Now that we understand how things move on their own,
or under the force of certain accelerations,
and we never discussed where these accelerations are coming from,
we're ready to discuss force
and what causes these accelerations
and what happens if we have more than one source
of acceleration for a body at a given time.
We'll discuss this in the context of Newton's laws,
referencing Isaac Newton and that will be where we start.
The first thing we need to understand
is that we're going to introduce one new variable
to the three that we've already introduced
to the position, velocity and acceleration.
And this new variable is the mass.
The mass of an object is sort of a measure
of how much it does or doesn't wanna move
if you start pushing on it or how hard it is to stop
if it's already gotten going.
The mass is represented with the symbol m in our equations
while its units are kilograms which are represented by kg as units
and so when you see m in our equations
you should always have in your head
sort of an intuitive idea of a mass and how mass of an object is.
Jumping right now into Newton's three laws,
we have here a great picture of Isaac Newton,
who was something of a godfather of modern Physics
and came up with many, many, many of the ideas that we use,
entire terminologies and ways of thinking about things
not to mention coming up with one of the discoveries of calculus
in his spare time.
His three laws about motion,
would come from him observing data from prior scientists
and really using his intuition.
Our first that objects will stay in motion
unless they are acted on by outside forces,
specifically if it's sitting still,
that velocity won't change
unless it's acted on by a force and will stay sitting still.
Also, if it's moving, it will keep moving
unless an outside force acts on it to stop it from moving.
This is contrary to the idea of some people
who thought that if you move something,
it would naturally want to slow down and naturally want to come to a stop,
but what they were thinking of was external forces
like friction and things like this bringing things to slow down.
And Newton correctly surmised that really things would keep moving
unless there is something to stop them.
Secondly, and the one that you should really, really be careful
to understand and remember,
as we do problems going forward, is that the force of an object,
the force on an object will be equal to its mass times its acceleration.
We're gonna be using this equation right here F equals ma over and over again
as we do example of Newton's law of force type problems.
And finally, any time a force is acting from one object to another,
there will be an equal and opposite force on the first object.
This is often said as for every action,
there is an equal and opposite reaction.
For every force,
there is a reaction force equal in magnitude but in the opposite direction.
The first thing I'd like to do before we jump into the rest of this lecture
is introduce some notation
because we are going to be talking about many variables,
sometimes vector, sometimes velocity, sometimes acceleration,
and so we'll use different notations for each of these.
The first is that for vectors,
we talked a little bit about the idea of drawing an arrow over a vector
to represent that it is a vector having different components,
in different directions.
For vectors I will use bold letters,
so like this bold letter A rather than drawing arrows over things.
For velocity vectors,
I'll use blue arrows in the diagrams that we're going to draw,
so if you see a blue arrow,
it is not a force contributing to the motion of an object,
it's just representing the actual motion, the actual velocity, of that object.
On the other hand,
we'll use red arrows for actual forces acting on objects,
trying to push them one way or the other.
Let's take the three laws and apply it to an actual physical object
like the one you see here.
It has a mass and right now it has a velocity.
Newton's first law simply says that this velocity vector
will stay in the apple's velocity vector
unless some force acts on it so that velocity vector V
will be a constant always.
His second law says that if instead we apply a force on this object
and start pushing it in the given direction,
and this object has a mass, m
then the force on that object will be equal
to its mass times the acceleration of the object
and finally suppose that we now introduce a third object,
something we should say immediately is
as you see in the second box here still,
the units of force are the units of mass times acceleration,
and so the units as what those brackets mean around F
are kilograms for the mass times the units of acceleration
which are meters per units squared,
and so the units of force are kilograms meters per seconds squared,
and we abbreviate these units as Newtons or big N
and so if you see that big N, it's just a unit label,
it just labelling that whatever number we've come up
with like 5 and 5 Newtons are just 5 kilometers meters per seconds squared
which you can always remember by remembering F equals ma
and knowing the units of m and a.
In this picture what I've also done is added a second object
with a force acting on the first object,
and Newton's third law says that whatever force
the first object is applying on the second object
the second object is also applying backwards on the first object.
And so as vectors, we would say that the vectors have equal magnitude
but opposite directions,
and that's the reason for the minus sign in that equation.
The very first thing we should discuss about Newton's third law
is a very common misunderstanding
or confusion about what Newton's third law is saying.
If I say that for every action, there is an equal and opposite reaction,
where that forces are always equal and opposite,
you can immediately stop me and say
that can't be true because I know if a truck like this hits a bug like that,
there's no way that the forces on these two objects are equal.
Well, in fact, Newton's third law says
that there is an equal and opposite force
on both of these objects, different direction but equal in magnitude.
So let's clear up some confusion here,
it is true that these forces are equal in magnitude,
that the mass times the acceleration of each object will be the same,
so the mass times the deceleration of the truck really,
as the bug hits the wind shield,
will be equal and opposite to the mass times the acceleration of the bug.
The difference is that the truck has humungous mass
while the bug has a very, very tiny mass.
What this means is that the bug will experience a huge acceleration,
while the truck will experience and very tiny deceleration
and these are accelerations that we actually feel,
and you know the accelerations are as they are,
because these two quantities, the mass and the acceleration
have to be equal while the masses are so very different
that means that the acceleration have to compensate
to make the equality hold, to make Newton's third law still true.
And so we know the acceleration that the bug feels
will be tremendous while the acceleration or the deceleration,
slowing down of the truck will pretty well be insignificant
and so those accelerations that we actually feel and experience
as people or trucks or bugs
and keep that in mind as we go through further problems.