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Three samemass freight cars, why force on each is not same ? 
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#1
Dec2512, 03:16 AM

P: 30

[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
Dec2512, 03:41 AM

Mentor
P: 41,566

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.



#3
Dec2512, 04:01 AM

P: 30

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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