Question Number 107711 by ajfour last updated on 12/Aug/20
Commented by ajfour last updated on 12/Aug/20
$${If}\:{motion}\:{begins}\:{from}\:{rest}\:{when} \\ $$$${blue}\:{block}\:{is}\:{at}\:{A}\:{and}\:{by}\:{the}\:{time}\:{it} \\ $$$${reaches}\:{B}\:{string}\:{goes}\:{slack},\:{then} \\ $$$${find}\:{length}\:{AB}. \\ $$$$ \\ $$
Answered by mr W last updated on 12/Aug/20
Commented by mr W last updated on 12/Aug/20
$${T}\:\mathrm{cos}\:\theta={ma}_{{x}} \\ $$$${mg}−{T}={ma}={ma}_{{x}} \mathrm{cos}\:\theta \\ $$$$\Rightarrow\frac{{T}\:\mathrm{cos}\:\theta}{{mg}−{T}}=\frac{\mathrm{1}}{\mathrm{cos}\:\theta} \\ $$$${T}\left(\mathrm{1}+\mathrm{cos}^{\mathrm{2}} \:\theta\right)={mg} \\ $$$$\Rightarrow{T}=\frac{{mg}}{\mathrm{1}+\mathrm{cos}^{\mathrm{2}} \:\theta}>\mathrm{0} \\ $$$${the}\:{string}\:{can}\:{never}\:{become}\:{slack}! \\ $$