Welcome back. And I will now do that same

problem in a much easier way. Let me clear it a little bit. So the original problem we said,

you know, we apply some force to m sub 0 and

that gives some acceleration, a sub 0. And then we said when we apply

the same force to a combination of m sub 0 and

m sub 1, we get 1/5 the acceleration. And we worked it through

with all the variables. What I’ll show you is you can

actually do this type of problem just by substituting

numbers. This is kind of quick and dirty,

but it’s good to do a reality check. And oftentimes, you can solve

the problem without having to go through all the

variable mess. So I can just pick some

numbers here. So I could say, well what if F

sub 0 is equal to 10 Newtons, m sub 0 is equal to– I don’t

know– 2 kilograms. Than a sub 0 is equal to– well, it would

be 10 divided by 2. Because force is equal to

mass times acceleration. So it’d be 5 meters per

second squared. And then in this case, this

would be 10 Newtons. 1/5 a sub 0? Well that will be 1/5 this. So it would be 1 meters

per second squared. And then we could solve for

what the new mass is. How would we do that? Well we have force, which is

10 Newtons, is equal to the sum of the masses. So m1 plus m sub 0. But m sub 0 we already learned

is 2 kilograms. Times the acceleration. Times 1/5 a sub 0, which is 1

meter per second squared. So then we have– this 1, we

could ignore it essentially. So then we essentially have that

10– and since all of our units are right, we can kind of

drop the units because we know they work out. 10 is equal to m1 plus 2. So you get m1 is equal to 8. And then once again, if we want

to know the ratio of m sub 0 to m sub 1, we can just

substitute the numbers. m sub 0 is 2 kilograms. m

sub 1 is 8 kilograms. So the ratio is 1:4. You probably find that

a little bit easier. Let’s do another problem. Whoops. Invert colors. OK. This next problem I think

you’ll find interesting. So let’s say I have a sky diver

and he’s in his sky diver position, falling

towards the ground. And let’s say he weighs 70

kilograms. So his mass is equal to 70 kilograms. Let’s say

that the terminal velocity is 120 miles per hour. So he’s moving downward at 120

miles per hour, which is actually accurate. I’ve gone sky diving. And if we convert that– you

could convert that for fun into the metric system. But I’ll do that for you. But it’s good to know just so

you have a sense of how fast you fall when you sky dive

before the parachute opens. This translates to about

53.6 meters per second. I’m reading this from a problem

from a website at the University of Oregon. But anyway, they are asking

us, what force does air resistance exert on

the sky diver? So let’s be clear

a couple things. This 120 miles per hour,

this is the sky diver’s terminal velocity. And if you’re not familiar with

what terminal velocity is, I will now explain

it to you. So when you fall from a plane,

you have a bunch of wind pushing on you. You have a lot of

wind resistance. It causes friction; it slows you

down as you can imagine. I mean that’s how a

parachute works. It creates a lot more resistance

from the wind and then you slow down. So the terminal velocity is the

velocity at which you no longer go faster than. So it’s the velocity at which

you stop accelerating or it’s the velocity you reach and you

don’t go any faster than that. It’s basically based on

your wind resistance. So at the terminal velocity

your acceleration is 0. So what we know is, is that

the force of the air– we could call that the air force. So we know that the force of

the air is exactly equal to the force of gravity. And how do we know that? Because the guy’s not

accelerating. It’s his terminal velocity. He’s at a very high speed. He had accelerated all the

way to this point. But the more he accelerated

and the faster he got, the more resistance the wind

provided up to a point where the wind provided so much

resistance that he stopped going any faster. And that’s the terminal

velocity. So at terminal velocity, the

force of the air is equal to the force of gravity. What’s the force of gravity? Well the force of gravity is

