Chapter 6: Q.39 (page 156)

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

Short Answer

Expert verified

Tension in rope 1 is $6035.5 N$

Tension in rope 2 is $4128.5 N$

Step by step solution

Given information

Weight of beam- $= 1000 K G$

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

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

Assumptions

Let rope $1$ be $R 1$ and rope $2$ be $R 2 .$

Tension of rope 1 $= T R 1$

Tension of rope 2 $= T R 2$

Point $0 (m g)$ is where two ropes are connected.

Calculation of tension in each rope

$A t p o i n t 0$

$\sum_{}^{} f x = 0$

localid="1649397086445" $T R_{1} \sin (20 °) =$ localid="1649397058574" $T R_{2} \sin (30 °)$

localid="1649614498151" $T R_{2} =$ localid="1649614527752" role="math" $2 \times T_{R 1}$ localid="1648026003669" $\sin (20 °)$ $— e q . 1$

$\sum_{}^{} f x = 0$

localid="1649614427856" $T R_{1} \cos (30)$ $+$ localid="1649396955821" $T R_{2} \cos (30 °)$ $= m g$

localid="1649396975732" $T R_{1} \cos (20 °) + 2 T R_{1} \sin (20 °)$ $= 1000$ $\times 9.8$

Tension in rope 1

$T R_{1}$ is $6035.5 N$

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 $4128.5 N$

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

Short Answer

Step by step solution

Given information

Assumptions

Calculation of tension in each rope

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