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A 135 kg scaffold is 6.60 m long and is suspended by two wires, one from each end. A 440 kg box sits 1.70 m from the left end.

What is the tension in the left-hand side wire? (Assume [tex]g = 9.8 \, \text{m/s}^2[/tex].)

Answer :

Answer:

Step-by-step explanation:

mass of scaffold, m = 135 kg

mass of box, m' = 440 kg

let the tension in the left wire is T.

take moments about the right end.

According to the diagram,

135 x g x 3.3 + 440 x g x (6.6 - 1.7) - T x 6.6 = 0

4365.9 + 21128.8 - T x 6.6 = 0

T x 6.6 = 25494.7

T = 3862.8 N

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Rewritten by : Barada

The tension in the left wire of a scaffold in static equilibrium can be found using the principle of moments. With the right end as the pivot, the sum of clockwise moments (from the scaffold's and the box's weight) equals the counter-clockwise moment (tension in the left wire × scaffold's length). The tension in the left wire is calculated to be 3875.14 N.

The weight of the scaffold acts at its center of mass, which is 3.3 m from the right end. Thus, the moment due to the scaffold is 135 kg × 9.8 m/s² × 3.3 m. Next, the weight of the box provides a moment calculated by 440 kg × 9.8 m/s² × (6.60 m - 1.70 m). These two moments must be balanced by the tension in the left wire × the full length of the scaffold (6.60 m).

To find the tension in the left wire ( Tleft):

Calculate the moments due to scaffold: (135 kg × 9.8 m/s² × 3.3 m).

Calculate the moments due to box: (440 kg × 9.8 m/s² × 4.9 m).

Sum the moments from the scaffold and box and set this equal to the tension in the left wire times the length of the scaffold (6.60 m).

Solve for Tleft.

After performing these calculations:

Moment due to scaffold = 135 kg × 9.8 m/s² × 3.3 m = 4363.5 N·m

Moment due to box = 440 kg × 9.8 m/s² × 4.9 m = 21212.4 N·m

Total moment = 4363.5 N·m + 21212.4 N·m = 25575.9 N·m

Now, we'll equate this total moment to the tension in the left wire times the length of the scaffold:

Tleft × 6.60 m = 25575.9 N·m

Tleft = 25575.9 N·m / 6.60 m = 3875.14 N

Therefore, the tension in the left wire is 3875.14 N.