EDUCATION SYSTEM IN TANZANIA: Newton's Third Law

Idea: Forces in nature always exist in pairs. Newton's third law states: For every action, there is an equal and opposite reaction. When two bodies interact:

$\displaystyle\vec{F}_{2\,\,{\:\rm on}\,\,1}^{}$ = - $\displaystyle\vec{F}_{1\,\,{\:\rm on}\,\,2}^{}$ .

(4)

Where $\vec{F}_{\:\rm 2~on~1}^{}$ is the force exerted on body 1 by body 2 and $\vec{F}_{\:\rm 1~on~2}^{}$ is the force exerted on body 2 by body 1. For Example: When an object falls towards the earth, the earth exerts a force on it that causes it to accelerate towards the earth. According to Newton's third law, the object exerts a force on the earth as well, and the earth accelerates towards the object. Why don't we feel the earth accelerate?
Solution:

2nd Law	$\textstyle\rightarrow$	m_ea_e = $\displaystyle\vec{F}_{\:\rm obj~on~earth}^{}$
3rd Law	$\textstyle\rightarrow$	$\displaystyle\vec{F}_{\:\rm obj~on~earth}^{}$ = - $\displaystyle\vec{F}_{\:\rm earth~on~obj}^{}$ $\displaystyle\equiv$ - $\displaystyle\vec{w}$
	$\textstyle\Rightarrow$	$\displaystyle\vec{a}_{e}^{}$ = - $\displaystyle\vec{w}$ /m_e
	$\textstyle\Rightarrow$	\| $\displaystyle\vec{a}_{e}^{}$ \| = $\displaystyle\left(\frac{m_{\:\rm obj}}{m_e}\right)g$ $\displaystyle\ll$ g.