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Question Number 81843 by TawaTawa last updated on 15/Feb/20

Commented by mr W last updated on 16/Feb/20

Commented by mr W last updated on 16/Feb/20

$$\frac{T_1}{\sin (\frac{\pi }{2}-{\theta }_2)}=\frac{T_2}{\sin (\frac{\pi }{2}-{\theta }_1)}=\frac{F_g}{\sin ({\theta }_1+{\theta }_2)}$$$$\Rightarrow T_1=\frac{F_g\cos {\theta }_2}{\sin ({\theta }_1+{\theta }_2)}$$$$\Rightarrow T_2=\frac{F_g\cos {\theta }_1}{\sin ({\theta }_1+{\theta }_2)}$$

Commented by TawaTawa last updated on 15/Feb/20

$$\mathrm{Please}\mathrm{help}\mathrm{me}.$$

Commented by TawaTawa last updated on 15/Feb/20

$$\mathrm{Please}\mathrm{help}\mathrm{me}.$$

Commented by TawaTawa last updated on 16/Feb/20

$$\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}.\mathrm{I}\mathrm{appreciate}\mathrm{your}\mathrm{time}$$

Answered by ajfour last updated on 15/Feb/20

Commented by ajfour last updated on 15/Feb/20

$$T_1\cos {\theta }_1=T_2\cos {\theta }_2$$$$T_1\sin {\theta }_1+T_2\sin {\theta }_2=F_g$$$$\Rightarrow T_1\sin {\theta }_1+\frac{T_1\cos {\theta }_1\sin {\theta }_2}{\cos {\theta }_2}=F_g$$$$T_1=\frac{F_g\cos {\theta }_2}{\sin ({\theta }_1+{\theta }_2)}.$$

Commented by TawaTawa last updated on 16/Feb/20

$$\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}.\mathrm{I}\mathrm{appreciate}\mathrm{your}\mathrm{time}$$

Answered by mind is power last updated on 15/Feb/20

$${\overrightarrow{f}}_g+{\overrightarrow{T}}_3=\overrightarrow{0}$$$$\Rightarrow F_g=T_3..1$$$$byprojection\left({yy}^{\prime }\right)$$$${\overrightarrow{T}}_3+{\overrightarrow{T}}_{2}sin\left({\theta }_2\right)+{\overrightarrow{T}}_{1}sin\left({\theta }_1\right)=0..2$$$$projection\left({xx}^{\prime }\right)$$$$\Rightarrow T_{1}cos\left({\theta }_1\right)=T_{2}cos\left({\theta }_2\right)\Rightarrow T_2=T_1\frac{cos\left({\theta }_1\right)}{cos\left({\theta }_2\right)}...3$$$$(1\mathrm{\&}2\mathrm{\&}3\Rightarrow$$$$T_{1}sin\left({\theta }_1\right)+T_1.\frac{sin\left({\theta }_2\right)cos\left({\theta }_1\right)}{cos\left({\theta }_2\right)}-F_g=0$$$$\Rightarrow T_1\left(\frac{sin\left({\theta }_1\right)cos\left({\theta }_2\right)+sin\left({\theta }_2\right)cos\left({\theta }_1\right)}{cos\left({\theta }_2\right)}\right)=F_g$$$$sin\left({\theta }_1\right)cos\left({\theta }_2\right)+cos\left({\theta }_1\right)sin\left({\theta }_2\right)=sin({\theta }_1+{\theta }_2)\Rightarrow$$$$\Rightarrow T_1=\frac{F_{g}cos\left({\theta }_2\right)}{sin({\theta }_1+{\theta }_2)}$$$$$$$$$$$$$$

Commented by TawaTawa last updated on 16/Feb/20

$$\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}.\mathrm{I}\mathrm{appreciate}\mathrm{your}\mathrm{time}.$$

Commented by mind is power last updated on 16/Feb/20

$$withePleasurmiss$$

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