How do you solve for the mass of a hanging object with two given forces?

[Whotto]

Homework Statement

A mass suspended by a string is held 24^o from vertical by a force of 13.8N as shown. Find the mass.

[PLAIN]http://img525.imageshack.us/img525/3421/problem32.jpg

2. The attempt at a solution

[PLAIN]http://img205.imageshack.us/img205/6100/attemptv.jpg

I've split it up the two given forces (F, and F_T) by their axis and got the two equations:

1. $$13.8N Sin\ominus + F_{T}Cos24 = mg$$2. $$13.8N Cos\ominus = F_{T}Sin24$$

Continuing on to solving for F_T with equation two, I get

3. $$F_{T} = \frac{Sin24}{13.8N Cos\ominus}$$

I plug equation 3 into 1 to get

$$13.8N Sin\ominus + \frac{Sin24}{13.8N Cos\ominus}Cos24 = mg$$

and solving for m to get:

$$\frac{13.8N Sin\ominus 13.8N Cos\ominus + Sin24Cos24}{9.8m/s^{2}} = m$$

3. Where I'm stuck

I can't get theta to solve for m. I have tried to get it through geometry and any other ways I could think of. Am I missing information in order to solve this problem, or am I just not doing this correctly?

Any help would be appreciated. Many thanks!

 

[Aditya Tarey]

Resolve Forces in tangential direction and equate them no need of the angle you assumed.
Take coordinate axis as y=tension x=F this solution is possible if angle between F and Tension is 90

 

[Whotto]

Resolve Forces in tangential direction and equate them no need of the angle you assumed.
Take coordinate axis as y=tension x=F this solution is possible if angle between F and Tension is 90

Thanks for your reply!

But the diagram does not tell me the angle is 90. Wouldn't that mean I cannot assume it is 90?

 

[Aditya Tarey]

otherwise angle should be given. Always take coordinate axis in such a way that variables in question are reduced this is the concept to minimize the time you take for problem solving.

 

[Whotto]

All right, seems fairly odd to me that they would go against what teachers have taught.

Thanks!

 

[Aditya Tarey]

You must have seen problems on projectile motion on an incline . What coordinate axis did you choose?

 

[Whotto]

I got the answer now.

I have thought about why we would change the axis for the inclined planes, but that is due to the fact we knew the Normal force is perpendicular to the surface. The confusion that I had with this problem is that there is no indication that the angle between the string and force is 90 degrees.

But once I changed the axis to make the string perpendicular to the x axis, I got the right answer.

Nevermind me, I'm too picky.

Your help has been much appreciated Aditya Tarey!