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- - **Three same-mass freight cars, why force on each is not same ?**
(*http://www.physicsforums.com/showthread.php?t=660775*)

three same-mass freight cars, why force on each is not same ?Quote:
[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 |

Re: three same-mass freight cars, why force on each is not same ?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. |

Re: three same-mass freight cars, why force on each is not same ?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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