Question Number 108922 by ajfour last updated on 20/Aug/20
Commented by ajfour last updated on 20/Aug/20
$$\:\:\:\:\:\:\:{Neglect}\:{friction}.\:{Find} \\ $$$$\:\:\:\:\:{initial}\:{acceleration}\:{of}\:{M}. \\ $$
Answered by mr W last updated on 20/Aug/20
Commented by mr W last updated on 20/Aug/20
$${a}_{\mathrm{1}} ={A}+{a} \\ $$$${T}={m}_{\mathrm{0}} {a} \\ $$$${T}={MA} \\ $$$${mg}−{T}={ma}_{\mathrm{1}} ={m}\left({A}+{a}\right) \\ $$$$\Rightarrow{a}=\frac{{M}}{{m}_{\mathrm{0}} }{A} \\ $$$$\Rightarrow{mg}−{MA}={m}\left({A}+\frac{{M}}{{m}_{\mathrm{0}} }{A}\right) \\ $$$$\Rightarrow{A}=\frac{{g}}{\mathrm{1}+\frac{{M}}{{m}}+\frac{{M}}{{m}_{\mathrm{0}} }} \\ $$$$\Rightarrow{a}=\frac{{g}}{\mathrm{1}+\frac{{m}_{\mathrm{0}} }{{m}}+\frac{{m}_{\mathrm{0}} }{{M}}} \\ $$
Commented by ajfour last updated on 21/Aug/20
$${Straight}\:{way}\:\&\:{great}\:{way},\:{thank} \\ $$$${you}\:{Sir}!\:{Can}\:{we}\:{discuss}\:{what}\: \\ $$$${happens}\:{after}\:{a}\:{while}\:{when}\:{m} \\ $$$${even}\:{accelerates}\:{towards}\:{left}..? \\ $$
Commented by mr W last updated on 21/Aug/20
