Question

8) This one requires some trig... I don't expect anyone to get this one right! Two ropes are holding a 6 kg

sign up. Each rope makes a 45° angle with the ceiling. What is the force exerted by each rope?
Eat
At
Joe's

Answer 1

42 N

Step-by-step explanation:

Draw a free body diagram of the sign. There are three forces: two tension forces at 45° from the horizontal, and weight force mg straight down.

The vertical component of the tension forces can be found with trigonometry:

sine = opposite / hypotenuse

sin 45° = Tᵧ / T

Tᵧ = T sin 45°

Sum of forces in the y direction:

∑F = ma

2Tᵧ − mg = 0

Tᵧ = mg/2

T sin 45° = mg/2

T = mg / (2 sin 45°)

T = mg / √2

Given that m = 6 kg:

T = (6 kg) (9.8 m/s²) / √2

T ≈ 42 N