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