Question #ce495

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Answer 1 · 2016-04-28T16:59:39

69.3N

The diagram below will help
enter image source here

The system is in equilibrium so the vertical and horizontal force must balance.

Considering vertical forces:

$T 1 \cdot cos 50 + T 2 \cdot cos 45 = m g$ $T1*cos50+T2*cos45=mg$

$m g = 10 \cdot 9.81 = 98.1 N$ $mg=10*9.81=98.1N$

And Horizontal force

$T 1 \cdot sin 50 = T 2 \cdot sin 45$ $T1*sin50=T2*sin45$

Rearranging
$T 2 = T 1 \cdot \frac{sin 50}{sin 45}$ $T2=T1*sin50/sin45$
And substituting this into the first equation

$T 1 \cdot cos 50 + T 1 * \frac{sin 50}{sin 45} \cdot cos 45 = 98.1$ $T1*cos50+T1**sin50/sin45*cos45=98.1$

$T 1 (cos 50 + \frac{sin 50}{sin 45} \cdot cos 45) = 98.1$ $T1(cos50+sin50/sin45*cos45)=98.1$

Solving gives $T 1 = 69.63 N$ $T1=69.63N$