How Do You Calculate the Tension in Cords with Varying Angles and Loads?

[anteaters]

Homework Statement

Figure P4.24 shows loads hanging from the ceiling of an elevator that is moving at constant velocity. Find the tension in each of the three strands of cord supporting each load, given that θ1 = 40°, θ2 = 50°, θ3 = 62°, m1 = 3 kg, and m2 = 6 kg.

Homework Equations

F = mg(sin theta)

The Attempt at a Solution

it asks for the answers for all of the T's but i found it for T_{1 - 3} for (a), and T₃ for (b). I tried doing T₁ = 6(9.8)(sin62) for part a, image B but it told me i have the wrong answer. and I'm completely lost on T₂ for part b.

any suggestions?

 

[alphysicist]

Homework Statement

Figure P4.24 shows loads hanging from the ceiling of an elevator that is moving at constant velocity. Find the tension in each of the three strands of cord supporting each load, given that θ1 = 40°, θ2 = 50°, θ3 = 62°, m1 = 3 kg, and m2 = 6 kg.

Homework Equations

F = mg(sin theta)

The Attempt at a Solution

it asks for the answers for all of the T's but i found it for T_{1 - 3} for (a), and T₃ for (b). I tried doing T₁ = 6(9.8)(sin62)

This is close, but notice that it would make T₁ be smaller than T₃, which can't be true here.

Instead, you want the y component of T₁ to cancel out the y component of T₃ (since T₂ has no y component). What are the y components of those two strings?

 

[anteaters]

okay i was looking through my book and realized what to do. i was just plugging and chugging with numbers instead of looking at the problem and actually solving it. so for T₁ i needed to realize that m(a) = 0 because the acceleration of the system = 0. so the only other force in the y direction was T₃. so i found T₁(sin 62) - T₃ = 0. then i solved for T₁ by doing 58.8/sin 62 = 66.59...
now for T₂, would i set it up as T₂ - T₁(cos 28) = 0? i got 28 because in the x direction the angle would be 28 degrees below the axis in a negative direction. or would it be sin 28? any help would be appreciated

 

[anteaters]

nevermind, i figured it out. it was sin 28. thanks for your time alphysicist.