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Motion of a system of particles

  1. Jan 19, 2009 #1
    1. The problem statement, all variables and given/known data
    The vector position of a 3.15 g particle moving in the xy plane varies in time according to the following equation.
    r1 = (3i+3j)t + 2jt^2


    At the same time, the vector position of a 5.00 g particle varies according to the following equation.
    r2= 3i-2it^2 -6jt

    For each equation, t is in s and r is in cm. Solve the following when t = 2.50:
    (a) Find the vector position of the center of mass.

    i cm
    j cm

    (b) Find the linear momentum of the system.
    i g-cm/s
    j g-cm/s

    (c) Find the velocity of the center of mass.
    i cm/s
    j cm/s

    (d) Find the acceleration of the center of mass.
    i cm/s2
    j cm/s2

    (e) Find the net force exerted on the two-particle system.
    i μN
    j μN


    2. Relevant equations
    im really not sure about this
    i think for some of them you would use p=mv
    and for the center of mass you use 1/M integral of r??


    3. The attempt at a solution
    im not sure what to do first
    am i plugging in for t first? and then what do i do?
     
  2. jcsd
  3. Jan 19, 2009 #2

    LowlyPion

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    Yes you will need to evaluate the vector function at the time given and determine position.

    Basically your center of mass is a function of the motion of both particles, so you will need to develop the answers from the vector form of the Center of Mass equation.

    The acceleration will let you find the net force by ordinary means.
     
  4. Jan 19, 2009 #3
    ok im still a bit confused
    so i plug in the value of t into both equations and then what..im not getting it right
     
  5. Jan 19, 2009 #4

    LowlyPion

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    OK, for the first one you have the values of R1 and R2 @ t=2.5 in terms of i,j.

    The weighted average of their positions then means that you multiply each by the mass of the appropriate particle and then divide by the total mass of the particles. These are all scalar operations on the i,j dimensions of each vector @ 2.5.
     
  6. Jan 19, 2009 #5
    o so by doing this
    it'll give me the vector position of each?
     
  7. Jan 19, 2009 #6

    LowlyPion

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    Each R vector is a function in t.

    But at any t, you have a value for R, and hence the displacement vector for each particle.

    You are simply evaluating the vector at that time and applying the rules for determining the center of mass.
     
  8. Jan 19, 2009 #7
    oo so by evaluating each at t..then i just multiply by the masses
    and add them up..and then divide everything by the total mass?
     
  9. Jan 19, 2009 #8

    LowlyPion

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    Yes, that's what the center of mass is.

    In this case though they give you the i,j components, but they can be dealt with independently.
     
  10. Jan 19, 2009 #9
    nevermind- just added the vectors
     
    Last edited: Jan 19, 2009
  11. Jan 20, 2009 #10
    (e) Find the net force exerted on the two-particle system.
    i μN
    j μN


    Shouldn't the net force exerted for i and j just be the :

    acceleration i-hat * (m1 + m2)
    and
    acceleration j-hat * (m1 + m2)

    I have part D for acceleration as
    r1 : 4 j
    r2 : -4 i

    I'm doing this and am getting the wrong answer.
     
  12. Jan 20, 2009 #11
    bump for question due today.
     
  13. Jan 20, 2009 #12
    so i figured out the vector position of the center of mass

    now im trying to find the velocity of the center of mass
    i have no idea how to do this..i know its going to be P/M but how do i get the velocities?
     
  14. Jan 20, 2009 #13
    take the derivative of the position vectors and to find the velocity vectors.
     
  15. Jan 20, 2009 #14
    yea i figured it out
    thanks a lot guys for your help :)
     
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