What is the tension in the rope attached at -4mxˆ?

In summary, the problem involves a 100kg mass suspended by three ropes with known coordinates and a known attachment point. The goal is to find the tension in the rope attached at -4mxˆ using vector equations and the fact that the sum of all the force vectors is equal to zero. This results in three equations for three unknowns, allowing for the determination of the tension in the desired rope.
  • #1
mrcheeses
31
0

Homework Statement


A 100kg mass is supended by 3 ropes. one rope is attached at a point 1mxˆ + 1myˆ, one is attached at 1mxˆ - 1myˆ and one is attached at -4mxˆ. The three ropes all connect at -1mzˆ, at which point the mass is attached. What is the tension T in the rope attached at -4mxˆ?



Homework Equations


Fnet=0
Fg=mg


The Attempt at a Solution


I have no idea how to do this. Do I need to find the angles in between each rope?
 
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  • #2
You should represent the tension of each rope vectorially. Which is not hard, as you are given the coordinates of each rope's endpoints, and the rope is a straight line between the endpoints.
 
  • #3
If you bother with the angle and different planes, you could, but it is more convenient to solve this with vectors.
First, you need to set up vector equations for the 4 forces involved.
Since you can work out the direction of each Force vectors, the magnitudes are the 3 unknowns.
Then, all of the Force vectors add up to a null vector. In other words, forces in each direction (i,j,k) add up to 0.
And by then you are left with 3 equations for 3 unknowns.
 

Related to What is the tension in the rope attached at -4mxˆ?

What is equilibrium in 3 dimensions?

Equilibrium in 3 dimensions is a state in which all forces acting on an object cancel each other out, resulting in a stable and balanced system. In other words, the object is not experiencing any acceleration and is at rest or moving with a constant velocity.

What are the factors that affect equilibrium in 3 dimensions?

The factors that affect equilibrium in 3 dimensions include the magnitude and direction of forces acting on the object, the object's mass and inertia, and the presence of any external factors such as friction or air resistance.

How is equilibrium in 3 dimensions represented mathematically?

Equilibrium in 3 dimensions is represented mathematically using vector equations. These equations take into account the magnitude and direction of forces acting on the object to determine whether the object is in a state of equilibrium or not.

Why is understanding equilibrium in 3 dimensions important in science?

Understanding equilibrium in 3 dimensions is important in science because it allows us to analyze and predict the behavior of objects and systems in various situations. This understanding is crucial in fields such as physics, engineering, and chemistry.

How can equilibrium in 3 dimensions be applied in real-world situations?

Equilibrium in 3 dimensions can be applied in real-world situations to design and build structures, machines, and other systems that are stable and balanced. It can also be used to analyze the forces acting on objects in motion, such as airplanes or satellites, to ensure they are in a state of equilibrium and functioning properly.

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