Transitional Equilibrium: Tension Problem

[CLeSure]

Homework Statement

A box with a weight of 200 Newtons is hung from ropes as shown below. Calculate the tension in each of the three ropes supporting the box.

Homework Equations

$$\Sigma$$F$$_{x}=0$$
$$\Sigma$$F$$_{y}=0$$

The Attempt at a Solution

We know right from the start that the tension of T3 is going to be 200N.

To begin solving for the tensions of T1 and T2, I started by setting up X and Y component equations:

$$\Sigma$$F$$_{x}= -T1cos(30) + T2cos(50) + 200cos(270) = 0$$
$$\Sigma$$F$$_{y}= T1sin(150) + T2sin(50) + 200sin(270) = 0$$

Looking at the X component equation, I figured it would be easiest to solve for T2 in terms of T1, my result being:

T2 = T1cos(30) / cos(50)

I substituted the value of T2 into the component Y equation, and solved for T1:

$$\Sigma$$F$$_{y}= T1sin(150) + [T1cos(30) / cos(50)]*sin(50) + 200sin(270) = 0$$

I then took my value for T1 and applied it to the original X component equation, and solved for T2.

My problem is the solved values I get for T1 and T2 don't end up adding to equal 0 when in either equation. I realize I must have made an error in my equations, most likely in the trig functions. Any help on identifying where my logic in setting up the equations went wrong would be much appreciated.

Thanks,

Chris

 

[Antenna Guy]

Draw a vector to define 0deg, and check your angles.

T1, T2, and T3 should be the same sign in both sums.

Regards,

Bill

 

[LowlyPion]

My problem is the solved values I get for T1 and T2 don't end up adding to equal 0 when in either equation. I realize I must have made an error in my equations, most likely in the trig functions. Any help on identifying where my logic in setting up the equations went wrong would be much appreciated.

What values did you get?

 

[CLeSure]

what values did you get?

t1 = 130.541
t2 = 175.877

 

[LowlyPion]

t1 = 130.541
t2 = 175.877

That's pretty much what I get.

And I'd say that's correct.

All I can think is that you have reversed T1 and T2 in plugging them back into check them. Because if those are the equations that spawned the answers, you should expect that they will calculate back to equal 0, since that's what the components are supposed to add to. If your differences are small then it's likely just rounding errors. If they are large, then it must be putting the wrong values with the wrong angles.

 

[CLeSure]

That's pretty much what I get.

And I'd say that's correct.

All I can think is that you have reversed T1 and T2 in plugging them back into check them. Because if those are the equations that spawned the answers, you should expect that they will calculate back to equal 0, since that's what the components are supposed to add to. If your differences are small then it's likely just rounding errors. If they are large, then it must be putting the wrong values with the wrong angles.

Thanks for taking the time to help. I rechecked my answers by putting them back into the X-component equation and they equal out to zero. I must have messed up when I was checking my answers before. Thanks!

Chris