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Troubles with a Dynamics exercise

  1. Mar 28, 2013 #1
    1. The problem statement, all variables and given/known data

    Two carts (1&2) on a flat surface, are pushed by an external force (##\vec{F}##), exerted on 1 (the carts are motionless and touching each other).

    Consider the two objects as particles and take no notice of any friction.

    F=12N; mass of 1 (##m_1##)=4,0 kg; mass of 2 (##m_2##)= 2,0 kg.
    Find the intensity and the direction of the force exerted by 1 on 2 (##\vec{F_{12}}##) and the force exerted by 2 on 1 (##\vec{F_{21}}##)


    3. The attempt at a solution
    I tried solving the system given by:
    ##\vec{F_{12}}=\vec{F} - \vec{F_{21}}## and ##\vec{F_{21}}= m_2 * a##

    obtaining:
    ##m_1 * a = 12 - m_2 *a## ##\Rightarrow## ##a=2,0 m/s^2##

    and thus:
    ##\vec{F_{21}}=2,0kg * (-2,0 m/s^2)=-4 N## with the minus sign, as this force is opposite to F
    ##\Rightarrow## ##\vec{F_{12}}=16N##
    which, according to my textbook is not the right result.
    I don't get where are the mistakes, though. Can anyone help me please?
     
  2. jcsd
  3. Mar 28, 2013 #2
    Your first equations are not right - you're mixing forces acting on different objects.
    You need to draw some free-body diagrams and then apply Newton 2 to them.

    What will be the relation between the 2 forces you're asked to find?
     
  4. Mar 28, 2013 #3

    Doc Al

    User Avatar

    Staff: Mentor

    This violates Newton's 3rd law.
     
  5. Mar 28, 2013 #4
    allright, should it be like this then?
    i find the acceleration, which is:
    ##a=\frac{\vec{F}}{m_1+m_2}## = ##2 m/s^2##
    in the free-body diagram of 1 there is ##\vec{F_{21}}##
    so I multiply the acceleration for ##m_2##, which gives ##\vec{F_{21}}=-4N## (because its direction is opposite to that of the x-axis)
    and, for Newton 3, there must be an equal and opposite force, which means ##\vec{F_{12}}=4N##
     
  6. Mar 28, 2013 #5
    Yes, this looks right :)
    You can check the answer by seeing that the resultant force on m1 is therefore 8N which agrees with its acceleration.
     
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