Quickie

[physicsss]

OK, three blocks on a fricionless horizontal surface are in contact on each other, a force is applied to block 1, m1, m2, m3, respectively. And m1=m2=m3.

how come the force of contact that block one exerts on block is F(m2+m3) / (m1+m2+m3) instead of just F*m2/(m1+m2+m3). ( I know that a is F/(m1+m2+m3).)

[Pyrrhus]

Think about Action and Reaction Forces [Contact Forces] acting on each block.

[Leong]

Right direction : Positive; Left direction: Negative.

\begin{multline*}
\begin{split}
&Newton's\ 2nd\ Law:\\
&\sum \vec{F}=m\vec{a}\\
&Consider\ m_1:\\
&F+(-Fm_1m_2)=m_1a\\
&F=m_1a+(Fm_1m_2)\ .........(1)\\
&Consider\ m_2:\\
&Fm_2m_1+(-Fm_2m_3)=m_2a\ .....(2)\\
&Consider\ m_3:\\
&Fm_3m_2=m_3a\ .....(3)\\
&(3)\rightarrow(2):\\
&Fm_2m_1=m_2a+m_3a\ .....(4)\\
&(4)\rightarrow(1):\\
&F=m_1a+m_2a+m_3a\ .....(5)\\
&From\ (4):\\
&Fm_2m_1=(m_2+m_3)a\\
&=\frac{F(m_2+m_3)}{m_1+m_2+m_3}\\
\end{split}
\end{multline*}