Solving 2D Force Systems for Calculating Equilibrium

In summary: 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.
  • #1
Oxford365
25
0

Homework Statement


I attached a picture of the question.
FullSizeRender (2).jpg

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.
 
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  • #2
Oxford365 said:

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.
 
  • #3
SteamKing said:
Start by drawing a free body diagram and labeling the forces acting on the sack.
SteamKing said:
Start by drawing a free body diagram and labeling the forces acting on the sack.
 

Attachments

  • FBD.jpg
    FBD.jpg
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  • #4
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
SteamKing said:
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.
FullSizeRender (4).jpg

Any advice for a new plan of attack?
 
  • #6
Oxford365 said:
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?
 
  • #7
SteamKing said:
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?
 
  • #8
Oxford365 said:
The vertical components must equal 981 correct?
Yes.
 
  • #9
SteamKing said:
Yes.
I'm not really seeing how I need to set up system of equations based on this
 
  • #10
Oxford365 said:
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.
 
  • #11
Oxford365 said:
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.
 
  • #12
haruspex said:
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.
 
  • #13
Oxford365 said:
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.
 

FAQ: Solving 2D Force Systems for Calculating Equilibrium

1. What is a 2-dimensional force system?

A 2-dimensional force system is a physical system in which forces act on an object in two dimensions, typically represented by the x and y axes. This type of force system is commonly used in physics and engineering to analyze the effects of forces on an object.

2. How do you calculate the resultant force in a 2-dimensional force system?

The resultant force in a 2-dimensional force system can be calculated by breaking down the individual forces into their x and y components and then adding them algebraically. The magnitude and direction of the resultant force can then be determined using trigonometric functions.

3. What is the difference between a concurrent and a non-concurrent 2-dimensional force system?

In a concurrent 2-dimensional force system, all of the forces intersect at a single point, while in a non-concurrent system, the forces do not intersect at a single point. This difference can affect how the resultant force is calculated and the overall stability of the system.

4. What factors can affect the balance of forces in a 2-dimensional force system?

The balance of forces in a 2-dimensional force system can be affected by factors such as the magnitude and direction of the forces, the distance between the forces, and the angle at which the forces act on the object. External factors such as friction and air resistance can also impact the balance of forces.

5. How is the equilibrium of a 2-dimensional force system determined?

The equilibrium of a 2-dimensional force system is determined by ensuring that the sum of all forces acting on an object is equal to zero. This means that the object is either at rest or moving at a constant velocity in a straight line. In other words, the net force and net torque in the system must both be zero for equilibrium to be achieved.

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