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Question Number 19355 by Tinkutara last updated on 10/Aug/17

$$\mathrm{Two}\mathrm{blocks}\mathrm{are}\mathrm{placed}\mathrm{on}\mathrm{a}\mathrm{smooth}$$$$\mathrm{horizontal}\mathrm{surface}\mathrm{and}\mathrm{connected}\mathrm{by}\mathrm{a}$$$$\mathrm{string}\mathrm{pulley}\mathrm{arrangement}\mathrm{as}\mathrm{shown}.$$$$\mathrm{If}\mathrm{a}\mathrm{force}F\mathrm{starts}\mathrm{acting}\mathrm{on}\mathrm{block}{m}_1,$$$$\mathrm{then}\mathrm{find}\mathrm{the}\mathrm{relation}\mathrm{between}\mathrm{acceleration}$$$$\mathrm{of}\mathrm{both}\mathrm{masses}\mathrm{and}\mathrm{their}\mathrm{values}$$

Commented by Tinkutara last updated on 10/Aug/17

Commented by ajfour last updated on 10/Aug/17

$$\mathrm{F}-3\mathrm{T}={\mathrm{m}}_1{\mathrm{a}}_1...\left(\mathrm{i}\right)$$$$4\mathrm{T}={\mathrm{m}}_2{\mathrm{a}}_2...\left(\mathrm{ii}\right)$$$${4\mathrm{a}}_2={3\mathrm{a}}_1...\left(\mathrm{iii}\right)$$$$\Rightarrow \mathrm{F}-\frac{{3\mathrm{m}}_2{\mathrm{a}}_2}{4}=\frac{{4\mathrm{m}}_1{\mathrm{a}}_2}{3}$$$$\Rightarrow {\mathrm{a}}_2=\frac{12\mathrm{F}}{{16\mathrm{m}}_1+{9\mathrm{m}}_2}$$$$\mathrm{and}{\mathrm{a}}_1=\frac{16\mathrm{F}}{{16\mathrm{m}}_1+{9\mathrm{m}}_2}.$$

Commented by Tinkutara last updated on 10/Aug/17

$$\mathrm{Thank}\mathrm{you}\mathrm{very}\mathrm{much}\mathrm{Sir}!$$

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