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Math Help - Collision question.

  1. #1
    Junior Member silvercats's Avatar
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    Collision question.

    10KG ball travels at a speed(velocity) of 5ms and hits a 4KG balls which is travelling at the speed of 2ms and travelling to the same direction and 1st one.what are the velocities of two balls after the collision.

    take e=1/2

    I did this but never got the answer in the back of the book.here is how i did
    it
    M1 <<< doesn't mean M multipied by 1.it is just the notation

    by using
    (M1*U1 + M2*U2) = (M1*V1 + M2*V2) ---->(left drirection)

    10*5 + 4*2=10*V1 + 4*v2 =
    58=10*V1 + 4*v2 ------ (1)

    using e(U1+U2)=V1+V2
    1/2*(5-2)=V2-V1
    =(3/2)=V2-V1 -------(2)[!--?can somebody tell me why is this 5-2,not 5+2
    even they are travelling to the same direction?(book says so,that is why i
    substracted them]

    (2) equation * 4
    and (1)eq-multiplied (2)nd equation gives:

    58-6=10*V1+4V2 - 4*V2+4*V1
    52=14V1
    v1=13

    but that is not the answer given on the book.what is the error?

    thanks.
    Last edited by mr fantastic; May 5th 2011 at 08:06 PM. Reason: Deleted excessive use of ellipses in title.
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  2. #2
    Senior Member bugatti79's Avatar
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    Quote Originally Posted by silvercats View Post
    10KG ball travels at a speed(velocity) of 5ms and hits a 4KG balls which is travelling at the speed of 2ms and travelling to the same direction and 1st one.what are the velocities of two balls after the collision.

    take e=1/2

    I did this but never got the answer in the back of the book.here is how i did
    it
    M1 <<< doesn't mean M multipied by 1.it is just the notation

    by using
    (M1*U1 + M2*U2) = (M1*V1 + M2*V2) ---->(left drirection)

    10*5 + 4*2=10*V1 + 4*v2 =
    58=10*V1 + 4*v2 ------ (1)

    using e(U1+U2)=V1+V2
    Your error is the restitution equation. It should be

    \displaystyle \frac{v_2 - v_1}{u_1 - u_2}
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  3. #3
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by silvercats View Post
    using e(U1+U2)=V1+V2
    1/2*(5-2)=V2-V1
    =(3/2)=V2-V1 -------(2)[!--?can somebody tell me why is this 5-2,not 5+2
    even they are travelling to the same direction?(book says so,that is why i
    substracted them]

    (2) equation * 4
    and (1)eq-multiplied (2)nd equation gives:

    58-6=10*V1+4V2 - 4*V2+4*V1
    52=14V1
    v1=13

    but that is not the answer given on the book.what is the error?

    thanks.
    There are two errors, actually. First is the one bugatti79 pointed out. Actually u2 - u1 = 2 - 5 = -3 because both objects are moving in the positive direction before the collision.

    I get v1 = 32/7 = 4.571 m/s and v2 = 43/14 = 3.071 m/s.

    IMPORTANT: Also note that the unit for mass is kg not KG. Also the unit for speed is m/s not ms.

    -Dan
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  4. #4
    Junior Member silvercats's Avatar
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    book's back side says 26/7 ,73/14 O.o :/
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  5. #5
    Senior Member bugatti79's Avatar
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    Quote Originally Posted by silvercats View Post
    book's back side says 26/7 ,73/14 O.o :/
    Which is what i got.

    The 2 equations are

    58=10V1+4V2 ( You have this)
    1.5=-V1+V2 (You didnt have this because of incorrect restitution formula)
    Note that u1 =5 and u2=2

    make sense?
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  6. #6
    Junior Member silvercats's Avatar
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    yes.but why is that it is v2-v1 and not v1-v2
    and it is u1-u2 not u2-u1 if direction is not the problem but relative velocity?
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  7. #7
    Junior Member silvercats's Avatar
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    I get v1 = 32/7 = 4.571 m/s and v2 = 43/14 = 3.071 m/s.
    book's back side says 26/7 ,73/14 O.o :/
    has topsquark made a mistake?it looks like it
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  8. #8
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by silvercats View Post
    has topsquark made a mistake?it looks like it
    Why trust the book's answers? Or mine for that matter? Plug them into the equations and see for yourself. We have
    10 \cdot 5 + 4 \cdot 2 = 10v_1 + 4v_2

    \frac{1}{2} = \frac{v_2 - v_1}{u_1 - u_2} = \frac{v_2 - v_1}{5 - 2}

    I had the COR equation mixed up. Ah well. I now agree with your book.

    -Dan
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  9. #9
    Junior Member silvercats's Avatar
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    hehe....good. btw why is that it is v2-v1 and not v1-v2
    and it is u1-u2 not u2-u1 if direction is not the problem but relative velocity? asking again.this the biggest problem for me now.can some one explain..?
    What is these balls traveled to opposite directions? (i am cool with the momentum question with this,but that other equation which has 'e')
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  10. #10
    Senior Member bugatti79's Avatar
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    Quote Originally Posted by silvercats View Post
    hehe....good. btw why is that it is v2-v1 and not v1-v2
    and it is u1-u2 not u2-u1 if direction is not the problem but relative velocity? asking again.this the biggest problem for me now.can some one explain..?
    What is these balls traveled to opposite directions? (i am cool with the momentum question with this,but that other equation which has 'e')
    You would need to see the derivation of this equation to see why it is this way. THis equation holds for 1d impact between particles.

    As I have already said, once you know the magnitude and direction of the initial velocities you can determine the final velocities. You can assume a direction of the final velocities and if the calculation yields a negative answer, then the particle is acting acting in the opposite direction to what you assumed.
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