Hi. It's Mr. Andersen and this AP Physics essentials video 42. It is on the vector sum
of forces. And we are going to start with a simple demonstration. And so imagine that
I have a 1.0 kilogram mass attached to two force meters. Again these measure in newtons.
And so what is the force in the vertical? Well the 1.0 kilogram mass, to figure out
the force of gravity, we simply take the mass times the gravitational field strength. So
it is going to be 9.8 newtons. And so what do you think each of those two scales are
going to read, if they are both splitting that force? Well it should be around 5 newtons.
And it is. As long as they are acting in the vertical. But let me give you that same problem
again. Now we have the 1.0 kilogram mass here. So a 10 newton force, roughly a 10 newton
force down. And so what are each of those force meters going to read if they are now
separated by a 90 degree angle? In other words they are exerting forces in a different direction?
Will it each be 5 newtons again? Will it be less than 5 newtons? Will it be greater than
5 newtons? Well it ends up being around 7.1. And that seems like a weird number. And the
reason why is that we are applying those forces as a different angle. And so those are vector
forces. And if you want to figure out the sum of those two forces we have to do a vector
sum. And so if you have any object, let's take an object on an inclined plane, and we
look at all the force vectors acting on it. So let's quickly do that. We have gravity.
We have a normal force. Let's say we are applying a force up the inclined plane. And there is
a frictional force in the other direction. So what you do is you take all of those forces
and then we have to make a vector sum. Now remember to add vectors it is okay to move
them, but you have to keep their magnitude and their direction the same. And so I am
going to line them up from tail to tip to tail to tip to tail to tip to tail to tip.
And if you go from the tail of the first vector to the tip of the last one then you get the
vector sum. And there is a lot of different ways that you could do that. But it is going
to tell us the overall force acting on that object. And therefore it is going to tell
us its acceleration. So we can use free-body diagrams to identify the force vectors. And
then use vector sum to figure out the overall acceleration of the object using Newton's
second law. And if you want to play around with this in the physics lab you can use a
force table. And so a force table is simply a circle. And then we have pulleys around
the outside with a ring in the middle and we can attach different strings to it and
apply different forces to that ring in the middle. It does not go shooting of because
you have a little peg right here in the middle. And so let's say we put a 1.0 kilogram mass
here, here and here. What do we have? 10 newton force at each of those levels. And so let's
say I give you a problem like this in the physics lab. We have a 10 newton force acting
to the right, down and to the right and down and to the left. Could you figure out what
the vector sum is? In other words, what is the sum of all of those? Well you can just
play around with it using a force table. In other words I can attach a force meter on
this side and I can simply pull it until I get that ring right in the middle balanced
around that peg. And so what kind of force do we have? It ends up being right around
17 newton force. Now if you do not have a force table and you can not figure that out,
you are going to have to do a little bit of physics. And so we can do a free-body diagram,
all of the forces acting on that ring in this case. And then I am going to have to do a
vector sum. And so we are going to use a phet simulation to show you how that works. So
what I have done on the left here is I have my forces. They are each roughly 10 newton
forces at the correct angle. And so what you can do is click on the sum of the forces and
it shows you where those forces all add up. Now how does that work? Remember tail to tip
to tail to tip to tail to tip. And I could do it that way. So you could literally move
those force vectors and then line them up. Another way to think about this, and another
way to solve it is to break it down into their x and y components. And so if I show you the
x and y components you could see they look like this. And so if I take just that x, this
one goes to the left, this one goes to the right. That one goes to the right. You can
see why the overall sum goes to the right. And so I could do the same thing here. Those
two go down. This one does not. So we are going to go double down like that. And so
that is going to be my vector sum. So you could solve them just drawing vectors. You
could use mathematics. You could use trigonometry, Pythagorean Theorem. There are a lot of ways
you can figure out the vector sum. But once you do you can apply Newton's second law.
So we are going to use another simulation here. What I am going to do is I am going
to take a bucket and then we are going to have this robot apply a force to it. This
the sum of the forces. Now the whole simulation is paused right now here. But watch what happens
as I apply a force to the right, the frictional force is equaling that. So the sum of force
is a zero. But if I keep pushing it to the right we are going to exceed that frictional
force. Now let me start the simulation. So what is going on, the vector sum is to the
right. And so since the vector sum is to the right the acceleration is going to be to the
right. And it is going to keep speeding up and eventually the robot cannot go fast enough.
So now we have the sum of forces in the opposite direction. And so why? That is friction. If
we reduce the friction, what happens? No net force and it just keeps moving over time.
And so you can solve problems knowing this. And so let's use the same simulation. I have
a robot pushing to the right with a 150 newton force. We have a frictional force in the opposite
direction of 100 newtons. And then we have a mass of 50 kilograms. So could you figure
out the acceleration of this box as you are pushing it across the ground? Well you are
going to use Newton's second law. So we are going to rearrange it like this. What is my
net force? Well we have 150 newtons to the right. 100 newtons to the left. So we are
going to have a 50 newton force pushing in the right. What is my mass? It is 50. So again
it is 50 over 50 or we are going to have an acceleration of 1. And you can read that kind
of right up here. So what is going to happen to that box? It is going to accelerate to
the right and the acceleration is going to be 1.0 meter per second square. Now let me
give you a problem. In this simulation we have taken a small child and we are going
to push that with a robot. So a 40 newton force to the right and 50 newton frictional
force to the left. The acceleration is going to be right around 9 meters per second squared.
In other words it is going to accelerate to the right quicker. And so could you use Newton's
law to figure out the mass of this child? I will put the answer down in the video description
down below. But you can take a stab. And so again, did you learn to use a force table
to play around with these net forces? Did you learn to re-express it as a free-body
diagram so you can eventually figure out the vector sum? And then finally can you use Newton's
law, once you have that vector sum to figure out the acceleration? I hope so. And I hope
that was helpful.