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Newton's Second Law Question

  1. Jul 26, 2012 #1
    1. The problem statement, all variables and given/known data
    A certain force gives object m1 an acceleration of 12.0 m/s2. The same force gives object m2 an acceleration of 3.30 m/s2. What acceleration would the force give to an object whose mass is (a) the difference between m1 and m2 and (b) the sum of m1 and m2.


    2. Relevant equations
    F=ma


    3. The attempt at a solution
    I found these two solutions online:
    http://www.physforum.com/index.php?showtopic=6754
    http://www.jiskha.com/display.cgi?id=1286634662
    but I can't follow their math. I tried manipulating the above equation similarly, to no avail.

    Any help is greatly appreciated!
     
  2. jcsd
  3. Jul 27, 2012 #2
    Which part that you do not understand.
    Use the formula a=F/m.
     
  4. Jul 27, 2012 #3

    SammyS

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    Hello Slusho. Welcome to PF !

    What are those manipulations? What have you tried?

    F = m1a1 and F = m2a2, where a1 = 12.0 m/s2 and a2 = 3.30 m/s2 .

    Therefore, [itex]\displaystyle m_1=\frac{F}{a_1}\text{ and } m_2=\frac{F}{a_2}\,.[/itex] Correct?

    Now, use all this with F = (m1 + m2)a1+2 to find a1+2 .

    How's your algebra?
     
  5. Jul 27, 2012 #4
    I figured it out!

    [tex]F=(\frac{F}{a_{1}}+\frac{F}{a_{2}})a_{1+2}[/tex]
    [tex]\frac{1}{a_{1+2}}=\frac{1}{F}(\frac{F}{a_{1}}+ \frac{F}{a_{2}})[/tex]
    [tex]\frac{1}{a_{1+2}}=\frac{1}{a_{1}}+\frac{1}{a_{2}}[/tex]

    Thank you so much for you help! I had to work it several ways for a good half hour until I did it correctly.
     
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