A lamp with a mass m = 42.6 kg is hanging from wires as shown. The tension ₁ in the vertical wire is A) 210 N B) 417 N C) 570 N D) 360 N E) 730 N

Question

Quizplus · Accepted Answer

We can use Newton's second law to solve for the tension in the diagonal wire:
ΣF = ma
T - mgcosθ = 0
T = mgcosθ
where θ is the angle between the vertical wire and the diagonal wire.
We can use trigonometry to find cosθ:
cosθ = adjacent/hypotenuse = 90 cm / 120 cm = 0.75
Substituting this into the equation for T, we get:
T = (42.6 kg)(9.81 m/s²)(0.75) = 313 N
Since the tension in the horizontal wire is equal to the tension in the diagonal wire, the answer is 417 N (the tension in the vertical wire has no effect on the other wires).

A Lamp with a Mass M = 42