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Equilibrium of a point is a fundamental concept in engineering mechanics
and to be in equilibrium - that is to not move -
every point in a structure must satisfy one simple condition.
If that condition is not met,
bad things can happen.
Do you know what that condition is?
To answer this question, consider a tug-of-war
where the point we focus on is the ring between the ropes.
We can represent the force that the person on the left exerts on the ring using an arrow.
We draw that arrow in such a way that it indicates where the force acts,
its direction,
and its magnitude.
We call an arrow of this kind of vector,
and we create another vector to represent the force exerted by the person on the right.
For equilibrium to exist,
the two forces on the ring must be equal and opposite.
Or as an engineer might say,
"The vector sum of the forces on the ring
must equal zero."
If the forces on the ring do not balance
--- "oops" ---
then the ring will move.
We can quantify the forces involved in the tug-of-war by using spring scales
and in doing so, verify that the forces are equal and opposite.
We can add the vectors associated with these forces
by making their lengths proportional to the loads they carry.
We put the first vector, V1, on graph paper
and place the next vector, V2,
so that it starts where V1 ended.
The distance between the tip of the last arrow added
and the start of the first one, is the vector sum.
If these two arrows did not overlay each other
it would be easier to see their sum.
However, in this case,
the second arrow exactly overlies the first,
and it ends where the first one began;
meaning that the sum of the two vectors is exactly zero.
If we add a third spring scale,
the angles and forces will change
until the applied tensions re-balance
and the ring stops moving.
For this particular arrangement of the spring scales,
which force do you think is the largest?
Which is the smallest?
Can you prove your answers?
You might want to pause the video at this point, so you can think about your answers.
The spring scales indicate that the acting forces are
30, 26 and 15 Newtons, as shown.
Were you correct in your guesses
about which force was the largest
and which was the smallest?
If so, good for you!
To check whether these forces add to zero
in a vector sense
we sum them graphically:
V1
plus V2
plus V3.
And, as in the previous example, they do sum to zero.
These forces are proportional to the ones
in the ropes carrying this suspended bucket.
If one of the upper thin ropes is not able
to produce the force demanded of it,
the system will fail.
It does not matter how many forces we apply to a point -
whenever it is in equilibrium,
the sum of the forces turns out to be zero.
Spiderwebs often have many forces acting at a point,
and even these points satisfy the general rule:
"For a point to be in equilibrium, the vector sum of the forces acting on it must be zero"
This is the simple condition that all points in a structure must satisfy, for them to be in equilibrium.
For simplicity this video has focused on well-defined points that experience tensile forces.
However, the principle we just stated applies to arbitrary points,
such as this stone in a large bridge.
And it describes how the compressive forces acting on it
must be related to each other so that it does not move.
If an object of interest is large enough
that the forces acting on it could cause it to rotate,
we must treat it as a rigid body, rather than as a point.
And that is the topic of the next video.
Thank you for watching this video.
We hope that you will enjoy some of our other engineering models videos.
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