin(35))^2}
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  3. #3
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    Quote Originally Posted by Linnus View Post
    In a game of marbles, a purple marble makes an off-center collision with a red marble of the same mass. Before the collision, the purple marble travels in the positive x direction and the red marble is at rest. After the collision, the purple marble's velocity of 0.0900 m/s makes a 35.0 degree angle above the positive x axis and the red marble's velocity makes an angle of negative 20.0 degrees with the axis. Find the initial speed of the purple marble.

    I think this is a completely elastic collision which means the kinetic energy is conserved. The momentum is also conserved. I'm a bit lost on how to do the problem because it doesn't tell me what is the red marble's final velocity (maybe I don't need it...).

    Thank you!
    I don't have much time for right now, but I can send you down the right path.

    Momentum is conserved in both the x and y directions (using the typically coordinate system.) So we have that, in the x direction:
    mv_{p0} = mv_{px} + mv_{rx}

    or
    mv_{p0} = m(0.0900)~cos(35) + mv_r~cos(20)

    and in the y direction:
    0 = mv_{py} + mv_{ry}

    or
    0 = m(0.0900)~sin(35) - mv_r~sin(20)

    As this is enough to solve the system, and we know that momentum has to be conserved, we should not assume that energy is.

    -Dan
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  4. #4
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    Ah yes...I totally meant to do my post assuming conserving momentum, not energy.

    *slaps forehead*

    Sorry for that
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