Tensions Equilibrium: Finding Unit Vectors

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In summary, the conversation discusses finding the unit vector of a force M = 20kN from a given diagram. The method involves using trigonometry to determine the components of the force vector based on its magnitude and direction. The final answer is given as 6.84i + 18.794j.
  • #1
allenw990
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Homework Statement


see pic

Homework Equations


The Attempt at a Solution


Ive worked out T1 which is T1=F1(-4i-5j-10k/11.8743) = T1(-0.337i-0.421j-0.842k)
and T2=F2(-4i-5j-10k/11.8743) =T2(0.337i-0.421j-0.842k)
and the next step is to find the unit vector of force M = 20kn but how do i work out unit vectors from the diagram if the lengths aren't given?

(the answer given is 6.84i + 18.794j for the unit vector of M=20kN but how??)
 

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  • #2
You obviously don't realize that a 'unit vector' has a magnitude = 1, which is why it's called a unit vector.

You know the magnitude of the force M (which = 20 kN) and you are shown the direction of the M vector in the diagram. The M-vector is parallel to the x-y plane and it makes an angle of 20 degrees with the positive y-axis. Ergo, you can work out the components of M using simple trigonometry.
 
  • #3
oh i get it now thanks
 

1. What is Tensions Equilibrium?

Tensions Equilibrium is a concept in physics that refers to the state of a system when all forces acting on it are balanced. This means that the net force on the system is equal to zero, resulting in a state of rest or constant motion.

2. What are unit vectors?

Unit vectors are vectors with a magnitude of 1 and are used to represent a particular direction in space. They are often denoted by a hat symbol (^) on top of the vector symbol.

3. How do you find unit vectors?

To find a unit vector, you need to divide a given vector by its magnitude. This will result in a vector with a magnitude of 1 in the same direction as the original vector.

4. Why is finding unit vectors important in Tensions Equilibrium?

In Tensions Equilibrium, unit vectors are used to represent the direction of the forces acting on a system. By finding the unit vectors, we can determine the magnitude and direction of each force, and check if they are balanced to achieve equilibrium.

5. What are some real-life applications of Tensions Equilibrium and finding unit vectors?

Tensions Equilibrium and finding unit vectors are used in various fields such as engineering, architecture, and even video game development. They are essential in designing structures and objects that can withstand forces without collapsing or breaking. For example, bridges, buildings, and roller coasters all utilize Tensions Equilibrium and unit vectors in their design and construction process.

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