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ato is offline
Dec25-12, 03:16 AM
P: 30
three cars of mass m are pulled with force F by a locomotive. Find forces on each cars ?
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

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

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

according to superposition principle,
because there is only one force i.e tension force due to string, exerted on A.
because two tension forces (from both A and C) is acting on B.
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

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

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 ,

thank you
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