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2 years ago

Two cables support a 800-lb weight, as shown. Find the tension in each cable.

Mathematics

1 answer:

jeka942 years ago

5 0

Answer:

892 lb (right)
653 lb (left)

Step-by-step explanation:

The weight is in equilibrium, so the net force on it is zero. If R and L represent the tensions in the Right and Left cables, respectively ...

Rcos(45°) +Lcos(75°) = 800

Rsin(45°) -Lsin(75°) = 0

Solving these equations by Cramer's Rule, we get ...

R = 800sin(75°)/(cos(75°)sin(45°) +cos(45°)sin(75°))

= 800sin(75°)/sin(120°) ≈ 892 . . . pounds

L = 800sin(45°)/sin(120°) ≈ 653 . . . pounds

The tension in the right cable is about 892 pounds; about 653 pounds in the left cable.

_____

This suggests a really simple generic solution. For angle α on the right and β on the left and weight w, the tensions (right, left) are ...

(right, left) = w/sin(α+β)×(sin(β), sin(α))

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