Mechanical Engineering: Particle Equilibrium
(3 of 19) Net Force = 0
Welcome to Survey Engineering lecture online and here we're going to take a look at the concept of the net force being equal to zero,
So here we have the same problem that we did in the previous two videos we had a hook on the attached to wall we pull on the hook with two forces 100 pound force in a direction 30 degrees above the horizontal a second force 45 degrees below the horizontal and you can see that there will be a net force in his direction sixteen point two degrees below the horizontal and the net force will have a magnitude of 200 point seven pounds.
if you want to know how that was done go take a look at video number two but what we're going to look at here is that if there's a net force and the net force is not equal to 0 then this hook should be pulled off the wall but something is preventing that from happening there's a third force that we haven't mentioned yet there's a reactionary force from the hook that pulls back on those two forces pulling on the hook so that nothing moves that means there must be another force a third force will pulls in the exact opposite direction with the exact magnitude like this let's draw that force so the hook actually pulls back in this direction with a force let's call it reactionary force and is equal to 200 point seven pounds in the exact opposite direction so that the resultant of the forces pulling on the hook will be equal in magnitude to the reactionary force of the hook pulling back in such a way that when you add these two forces together.
you get a zero resultant force now since this force here the resultant force that is the sum of these two forces pulling on the hook it's simply a sum of those two forces let's ignore the rep vector for a moment let's only consider this vector this vector and the resultant vector because if we add those three up vectorially they should add up to zero which means when we add the three vectors together the tip of the third vector should actually end up at the tail of the first vector so let's see if that happens so first of all we have a first vector F 1 so we can draw that up here it's a hundred-pound vector 100 pounds and that comes at an angle that should be lbs. let me write again lbs. and that comes at an angle of 30 degrees above the horizontal now we have a second vector of 150 pounds so let's make it about a 45 degree angle like this that's a little bit better so it would be hundred and fifty pounds at an angle of 45 degrees below horizontal and then if we take this third force the resultant force of the hook pulling back on the two forces because there's a reactionary force.
I should call reaction of force we've drawn it back in this direction notice this would be the reactionary force of the hook pulling back and this would be equal to 200 point seven pounds and notice when we add all three of those forces together they all come back to the same point therefore we can conclude therefore F net is equal to zero and therefore nothing moves so whenever we have a static situation we can be sure that all the components all the forces in the x-direction will add up to zero and all the forces in the y-direction add of the zero and the way we write that is as follows we could simply say that the sum of all the forces in the x-direction must add up to zero and the sum of all the forces in the y-direction must add up to zero because nothing is moving if that wasn't the case that hope could move the wall would move something with move something would actually accelerate because when there's a net force there will be an acceleration but since nothing was moving that meant the net force had to be zero which means the sum of all the forces acting on the hook must add up to zero so in a way it's not really the hook that's pulling.
but it's the wall keeping the hook attached that's preventing the hook from moving in the direction of the force pulling on it so we have a force pulling this way I have a force pulling that way we have a force pulling this way all three forces together will add up to zero because the net force equals zero when nothing is moving and that's how we do that and this is the result of that now we're going to use this information to solve some more complicated problems we have forces going on in all different directions but if nothing is moving nothing is accelerating we can always be sure that this the case so look at some examples that are a little more complicated in the Lecture to come.
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