# Equilibrium of a hanging mass

1. Aug 31, 2010

### Whotto

1. The problem statement, all variables and given/known data

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

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

2. The attempt at a solution

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

I've split it up the two given forces (F, and FT) 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 FT 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!

Last edited by a moderator: May 4, 2017
2. Sep 1, 2010

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

3. Sep 1, 2010

### Whotto

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

4. Sep 2, 2010

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.

5. Sep 2, 2010

### Whotto

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

Thanks!

6. Sep 2, 2010

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

7. Sep 8, 2010