Can I accurately determine wire tensions in a diagram using known equations?

[ConstableZiM]

Homework Statement

Hi, id like to know how to find the tensions in the diagram below.

I keep getting the wrong answer, the right answers are 181 and (i don't know the other)

How do I get the answers?

Homework Equations

T1+T2+T3=0
T3=mg

The Attempt at a Solution

I keep getting 686 for one of the answers

 

[gerben]

Draw a force triangle, Ft3 must be equal to the sum Ft1+Ft2. You know the directions of Ft1 and Ft2 and you know the length and direction of Ft3. So you get a triangle of which you know the angles and the length of one side, so you can find the length of the other sides.

 

[collinsmark]

Hello ConstableZiM,

Yes, one of the answers is ~181 N. I don't know where you got the 686 thought. Show us your work and maybe we can point you in the right direction.

[Edit: gerben beat me to the post.]

 

[ConstableZiM]

Ok, so this is what happened, I got the answer from the board, but the steps were not given... So I know one of the answers.

Ive been trying to figure it out for a long time now... here's what I did.

T2Sin30+T1Sin40 = 196
T1 = T2 + 196
So, T2Sin30 + T2 Sin40 - 196 Sin40 = 196
T2 = 281.8 <<< My latest attempt... Which is closer, but still wrong...

I don't really know what the length of T3 is gerben, I know the force is -196 N... This is the first time I've ever taken physics... So I'm still not used to the concepts and stuff...

 

[gerben]

The length of the force vector is just the amount of force (so the length of Ft3 is mg).
The direction of the force vector is the direction in which the force pulls.

 

[ConstableZiM]

THANKS! I get it now... I now know where the problem is, I substituted T1 into the equation from t1+t2+t3=0... It should have worked though, if that equation is true... I used the T1 value from the T2cos40=T1cos30 to substitute into T1 now... Why didn't it work with the other equation? Does the t1+t2+t3=0 equation only work with the vertical forces?

Again, thanks for the help.

 

[gerben]

The T1, T2 and T3 forces are not in the same direction, so you should not just add their lengths. You should add the 'components' of the forces in the same direction:

Notice that T3 pulls only vertically down, while T1 and T2 both pull a bit upwards but also a bit sidewards.

The amount that T1 pulls upwards (T1sin30) plus the amount that T2 pulls upwards (T2sin40) should be equal to the amount that T3 pulls downwards (mg). So, this gave you equation: T1Sin30+T2Sin40 = 196.

The amount that T1 pulls to the left (T1cos30) should be equal to the amount that T2 pulls to the right (T2cos40). So, this gave you equation: T1cos30 = T2cos40.

 

[ConstableZiM]

Thanks, I literally almost lost my head over this... Reeeaally helped me...