# Find tension in three ropes suspending same mass

A bird feeder is hanging off of a branch by 3 ropes. Rope1 and Rope2 are tied to the branch and both conect to rope3. Rope3 is conected to the birdfeeder. Rope 1 is 60 degrees of the branch and rope2 is 30 degrees.
Symbolicly find the tensions of all of the ropes.

We know that the tension of rope 3 would equal mass times gravity. t3=mg BUT, i was wondering if this would be a true statement. t1=66.6% of t3 and t2 would be 33.3% of t3?
I got these numbers just from doing a simple ratio assuming that the angle of rope 1 and 2 are proportional to the tension of rope3, but i do not know how to prove if that is right or wrong. Which is why I am posting this, my teacher had a different answer for what he was looking for, but i was curious just to see if that is a true statement about t1 and t2.

Doc Al
Mentor
You are correct that the tension in rope 3, T3 = mg. But your reasoning about the other tensions is not correct.

The right way to do it is to apply the condition for equilibrium: Forces in the x-direction and y-direction must add to zero. Apply this condition at the point where the three ropes connect and see what you get.

ShawnD
$$\Sigma F_x = 0 = R_2 \cos (30) - R_1 \cos (60)$$
$$\Sigma F_y = 0 = R_1 \sin (60) + R_2 \sin (30) - mg$$