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QUESTION 10

A construction crew would like to support a 892 kg steel beam with two angled ropes as shown in the figure below. Their rope can support a
maximum tension of 5,479 N. What is the maximum value of such that the ropes will be able to support the beam without snapping. Round
to two decimal places and express the answer in degrees.

QUESTION 10 A Construction Crew Would Like To Support A 892 Kg Steel Beam With Two Angled Ropes As Shown In The Figure Below Their Rope Can Support A Maximum Te class=

Sagot :

whitneytr12

The maximum value of θ of such the ropes (with a maximum tension of 5,479 N) will be able to support the beam without snapping is:

[tex]\theta =37.01^{\circ}[/tex]

We can apply the first Newton's law in x and y-direction.

If we do a free body diagram of the system we will have:

x-direction

All the forces acting in this direction are:

[tex]T_{1}sin(\theta)-T_{2}sin(\theta)=0[/tex]    (1)

Where:

  • T(1) is the tension due to the rope 1
  • T(2) is the tension due to the rope 2

Here we just conclude that T(1) = T(2)

y-direction

The forces in this direction are:

[tex]T_{1}cos(\theta)+T_{2}cos(\theta)-W=0[/tex]   (2)

Here W is the weight of the steel beam.

We equal it to zero because we need to find the maximum angle at which the ropes will be able to support the beam without snapping.

Knowing that T(1) = T(2) and W = mg, we have:

[tex]T_{1}cos(\theta)+T_{1}cos(\theta)-m_{steel}g=0[/tex]

[tex]2T_{1}cos(\theta)-m_{steel}g=0[/tex]

[tex]2T_{1}cos(\theta)=m_{steel}g[/tex]

T(1) must be equal to 5479 N, so we have:

[tex]cos(\theta)=\frac{m_{steel}g}{2T_{1}}[/tex]

[tex]cos(\theta)=\frac{892*9.81}{2*5479}[/tex]

[tex]cos(\theta)=\frac{892*9.81}{2*5479}[/tex]

[tex]cos(\theta)=0.80[/tex]

Therefore, the maximum angle allowed is θ = 37.01°.

You can learn more about tension here:

https://brainly.com/question/12797227

I hope it helps you!

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