Newton's second law calculations | Physics | Khan Academy

- [Lecturer] Let's solve
a couple of problems

on Newton's second law.

Here's the first one.

We have an elevator, which is moving up.

And let's say the mass of the elevator,

including the passenger
inside, is 1,000 kilograms.

Now the force, the tension
force of the cable,

let's say that's about 7,800 newtons,

our goal is to figure
out what the acceleration

of this elevator is.

We're also given that the
gravitational force acting

on that elevator, including
the passenger over here,

is about 9,800 newtons.

So, how do we figure this out?

Well, the first thing
that comes to my mind is,

"Hey, we have some forces

and we have some motion
variables like acceleration.

What connects forces and motion variables?

What connects forces and motion?

Newton's second law.

So, the first thing I try to do

before applying Newton second law is I try

to draw a free body diagram.

So lemme do that.

What's the way to draw
a free body diagram?

We try to get rid of unnecessary details.

Use a box to represent
your object of interest.

Our object of interest is this elevator

and the person over here.

So, that's our box.

It's mass is 1,000 kilograms

and let's draw all the
forces acting on it,

which are the forces acting on it.

Well, we have an upward
force that's tension

and we have a downward force
that's the force of gravity

and our goal is to calculate
what the acceleration is.

And how do we do that?

Well, we use Newton second law,

which says the acceleration

should equal the net
force acting on an object

divided by its mass.

And of course, since we're
dealing with vectors,

we can put arrow marks over here.

The direction of the
acceleration will be the same

as the direction of the net force.

Okay, now we can calculate
the net force from this

and we can calculate, we know the mass,

so from that we can
calculate the acceleration.

So why don't you pause the video

and see if you can plug in the numbers

and find the acceleration yourself first.

All right, let's try.

So our acceleration
would be the net force.

How do I figure the net force out?

Well, the total force,

well they're since in
the opposite direction,

we'll subtract them.

So, I'll just take the bigger number.

So 9,800 newtons, which
is acting downwards.

We need to take care of the direction.

From that, I'll subtract
the smaller number,

that is 7,800 newtons
upwards divided by the mass,

which is 1,000 kilograms.

And if you simplify,

we will get 9,800 minus 7,800 is 2,000.

Nice numbers, 2000 newtons.

But what direction is it?

The downward one wins, right? It's bigger.

So, the net force will be
in the downward direction.

It's divided by 1,000 kilograms
and that gives us two.

So, our acceleration becomes

two meters per second square downwards.

Okay, we found our answer,

but one of the best ways to
gain deeper insights is to try

and see if this kind of makes sense.

Can you get a feeling for
what's going on over here?

Okay, now the first question

that we could be having
over here is, look,

the net force is downwards

because gravity is winning, right?

So the total force acting on
this elevator is downwards

and yet the elevator is moving up.

Why is that? (chuckles)

Well, remember, force does not dictate

the direction of motion.

Force tells you the direction
of acceleration, okay?

The elevator could be moving,

objects can be moving
whatever direction it wants.

When you put a force on it, it tells you

what direction it should accelerate.

So that's the key thing.

So, there is no problem that
the force is acting downwards,

but the elevator is moving upwards.

Secondly, what does it mean

that the acceleration is downwards?

See, if the net force is downwards,

the acceleration has to be downward.

But what does it mean
the elevator is moving up

and the acceleration is downwards?

Ooh, this means since the velocity

and the acceleration is
in the opposite direction,

this means the elevator is slowing down.

That's what it means for velocity

and acceleration to be in
the opposite direction.

If they're in the same direction,

it means they're speeding up.

So, this means our elevator is going up,

but it is slowing down, which
probably means that, you know,

it's probably about to stop.

Maybe this person has probably reached

his destination or something.

All right, onto the next problem.

This time we have a sledge at
rest whose is 70 kilograms.

Our goal is to push it

and accelerate to six meters per second

in about two seconds, let's say,

so that, you know, it
can nicely slide down

and we can enjoy the ride.

Now, there is going to
be some frictional force.

Even though we're on ice and everything,

there'll be some frictional force.

Let's say the friction

that this ledge will experience
is about 200 newtons.

The question now is what is
the force with which we have

to push on it so as to
achieve all of this?

So how do we figure this out?

Well, again, the first thing
that comes to my mind is

that look, we're dealing with
forces and we have motion.

