- [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.