Newton's second law | Middle school physics | Khan Academy

- [Instructor] According
to Newton's first law,

if the net force acting
on an object is zero,

the object's motion will not change.

This means, for example, if an
object is at rest on a table

or, say, somewhere in intergalactic space

where the net force is zero,

then the object will
continue to be at rest.

On the other hand, if
the object was moving,

and again, if the net
force on it was zero,

then it'll continue to move

with that exact same velocity forever.

But now, here's a question.

What if the net force acting
on an object is not zero?

Well, then the object's
motion will change.

So, a net force will
change the object's motion.

In other words, a net
force causes acceleration.

But how exactly are they connected?

That's what we're gonna find out

in this video, so let's begin.

So how do we do this?

Well, we take a bunch of masses,

apply a net force and measure that,

and then measure how much
acceleration they get

because of the net force.

And then if we do enough trials,
maybe we can see a pattern

and maybe we can see the
connection between them.

But of course, the big question is,

how do we measure net
force acting on an object?

And how do we measure
the acceleration of it?

Well, let's look at it one by one.

So first of all, how do
we measure a net force?

Well, a cool equipment that
we can use to measure forces

is a spring balance.

And the way the spring balance works

is that there's a spring over here.

So if you pull on it, say from this side,

then the spring is compressed

and therefore it pulls back,

and the number, the reading over here,

tells you exactly with how much force

the spring is pulling back on you.

So in this example, the
spring is pulling on my hand

with a force of exactly two newtons.

If you had pushed it from this end,

then the spring is pushing

with the force of exactly two newtons.

And now since I know

with exactly how much force it is pushing,

I can use this to push on our objects.

And look, I will now know
exactly with what force

we are pushing on the object.

Pretty cool, isn't it?

But wait a second. That is only one force.

Remember, our goal is to
figure out the net force.

How do we do that?

How do we figure out how much net force

is acting on an object?

Well, let's see, if you
were to keep these objects

on a table, then there are
forces in the vertical,

like gravity and normal force,

but they get balanced, they
are balanced, isn't it?

So we don't have to
worry about those forces.

We only have to worry about
the forces in the horizontal.

So one of the forces in the horizontal

is our spring force, which we know.

But what about the other forces?

The other forces are the force of friction

and air resistance.

We can minimize friction drastically

by using an air hockey table, right?

And if the velocities are not too high,

then even the air
resistance is very minimal.

So look, in the horizontal,

there's only one effective force,

and that is the spring force.

So that itself becomes the
net force. Amazing, right?

Okay, so that's how we
can measure the net force.

What about the acceleration?
How do we measure that?

Well, for that, we can use a motion sensor

which will periodically
monitor the velocity,

and it'll give you a velocity-time graph.

And by analyzing the graph,

we can measure the acceleration.

Okay, so with that, we
have everything needed.

We can go ahead and plan our experiment.

But how do we do that?

Well, one of the best ways to do that

is to think about the variables involved.

So, what are the variables
involved over here?

Well, we have the net force.

Since this is the variable that
we can change independently,

we call this the independent variable.

Then, of course, there is the acceleration

that we're gonna measure.

This acceleration is dependent
on the net force, right?

So we call this the dependent variable.

So now for our experiment,

we can push this object
with different net forces.

Say we'll do three trials,
and then for each of them,

we'll figure out what the acceleration is.

And by measuring the acceleration,

maybe we can make a connection

between the net force and
the acceleration, isn't it?

Okay, that sounds like a plan,

but there's another variable
over here, the mass.

What do we do about that?
Should we also change that?

Well, here's an important
thing about doing experiments.

You should always change
just one variable at a time.

Since you're already
changing the net force,

this particular variable,

we wanna make sure the mass is a constant.

So we're gonna use the same
value of the mass everywhere.

And therefore we call
this the control variable

because we're not changing that.

It's going to be a constant.

So what mass can we use?
Well, we can use any one.

Let's just use one kilogram mass.

So we now have our plan.

We're gonna push the one kilogram object

with different forces,
and we're gonna measure

what the acceleration's going to be.

All right, so, we'll start by pushing

with two newtons of force
on the one kilogram object.

