Question

Question) Block D of mass 100 kg is tied two two identical light ropes X and Y. The block is stationary and symmetrically
supported by X and Y as shown in the figure. Find tension in each rope
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Answer 1

Solution :

Let g = 10 m/sec

Weight of block = mg = 100×10 = 1000 N

$\sum f(x) \: =\:T_{2x}\: - \: T_{1x}$

$0 \: =\: T_{2x}\:-\:T_{1x}$

$T_{2x}\: =\: T_1x$

$T_2Cos\theta\: =\: T_1Cos\phi$

$\theta \: =\: \phi\: =\: 37^{\circ}$

$T_2\: =\: T_1$

Net forces Fy

$\sum Fy \: =\: T_{1y}\: +\: T_{2y}\: -\: W$

$0 \: =\: T_{1y}\: +\: T_{2y}\: -\: W$

$W \: =\: T_{1y}\: +\: T_{2y}$

$W \: =\: T_{1} Sin\theta \: +\: T_{2} Sin\phi$

$W \: =\: T_{1} Sin37^{\circ}\: +\: T_{2} Sin 37^{\circ}$

We got, $T_2\: =\: T_1$

$W \: =\: T_{2} Sin37^{\circ}\: +\: T_{2} Sin 37^{\circ}$

$1000 \: =\: 2 T_{2} Sin37^{\circ}$

$\dfrac{1000}{2.Sin37^{\circ}} \: =\: T_{2}$

$T_{2} \: =\: \dfrac{1000}{2.Sin37^{\circ}}$

$T_2\: =\: T_1\: =\: 833.3 N$

Answer

Tension in Rope X & Y are equal to 833.3 N.