Solving 2D Force Systems for Calculating Equilibrium

[Oxford365]

Homework Statement

I attached a picture of the question.

Homework 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.

 

[SteamKing]

Homework Statement

I attached a picture of the question.
View attachment 88666

Homework 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.

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

 

[Oxford365]

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

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

 

[SteamKing]

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.

 

[Oxford365]

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.

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?

 

[SteamKing]

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.
View attachment 88678
Any advice for a new plan of attack?

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?

 

[Oxford365]

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?

The vertical components must equal 981 correct?

 

[SteamKing]

The vertical components must equal 981 correct?

Yes.

 

[Oxford365]

Yes.

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

 

[SteamKing]

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

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.

 

[haruspex]

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.
View attachment 88678
Any advice for a new plan of attack?

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

 

[Oxford365]

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

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.

 

[haruspex]

I see. I changed all of the trig functions to the inverses,

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.