And once we let go of this,

the object will start accelerating,

and we will also keep that
contact for about a second.

So we'll put the force for about a second.

We'll try to make sure that
this stays at two newtons

so the force is a constant, okay?

So let's do that. And there we have it.

Once we let go of the contact,
the object stops accelerating

and it continues to move

within a straight line
with a constant velocity.

So let's look at what our
motion sensor has detected,

and let's see what the
velocity-time graph looks like.

There we have it. Let's see
if that graph makes sense.

For the first one second,
the object was accelerating

because there was a
net force acting on it.

And you can see, the
velocity is increasing.

After the one second, the contact is lost

and the object moves
with a constant velocity,

and that's why, look,
the velocity stays put.

But how much is the acceleration?

We have to look at this.

And you can see, the object's
velocity increased from zero

to two meters per second in one second.

So that is the acceleration.

Zero to two meters per
second in one second.

All right, we're gonna do second trial,

but this time, we're gonna
put four newtons of force.

And again, we'll push it for
about one second and let it go.

All right? Here we go.

Boom! What do we notice?

Well, we notice that the
object travels much faster.

So let's see what the
velocity-time graph looks like.

What does our motion sensor give us?

Now the velocity-time
graph looks like this!

Ooh, what is it saying?

Well, it's saying now in the first second

while the object was accelerating,

when the net force was acting,

the velocity increased from
zero to four meters per second.

And then the object continues to move

with a constant velocity
of four meters per second

because the contact was lost.

So now the acceleration is
zero to four meters per second

in one second.

The acceleration became higher

when the net force became higher.

Does this make intuitive sense?

I think yes, it makes intuitive sense

that when you apply a larger net force,

the object accelerates larger.

And we are also experimentally
seeing that. That's amazing.

Okay, if we did one more trial,

we get very similar results.

And this time, our motion sensor gives us

something like this.

And notice we get even
higher acceleration.

This time, the acceleration
is, in one second,

it goes from zero to
five meters per second.

So the acceleration has further increased.

So what is the connection that we see?

We see for a higher net force,

more the net force, more
is the acceleration,

provided the mass stays the constant.

We should always be careful
about the control variable

that we have used.

Amazing, isn't it?

But now this brings up the last question.

What if you want to vary the mass?

We want to see the effect of what happens

when the mass changes.

Well, we should always make sure

only one variable is changing.

So if we want to vary the mass,

we have to keep this variable the same.

So, we'll repeat this experiment.

This time, we'll keep
the net force the same.

Let's keep the net
force, say, four newtons.

And let's vary the mass. Let's
make the mass one kilogram.

Then let's repeat the
experiment with two kilograms

and maybe with four kilograms.

All right, first up,

we'll put four newtons for one kilogram.

We actually already did this,
but let's do it one more time.

We'll push it for one second, let it go.

And what does the motion sensor give us?

Well, it gives us an acceleration

of zero to four meters
per second in one second.

Okay, let's repeat this, four newtons,

but this time for two kilogram object.

Again, push it for about
a second, let it go.

What does the motion sensor give us?

(gasps) The acceleration is
smaller. Can you see that?

It went from zero to two meters
per second in one second.

Does that make sense? I think yes.

I mean, if you were to
push a heavier object

with the same force,

you intuitively expect
it to accelerate lesser.

And that's exactly what we get.

So as the mass increased,
the acceleration reduced.

So let's do one last trial.

This time, the mass is four kilograms.

Again, we push it with the same force,

four newtons, for about a second.

We can already see the
acceleration was much lower.

What does the motion sensor give us?

Well, it gives us (laughs)

much lower acceleration this time from,

it went from zero to one meters
per second in one second.

So what do we notice?

We notice that for a given force,

if that force is the same,
if the mass increases,

the acceleration reduces.

So more mass gives you less acceleration

for the exact same net force.

This is the essence of what we
call the Newton's second law.

Of course, we could be more quantitative,

but I think this captures
the essence beautifully.

Newton's second law is one
of the most important laws

in physics because it allows
us to predict the motion

provided we know the net
force acting on the object.