Question

The 1000 kg steel beam is supported by two ropes. What is the tension in each?

Short answer

Tension in rope 1 is$6035.5N$

Tension in rope 2 is$4128.5N$

Step-by-step solution

Given information

Weight of beam-$=1000KG$

Angle between rope $1$and perpendicular is$20°$

Angle between rope $2$and perpendicular is$30°$

Assumptions

Let rope $1$ be $R1$and rope $2$be $R2.$

Tension of rope 1$=TR1$

Tension of rope 2$=TR2$

Point $0\left(mg\right)$is where two ropes are connected.

Calculation of tension in each rope

$Atpoint0$

$\sum _{}^{}fx=0$

localid="1649397086445" $T{R}_1\sin \left(20°\right)=$localid="1649397058574" $T{R}_2\sin \left(30°\right)$

localid="1649614498151" $T{R}_2=$localid="1649614527752" role="math" $2\times T_{R1}$localid="1648026003669" $\sin \left(20°\right)$$—eq.1$

$\sum _{}^{}fx=0$

localid="1649614427856" $T{R}_1\cos \left(30\right)$$+$localid="1649396955821" $T{R}_2\cos \left(30°\right)$$=mg$

localid="1649396975732" $T{R}_1\cos \left(20°\right)+2T{R}_1\sin \left(20°\right)$$=1000$$\times 9.8$

Tension in rope 1

$T{R}_1$is $6035.5N$

Tension in rope 2 $T{R}_2$-

localid="1649397189749" $T{R}_2=$localid="1649396688322" $2\times 6035.5\times \sin 20°$

Tension in rope 2

$T{R}_2$is $4128.5N$