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5.4 a picture frame hung against a wall is suspended by two wires attached to its upper corners. if the two wires make the same angle with the vertical, what must this angle be if the tension in each wire is equal to 0.75 of the weight of the frame? (ignore any friction between the wall and the picture frame.,



Answer :

onyebuchinnaji

If the two wires make the same angle with the vertical, the angle must be 83.6⁰.

What is the angle between the wires?

The angle between the two wires is determined by applying the principle of parallelogram law of vector addition.

R² = a² + b² - 2abcosθ

where;

  • R is the resultant vector = weight of the frame = W
  • a is tension in first wire = 0.75W
  • b is the tension in the second wire = 0.75W
  • θ is angle between the two wires

W² = (0.75W)² + (0.75W)² - 2(0.75W x 0.75W) cosθ

W² = 1.125W² - 1.125W² cosθ

W² = 1.125W²(1 - cosθ)

W²/1.125W² = 1 - cosθ

0.8889 = 1 - cosθ

cosθ = 1 - 0.8889

cos θ = 0.1111

θ = arc cos(0.1111)

θ = 83.6⁰

Thus, the angle between the two wires is determined as  83.6⁰.

Learn more about resultant vector here: https://brainly.com/question/110151

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