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Math Help - position vector

  1. #1
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    Post position vector

    Hey All,

    How do you solve these two similar questions,

    1) point masses 2g, 4g, 5g ang 1g are situated at points A, B, C and D with the position vector 3i -4j, -i + 5j, i +7j, and 5i + j respectively. find the position vector of the centre of mass for these four particles.

    2) point masses 1g, 2g, and 5g are situated at the points A, B and C, with position vector 2i + j, i + 2j, and i - 3j respectively. find the position vector of the centre of mass for these three particles. If the 1g and 2g masses have their positions swapped, what is the consequent change in the x position of the centre of mass.

    Thank you
    Last edited by dadon; May 1st 2007 at 02:27 PM.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by dadon View Post
    Hey All,

    How would you solve these two similar questions,

    1) point masses 2g, 4g, 5g ang 1g are situated at points A, B, C and D with the position vector 3i -4j, -i + 5j, i +7j, and 5i + j respectively. find the position vector of the centre of mass for these four particles.

    2) point masses 1g, 2g, and 5g are situated at the points A, B and C, with position vector 2i + j, i + 2j, and i - 3j respectively. find the position vector of the centre of mass for these three particles. If the 1g and 2g masses have their positions swapped, what is the consquent change in the x position of the centre of mass.

    Thank you
    The centre of mass of massess m_1, m_2, .., m_n situated at v_1, v_2, ..., v_n is:

    V = [sum_{r=1 to n} m_r*v_r]/[sum_{r=1 to n} m_r]

    RonL
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  3. #3
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    Hi thanks for the reply.

    I'm still confused on what you have to do.
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by dadon View Post
    Hi thanks for the reply.

    I'm still confused on what you have to do.
    You take the weighted sum of the position vectors, with weights equal
    to the masses of the particles at each position divided by the total mass.

    For 1) this is:

    [2*(3i -4j) + 4*(-i + 5j) + 5*(i +7j) + 1*(5i + j)]/[2 + 4 + 5 + 1]

    ...... = {[2*3 - 4*1 + 5*1 + 1*5]*i + [-2*4 + 4*5 + 5*7 +1]*j}/12

    ...... = i + 4 j

    RonL
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  5. #5
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    so using ur method the answer to question 2)

    point masses 1g, 2g, and 5g are situated at the points A, B and C, with position vector 2i + j, i + 2j, and i - 3j respectively. find the position vector of the centre of mass for these three particles.

    =(9i -10j) / 8

    is this correct?

    and how do you answer this for the same question;

    If the 1g and 2g masses have their positions swapped, what is the consequent change in the x position of the centre of mass.

    Thanks
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  6. #6
    Grand Panjandrum
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    Quote Originally Posted by dadon View Post
    so using ur method the answer to question 2)

    point masses 1g, 2g, and 5g are situated at the points A, B and C, with position vector 2i + j, i + 2j, and i - 3j respectively. find the position vector of the centre of mass for these three particles.

    =(9i -10j) / 8

    is this correct?
    Yes

    and how do you answer this for the same question;

    If the 1g and 2g masses have their positions swapped, what is the consequent change in the x position of the centre of mass.

    Thanks
    NewCofM = [2(2i+j) + 1(i+2j) + 5(i-3j)]/8 = (10i - 11j)/8

    Therefore the change in position of the centre of mass is:

    (10i - 11j)/8 - (9i -10j) / 8 = (i - j)/8

    RonL
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