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Three same-mass freight cars, why force on each is not same ?

  1. Dec 25, 2012 #1

    ato

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    assuming the force F is exerted on car C and nearest to C is car B and remaining one is A.
    [tex]\vec{F}_{A}[/tex] is total sum of all (interbody-) forces on car A . similarly [tex]\vec{F}_{B}[/tex] and [tex]\vec{F}_{C}[/tex] are defined.

    assuming the forces that the question asks is [tex]\vec{F}_{A}[/tex],[tex]\vec{F}_{B}[/tex] and [tex]\vec{F}_{C}[/tex] and the given information is
    $$\vec{F}_{CO}=\vec{F}$$

    according to newton's 2nd law
    $$\vec{F}_{A}=\frac{d^{2}}{dt^{2}}m\vec{r}_{A}$$,
    $$\vec{F}_{B}=\frac{d^{2}}{dt^{2}}m\vec{r}_{B}$$ and
    $$\vec{F}_{C}=\frac{d^{2}}{dt^{2}}m\vec{r}_{C}$$

    but since
    $$\frac{d^{2}}{dt^{2}}\vec{r}_{A}=\frac{d^{2}}{dt^{2}}\vec{r}_{B}=\frac{d^{2}}{dt^{2}}\vec{r}_{C}$$, $$\frac{d}{dt}m =0$$

    so above five equations would give
    $$\vec{F}_{A}=\vec{F}_{B}=\vec{F}_{C}$$

    according to superposition principle,
    $$\vec{F}_{A}=\vec{F}_{AB}$$
    because there is only one force i.e tension force due to string, exerted on A.
    $$\vec{F}_{B}=\vec{F}_{BA}+\vec{F}_{BC}$$
    because two tension forces (from both A and C) is acting on B.
    $$\vec{F}_{C}=\vec{F}_{CO}+\vec{F}_{CB}$$
    because one external force of magnitude F and one tension force from B.

    according to 3rd law we also have,
    $$\vec{F}_{AB}=-\vec{F}_{BA}$$ and
    $$\vec{F}_{BC}=-\vec{F}_{CB}$$.

    so from above five equations,
    $$\vec{F}_{A}+\vec{F}_{B}+\vec{F}_{C}=\vec{F}_{CO}$$
    hence
    $$\vec{F}_{A}=\vec{F}_{B}=\vec{F}_{C}=\frac{\vec{F}}{3}$$
    but i dont undertand why its wrong because the solution says
    $$\vec{F}_{A}=\frac{\vec{F}}{3}$$,
    $$\vec{F}_{B}=\frac{2\vec{F}}{3}$$ and
    $$\vec{F}_{C}=\vec{F}$$

    the only problem think i can think of is may be the question is asking for different forces , because there are forces that have same value for example ,
    $$\vec{F}_{A}=\frac{\vec{F}}{3}$$,
    $$\vec{F}_{BC}=\frac{\vec{2F}}{3}$$,
    $$\vec{F}_{C0}=\vec{F}$$


    thank you
     
  2. jcsd
  3. Dec 25, 2012 #2

    Doc Al

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    Staff: Mentor

    The question is not asking for the net force on each car, which of course must be equal. It is asking for the force that C exerts on B and B exerts on A in terms of the force F that the locomotive exerts on C.
     
  4. Dec 25, 2012 #3

    ato

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    so the question was indeed asking for $$\vec{F}_{CO}$$,$$\vec{F}_{BC}$$ and $$\vec{F}_A$$ .

    i dont understand why not say so in the question, instead of being so short and confusing. i though the book was teaching physics not reading mind.

    thanks for the help Doc Al
     
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