Hi. It’s Mr. Andersen and this AP Physics essentials video 60. It is on Newton’s Second
Law, which when expressed is probably the most important equation in all of AP Physics,
F=ma. Now on your equation sheet there are a couple of things that are added to that.
So we could express it like this. Then net force which is a vector is equal to the mass
times the acceleration which is also a vector. And that net force and that acceleration are
always going to be in this same direction. But what does it mean to accelerate? It means
that if you apply a constant force to something it will get faster and faster and faster over
time. And the larger that mass is that slower the acceleration is going to be. And so let’s
put a really large mass right here and we are going to try to push on it. And so we
are applying a force from the right to the left into this large object. And so where
will the acceleration be? It should be to the left. But you could push on this as hard
as you could and it is never going to move anywhere. And the reason why is that there
is a force in the other direction. So there is going to be this frictional force of this
object that is opposing that motion. And so no matter how hard you push, there is going
to be no acceleration. So if we could remove it, now we are removing that frictional force
and now we can get a net force in that direction. So just because you are applying a force does
not mean there is going to be an acceleration because there could be opposing forces. But
if we do remove those opposing forces then we are going to start to get acceleration.
That means it is going to start slowly but it is going to get faster and faster and faster
as long as we keep applying that same force. Another things that is important to know is
if you have two objects that are within the same system, even though one might be applying
a force to the other, the system is not going to move. And so if you have a bicycle, even
though there are lots of forces within it, there is going to be no change in the center
of mass velocity. There is going to be no acceleration of the system itself. If we want
acceleration of a system then there has to be a force from one object outside that system
on another. And if we apply that force then there is going to be accelerations. The velocity
is going to start increasing. And that acceleration, which is a vector remember is equivalent to
the force, the net force divided by the mass. Or we could just express it as force equals
mass times acceleration. Now again if we have one system with two objects inside it, and
so I have a little simulation here. We have two spheres. So think of this whole rectangle
as one system. And so what I am going to do is attach a spring between the two. And now
I am going to point to where the center of mass is, which is right between the middle.
And so what I am going to do is unpause the simulation. And there is no acceleration.
That is because there is no force. There is no tension in the spring. And so now let me
pause the simulation again. I am going to stretch the spring. So now we know there is
a force inside there. Where is the center of mass? It is shifted to the right. And so
now let me unpause the simulation. And you can see that there is movement but the center
of mass is not moving. There is no acceleration there. How are mass and acceleration linked?
Well I have a simulation again. On the left side we have this set. So it is not going
to move. And so now I have two spheres. And if I let them go, nothing is going to happen,
because there is no tension. And so what I can do is I can stretch those two springs.
They are identical springs, and now what is going to happen, again if the left side is
totally fixed, we are going to get acceleration in that direction. But did you see the acceleration
was different? And so let’s look at that again. So we have two different accelerations.
Acceleration of the orange sphere and the silver sphere. Remember the force is going
to be the same, the force in the spring is going to be the same, so we get motion like
that. So which one has a greater acceleration? We would say the orange sphere has a greater
acceleration. So since the force is the same, what does that tells us about the mass of
that object? The mass has to be less since it has a greater acceleration it must have
a smaller mass. And so the one on the top has a 5 kilogram mass. The one of the bottom
is twice that. And so when we let it go, the one on the bottom is going to have an acceleration
that is half that on the top, because it has a mass that is twice as large. And so to apply
this, how do we measure acceleration in a simulation like this? Well imagine if we have
a 1 kilogram sphere and it is 4 meters off the ground. We are going to get acceleration
as it falls down. But how do we measure that? Well what we can do is use video simulation
or we could use a ticker tape. But what we can do is keep making marks every set amount
of time. And so what I am going to do is mark the center of mass as it changes over time.
And so it looks like that. So you can see the distance between those marks is getting
greater. So that implies that we are getting acceleration. In other words it is moving.
And so how could we figure out what that acceleration is? Well if I graph it we know have the change
in position over time and you can see that it is increasing in the negative. And the
distance between them is increasing so you know the velocity is increasing in the negative
as well. And so how could we figure out what that acceleration is? Well remember the slope
of the position versus time graph tells us its velocity. You can see it is increasing
here. But if we graph the velocity versus time graph then we have a straight line. So
that implies that we have a constant acceleration. The velocity continues to get greater and
greater and great in the negative. So if I calculate the slope of that we are seeing
a change of negative 8 meters per second during a 0.8 second period of time. And so if I divide
my change in velocity over time I am going to get an acceleration of around negative
10 meters per second squared. And you know it to be about negative 9.8 meters per second
squared. So now we know the mass. 1.0 kilogram. We know the acceleration, negative10 meters
per second squared. So could you figure out the force? Well it is just plugging it in.
And if we know the mass is 1.0 the acceleration is negative 10, what is going to be the net
force? It is going to be negative 10, in this case it is going to be negative 10 newtons.
It is going to be in the same direction that that acceleration was. And so what is causing
that, that is the force due to gravity. It is the weight of the object. And so what would
happen if we were to take that same 1.0 kilogram mass and we were to move it to the moon, where
the gravity is 1/6 what it is on the earth? And so what is going to happen to our force?
It is roughly 1/6 of what it is here. So it is around 1.6 newtons. So the mass has not
changed. We have a negative 1.6 newtons. And so what is going to be our acceleration? It
is going to be negative 1.6 meters per second squared. So it is going to take much longer
for it to accelerate and eventually reach the ground. So solving problems using Newton’s
second law are very simple. So let’s say we have a rocket and it is a 10 newton force
that is being applied to a rocket and it is a 20 kilogram rocket. Could you figure out
the acceleration of the rocket? Well, for sure. So we have 10 newtons. What is our mass?
It is 20 kilograms. And so we would simply divide 10 by 20 and we are going to have an
acceleration of 0.5 meters per second squared. But let’s say that we apply that force to
the rocket and then we just let it coast for awhile. So I am applying a force, we can see
the acceleration, but let’s say I turn the rocket off for awhile. Could you figure out
what that position versus time graph is going to look like? So again it is accelerating
to the right so we should have a curved line, but then it stabilizes for awhile. So the
velocity stays the same for awhile. In other words it has velocity and it is just going
to keep moving in that direction. So what would the accelerating versus time graph look
like? Well we have constant acceleration through here. The acceleration is getting greater.
But what is going to happen once we get rid of that force? Once we remove the force, what
happens to the acceleration? It should go to 0. And so the graph would look like this.
Here is going to be an area where we have a constant acceleration due to that constant
net force. But once we remove the net force it is still going to keep moving, it is just
not going to have any acceleration. So could you apply Newton’s second law to solve problems?
In this case we know the force. We know the mass. We could solve for the acceleration.
But if we know the acceleration and the mass we could solve for the force. And then finally,
could you use mathematical or visual representations to see if there is going to be a change in
the center of mass of a system? I hope so. And I hope that was helpful.