just the guy’s weight. So the force of gravity is equal

to the guy’s mass, 70 kilograms. And we have

our units right. 70 kilograms. Times the

acceleration of gravity. Well the acceleration of gravity

is 9.8 roughly meters per second squared. We could use a calculator

to calculate this. I feel cheap now. I could have done it

by hand anyway. 686. So it equals 686 Newtons. The second part of the

question– and this is interesting. If a sky diver pulls in their

arm and aims their body downward, so now the sky diver

looks more like this and he pulled in his arms and he

aimed his body down. So he’s diving, really. The terminal velocity can be

increased to about 180 miles per hour or 80.5 meters

per second. They give us this. We could’ve figured

it out though. So now he’s going

a lot faster. Roughly 50% faster than he

was, or maybe– well, 30% faster than he was

going before. He’s going a lot faster

and why is that? Because he’s more

aerodynamic now. We’ll do more on pressure later,

but I want you to get the intuition that when you’re

laying flat there’s just a lot of wind pressing against

your body. You have a lot of surface area

exposed to the wind. But when you’re diving in this

situation, like the sky diver is, he has a lot less

exposed to the wind. Really just his head. His head is breaking the

wind and nothing else. And that’s why it takes a lot

more speed for the force of the wind resistance to match

the force of gravity. So the question is asking, if

the sky diver pulls in their arms and aims their body

downward, the terminal velocity can be increased to

about 80.5 meters per second or 180 miles per hour. So he’s going very fast. What force does air resistance

now exert on the sky diver? And I’ll let you think about

that for a second. Maybe you want to pause it

and think of it yourself. And now that you’ve unpaused it,

I’ll tell you that this is a trick question. Because once again, the sky

diver has reached a new terminal velocity. By definition, at the terminal

velocity, the sky diver is no longer accelerating. The sky diver is not going any

faster because the wind resistance is so strong that

it completely matches the force of gravity. So once again, the wind

resistance, the force of the air or the force of the

wind, is equal to the force of gravity. And what is the force

of gravity? Well that’s his weight. And we already figured

that out. That was 686 Newtons. And I know what you’re

thinking. You’re saying, Sal, this

doesn’t make sense. He’s now going so much faster,

doesn’t the air exert more force on him? Well no. The air is exerting

the same force. If he was going that same speed,

but he was flattened out, I would agree with you. The air would be exerting

more force on him. But what’s happened now is that

he’s once again reached a state where his acceleration

is 0. It’s at a higher velocity

and I want you think a lot about this. He’s at a much higher

velocity now. On his head, for example,

there’s a lot more wind going by. But it’s pressing on a

smaller surface area. And I’m not going to go too

much into detail of pressure right now. But I want you to get

that intuition. So although the wind is going a

lot faster, it’s going a lot faster on a smaller area. And its actual force is

the exact same thing. And we know that because he’s

not accelerating anymore. Because he’s at his

terminal velocity. So think about that a bit. It’s a bit of a trick question,

but I think it gives you a good intuition on what

acceleration means, what terminal velocity means, and

it’ll start to give you a little bit of an intuition

on even wind resistance, on pressure. I’ll see you in the

next video.

THANKS~!

thanks.. your videos help a lot… been looking at the calculus ones and now physics :p

Thank you very much!!!

ration between mph and m/s is that there is about 0.4469'4' m/s is a mph. 1mile/hour = 1609meters/hour. 1609meters/hour=0.4469'4' meters per second.

There also has the bouyancy force acting on the person, therefore the gravity is not totally equals to the air resitance. the large surface area will decrease the terminal velocity.

So when the sky diver reaches terminal velocity, is he free falling?

Ha ha. 50 percent faster, or 33 percent faster? A lot faster…

What software are you using?

even in my uni , i get the profit!

thanks alot! 🙂

this is funny.

the terminal velosidy on a ant isn't a speed what wil kill the ant.

that is why ant's can't fall to there dead.

intuition

lol @ ariforce 😀

Thank you SO much for posting these videos, you helped me get full marks on my physics exam!! (: Btw, can you post some videos on thermal expansion and calorimetry? Thanks a bunch (:

Hi, Im not getting where the 1/5th acceleration figure is coming from. Please can you assist?

yeah i've gone sky diving, i know (haha)

this was an example from the previous video, "Newton's Laws Examples (Part 1)", where the acceleration is given.

Is this university level physics?

gr.11 physics

gr.11 physics

Lol @ him saying he feels cheap for not calculating the mass*g by hand. Dude, done those type of calculation by hand since middle school.

8???

"I feel cheap now." Lmao

@pheonixofpeace this is in a free fall as there is nothing artificial in resisting or assisting in his fall… watch felix baumgartner's story plz

why is mass 1, 8??? if you will transpose 10 to the other side of the equation it will be negative and it will give you an answer of -8 or will I just ignore the sign?

This would've been seriously great except for the fact that the video quality is bad :c

How did you get 53.6m/s from 120m/hr ?