Three blocks on a fricionless horizontal surface

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