A sign is hanging from three ropes as shown in the figure. The tension in the lefthand rope, T1, is 436.86 N. Angle θ1=62.6°, and angle θ2=53.5°.

Question

A sign is hanging from three ropes as shown in the figure. The tension in the lefthand rope, T₁, is 436.86 N. Angle θ₁=62.6°, and angle θ₂=53.5°.

What is the tension, T₂, in the righthand rope?

What is the mass of the sign?

Answer 1

Hope,

Since this is a static (unmoving) object, you will have to use your equations that the sum of all forces in the x-direction = 0 and the sum of all forces in the y direction = 0. However, here we do not know the weight of the sign, so we cannot use the y direction in this problem.

What you can do is find the x component of T1 based on the trigonometry of the diagram. Without knowing exactly which angle they've given you, I don't want to set that up for you. Then you know that the x component of T2 must be equal and opposite to that. Now you can use trignometry again in the opposite way - this time you'll find the hypotenuse, which will give you T2.

Now you know T1 and T2, and the angles of each. The WEIGHT of the sign will be equal and opposite to the sum of the y components of T1 and T2.

1. The last step will be to go from that weight to the mass of the sign, using W = mg.