We studied two-dimensional particle equilibrium
problems earlier in this course.
We solved this example, shown here, where
two men were placing a heavy crate, supported
by two cables on the floor.
Here all the forces, cable tension and the
weight of the crate are all in the same plane.
In this two-dimensional scenario, we have
two unknowns and two equations.
The unknowns are the cable tensions and the
two equations are the the sum of all the forces
along x-axis and the sum of all the forces
along y-axis.
Simple and straight forward.
Many engineering problems can be solved using
this two-dimensional particle equilibrium
approach.
However, there are problems that require three-dimensional
analysis.
Look at this hanging flower pot.
We have a beautiful marble queen pothos here.
Pay attention to the three cables supporting
this pot, and you will realize that these
cables, and the forces associated with each
cable, are not in the same plane.
In this situation, knowing the weight of the
flower pot, we want to find the tensions in
the three cables.
So, there are three unknowns, which means
we need three equations.
Since this is a three-dimensional problem,
we can sum up all the forces along x, y and
z-axes.
The process for solving 3-dimensional particle
equilibrium problem is exactly same as the
two-dimensional problem.
The only issue here is, how do we find the
projection of these forces onto x, y and z-axes?
Well, this can be done in a few different
ways depending upon what information is available.
One, Using the cosine value of the angle between
the force and the x, y and z-axis.
The second approach is using other available
angles and the third approach is using unit
vectors.
You can use whatever method is convenient
for a given problem.
Let us first look at each of these methods
in the next video.
