Solving Cable Tension Problem with Given Angles and Mass

[ChessFanatic]

Homework Statement

Two cables are attached to a 16.00 kg mass, or 160 N (Our teacher told us to use 10 for gravity). The angle between the cable on the left and the ceiling is 48 degrees. The angle between the cable on the right and the ceiling is 22 degrees. Calculate the tension in the cable on the left if the system is at rest. Calculate the tension in the cable on the right if the system is at rest.

I have been absent from class, so I can't really attempt at a solution. Any help would be appreciated.

Homework Equations

T₁cos(∅)₁=T₂cos(∅)₂

T₁/T₂=cos(∅)₂/cos(∅)₁

The Attempt at a Solution

 

[PhanthomJay]

1. You should draw your sketch more to scale to help with the geometry and trig.
2. The mass is given in kg, so you should calculate its weight in Newtons, not pounds.
3. Please show an attempt based on what you know about equilibrium and Newton's laws.

 

[ChessFanatic]

It's sort of hard to make a drawing to scale; i just drew that picture because it was a given and I thought it would help. I have already converted to Newtons.

 

[PhanthomJay]

Ok, then please show an attempt at a solution and someone will check your work and provide assistance if necessary.

 

[ChessFanatic]

Sorry, I put it in the post now, but I haven't been to class and I'm lost on how to do this type of problem. I've been watching videos on it, but I can't find anything similar to this problem in that the cables connect to two parts of the mass rather than just one point

 

[Vadar2012]

So far you have two unknowns and one equation. Do you know how that one was derived, from sum of forces? Now you need another equation. I'd recommend one that descrbies the tension in an individual cable. Or you could just do some simple trig to find the tensions.

 

[PhanthomJay]

Sorry, I put it in the post now, but I haven't been to class and I'm lost on how to do this type of problem. I've been watching videos on it, but I can't find anything similar to this problem in that the cables connect to two parts of the mass rather than just one point

For all intent and purpose, you can assume the mass is attached at one point, rather than splitting the weight between 2 points . As has been noted, you already have one equation in the horizontal direction, now you need to look in the vertical direction to get the other.