# 2-dimensional Force System

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1. Sep 14, 2015

### Oxford365

1. The problem statement, all variables and given/known data
I attached a picture of the question.

2. Relevant equations
∑Fx=0
∑Fy=0
100kg(9.8)= 981 N

I am not sure how to start this problem. Everything else in this chapter is a breeze so perhaps a small insight or how to start would be sufficient, thanks.

2. Sep 14, 2015

### SteamKing

Staff Emeritus
Start by drawing a free body diagram and labeling the forces acting on the sack.

3. Sep 14, 2015

### Oxford365

#### Attached Files:

• ###### FBD.jpg
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4. Sep 14, 2015

### SteamKing

Staff Emeritus
So far so good.

You are given the total length of the rope ABC and some other dimensions to help you figure out the angles.

You also know that this system is in static equilibrium, so you should start writing the equations of statics for this system.

5. Sep 14, 2015

### Oxford365

I set these equations up and I tried solving on my ti-89 but it did not work. I think I am thinking too much into this because it should be a fairly easy question.

Any advice for a new plan of attack?

6. Sep 14, 2015

### SteamKing

Staff Emeritus
The rope provides several pieces of information.

Since the sack is in static equilibrium, you know that the sum of the horizontal components of the tensions in rope segments AB and BC must equal zero.

Since the rope is a single continuous piece, the magnitude of the tension in segments AB and BC must also be equal.

What can you say about the sum of the vertical components of the tensions in segments AB and BC?

7. Sep 14, 2015

### Oxford365

The vertical components must equal 981 correct?

8. Sep 14, 2015

### SteamKing

Staff Emeritus
Yes.

9. Sep 14, 2015

### Oxford365

I'm not really seeing how I need to set up system of equations based on this

10. Sep 14, 2015

### SteamKing

Staff Emeritus
You may have to work thru a series of different calculations. Not every problem can be wrapped up in a neat system of equations to solve at one fell swoop.

11. Sep 15, 2015

### haruspex

You have written expressions like $\cos(\frac x{\sqrt{x^2+y^2}})$. Think about that again.

12. Sep 15, 2015

### Oxford365

I see. I changed all of the trig functions to the inverses, but it is still not working out, I can't seem to find a simpler way to relate the info I am given and write better equations.

13. Sep 15, 2015

### haruspex

That would not be right either. To be invoking trig functions, or inverses thereof, there must be terms in the equation that represent angles. You have no need of such here. You can do everything in terms of side lengths and their ratios.