Anonymous
Anonymous asked in Science & MathematicsMathematics · 10 months ago

1) There is a sign that weighs 3.7 kg and hangs from a horizontal pole. Two cables are used to support the sign as shown below. Find the tension in each wire. (hint: force of gravity = 9.8N/kg).

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• Pope
Lv 7
10 months ago

Let the left cable tension be L and the right R.

The sum of the vertical components must equal the weight of the load.

Lsin(51°) + Rsin(68°) = (3.7)(9.8)

The horizontal components must be equal and opposite.

Lcos(51°) - Rcos(68°) = 0

Solve those simultaneous equations. it should come to this:

L = (3.7)(9.8)cos(68°)/sin(61°) ≈ 15.5 N

R = (3.7)(9.8)cos(51°)/sin(61°) ≈ 26.1N

• david
Lv 7
10 months ago

tan 51 = y1/x ... x = [tan 51]/y1

tan 68 = y2/x ... x = [tan 68]/y2

y1 + y2 = 9.8(3.7) = 36.26 N

y2 = 36.26 - y1 <<<< sub above

x = [tan 68]/[36.26 - y1] = [tan 51]/y1 <<< solve for y1

[tan 51][36.26 - y1] = [tan 68]y1

[tan 51][36.26] - [tan 51]y1 = [tan 68]y1

[tan 68]y1 + [tan 51]y1 = [tan 51][36.26]

y1 = [tan 51][36.26] / [tan 68 + tan 51] = 12.0694

x = [tan 51]/y1 = 0.10232

left t = r = sqrt (x^2 + y1^2) = 12.07 N

right t = r = sqrt (x^2 + y2^2) <<< need y2

... y2 = x tan 68 = 0.25325

right t = r = 0.27314 N

• Ian H
Lv 7
10 months ago

3.7*9.8 = 36.26

Left: 36.26 *sin(51)/[sin(51) + sin(68)] = 16 .534 N

Right: 36.26 *sin(68)/[sin(51) + sin(68)] = 19.726 N

• Pope
Lv 7
10 months agoReport

The sum of the tensions could equal the load only if the cables were both vertical.