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Two masses connected by a spring

  1. Apr 30, 2012 #1
    1. The problem statement, all variables and given/known data
    Two masses ##m_1=2kg##, ##m_2=2m_1## are placed on the opposite edges of a spring of constant ##k_1=3N/m##, compressed of a length ##x_1=1.73cm##. The system is located on a smooth plane. At the right end of the plane there is a second spring of constant ##k_2=12N/m##. Once the first spring is at rest the masses are free to move (they are not fixed to the spring). So the situation is as follows:

    _________________M1 spring1 M2___________spring2 ||

    a) Find the velocity ##v_1,v_2## of masses ##m_1,m_2## respectively, when the first spring is at rest.

    b) Find the maximum compression ##\Delta x## of the second spring.

    2. Relevant equations
    Conservation of energy, conservation of momentum, potential energy of a spring


    3. The attempt at a solution

    a) The velocities must satisfy the system:
    $$\begin{cases}\frac{1}{2}m_1v_1^2+\frac{1}{2}m_2v_2^2=\frac{1}{2}k_1x_1^2 \\
    m_1v_1+m_2v_2=0\end{cases}$$
    ##\Rightarrow v_2=\sqrt{\frac{m_1k_1x_1^2}{m_2^2+m_1m_2}}=##
    ##\sqrt{\frac{2\cdot 3\cdot (0.0173)^2}{4^2+4\cdot 2}}=0.008 m/s##.
    Then ##v_1=-\frac{m_2}{m_1}v_2=-2v_2=-0.016m/s##.

    b) The value ##\Delta x## must satisfy:
    ##\frac{1}{2}m_2v_2^2=\frac{1}{2}k_2(\Delta x)^2 \Rightarrow \Delta x=\sqrt{\frac{m_2v_2^2}{k_2}}=\sqrt{\frac{4\cdot (0.008)^2}{12}}=0.0046m##

    Values are wrong on my textbook..
     
  2. jcsd
  3. Apr 30, 2012 #2
    What do you mean the values are wrong in your textbook? Do you mean your textbook gives you a solution that is different from your own? What is the given solution?

    Your work seems to make sense to me. Perhaps you shouldn't be rounding the value you get for v_2 when you work through the whole problem, ie pretend 0.00865 m/s is entirely significant until the end (also, you should probably round that to 0.009 if you're going to round)
     
  4. Apr 30, 2012 #3
    I talked to my professor and he agrees that the values found in my textbooks are wrong (what I meant before was that my result differs from that of the textbook). Anyway, thank you Alucinator for the tip about the rounding!
     
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