What connects forces and
motion? Newton's second law.

So, the first thing I'll
do is I'm gonna draw

a free-body diagram.

Again, I encourage you
to pause the video now

or anytime later on.

Whenever you feel more comfortable,

pause the video and see if
you can complete it yourself.

Okay, so anyways, let's first try

to draw a free-body diagram.

How do we do that?

Well, again, we'll take
the object of our interest.

In this case, the object of
our interest is this ledge

whose mass is 70 kilograms
and just make it a square

and then draw all the forces acting on it.

What are the forces acting on it?

I know there's frictional
force acting backwards

of 200 newtons, but then I
also have the applied force

by this person, which I,
we need to figure out.

This is what we need to calculate.

That is the applied force.
What are other forces?

Well, I know that there's
also gravity acting on it

and then there's a normal
force acting on it upwards.

But we know that these forces are balanced

and so they're not going to be useful.

They're not going to affect
our situation over here.

So, I'm just gonna draw them over here.

They're there, of course, but
they're completely balanced.

They're in the verticals,
they're not gonna affect it,

so we'll not draw it.

Okay, now that I have
my free-body diagram,

let's go ahead and write
down on Newton second law.

It says acceleration should
always equal the net force,

which let me draw using pink now.

Net force divided by the mass.

Divided by the mass.

Okay, so what do we do next?

I need to find this applied force.

So this means if I can
calculate the net force,

then I can figure out what
the applied force is, right?

So, from Newton's second law,

I just need to figure out
what the net force is.

For that, I ask myself, do I know m?

I do. I know that m is 70 kilograms.

Do I know the acceleration?

Hmm, it's not given directly,

but wait a second, I know
the initial velocity,

I know the final velocity and I know

that the change in velocity
should happen in two seconds.

Whoo-hoo!

That means I can calculate the
acceleration from this data.

I can plug in and from
that I can figure out

what the total force is going to be,

the net force is going to be.

And from that we can figure out

what the applied force should be.

Okay, so if you haven't done this before,

why don't you now pause the video

and see if you can put it all together

and solve the problem?

Okay, let's do this.

So, let me first calculate
the acceleration.

So our acceleration is going

to be, well how do we figure this out?

This is the final velocity
minus the initial velocity

divided by the time taken.

So, that's going to be, in our case,

the final velocity is
six meters per second

to the right minus...

What's the initial velocity?

Well, it's zero, it's at rest.

So there is no initial velocity divided

by time is two, two seconds.

That gives us what?

That gives us six by two is
three meters per second squared

to the right.

So I know my acceleration has to be

to the right, which is
good news. (chuckles)

It has to be to the right.

We want this ledge to move to the right.

So, that makes sense.

So, we are on the right track over here.

Okay, now, I can plug in

and figure out what the
net force is going to be.

So, if I just simplify that,
so net force is going to be,

if I rearrange this equation
multiply by m on both sides.

So I get net force to be
mass times the acceleration.

And so now I can plug in
for mass and acceleration.

What do I get? Well I get 70 kilograms.

That's the mass,

times the acceleration is three
meters per second squared,

70 times three, seven times these 21.

So, this is 210.

So, I get that my net force is 210 newtons

to the right of this,

this acceleration was to the right.

So, this will also be to the right.

So, now that I've found my
net force, so my net force,

the total force will be to the right

and that is 210 newtons.

From that, can I calculate
the applied force? Yes.

So now, first of all,

I know my applied force should be bigger.

It has to be bigger

because my total force
should be towards the right,

which means if I subtract
the two from this,

if I subtract this number,
I should get this number.

That's the net force, all right?

So now, now that I know all the directions

and everything, I can
just subtract the numbers.

So I can now say, "Hey, my net force

that is 210 newtons should
equal this bigger number,

the bigger force minus 200 newtons.

Now, to get applied force,
I just add 200 on both sides

so that I can get rid of this.

And look, the applied
force becomes 210 plus 200.

That is 410 newtons.

And I already know it's to the right,

so I know it's direction.

So if I were to write down its direction,

it's going to be, oops. (chuckles)

Okay. Okay.

I mean, okay, not the most
organized board over here,

but let me just write it down
a little bit more neatly.

So 410 newtons to the right.

That's how much force we need to apply

for all of this to happen.