When I say “work,” what’s the first

thing that comes to mind? Maybe a cubicle? Or a briefcase?

Or that history exam that’s coming up soon? But if you’re a physicist, work has a very specific meaning — one that has very little to do with spreadsheets or the fall of the Roman

Empire. Today, we’re going to explore that definition

— and how it connects to one of the most important principles in physics: conservation

of energy. We’ll also learn what physicists mean when

they talk about another concept that comes up a lot in daily life: power. So let’s get to…work. [Theme Music] So far in this course, we’ve spent most of our time talking about forces, and the way they make things move. And you need to understand forces before you

can understand work. Because work is what happens when you apply

a force over a certain distance, to a system — a system just being whatever section of the universe you h appen to be talking about at the time. For example, if you’re using a rope to drag

a box across the floor, we might say that the box is your system, and the force you’re

using to pull on it is an external force. So, let’s say you’re pulling on this box-system by dragging it straight behind you, so the rope is parallel to the ground. If you use the rope to pull the box for one

meter, we’d say that you’re doing work on the box. And the amount of work you’re doing is equal

to the force you’re using to pull the box, times the distance you moved it. For example, if you pulled the rope — and

therefore the box — with a force of 50 Newtons, while you moved it 5 meters, then we’d say

that you did 250 Newton-meters of work on the box. More commonly, however, work is expressed

in units known as Joules. Now, sometimes, the force you apply to an

object won’t be in exactly the same direction as the direction in which the object is moving. Like, if you tried to drag the box with your hand higher than the box, so that the rope was at an angle to the floor. In that case, the box would move parallel to the floor, but the force would be at an angle to it. And in such an instance, you’d have to use one the tricks we learned back when we first talked about vectors. Specifically, you must separate the force you’re using on the rope into its component parts: one that’s parallel to the floor,

and one that’s perpendicular to it. To find the part of the force that’s parallel to the floor — that is, the one that’s actually pulling the box forward — you just have to multiply the magnitude of the force by the cosine of the rope’s angle to the ground. You’ll remember that we typically designate

an angle in a system as theta. So, to calculate the work you did on the box,

you just multiply the horizontal component — or F times the cosine of theta — by the

distance you moved the box. That’s one way physicists often write the

equation for work — they’ll set it equal to force, times distance, times the cosine

of theta. And that equation will fit any scenario that involves a constant force being applied over a certain distance. But what if the force isn’t constant? What if, say, you started out pulling hard

on the box, but then you started to get tired, so the amount of force you exerted on the

box got smaller and smaller the farther you dragged it. To calculate the work you did in that case,

you’d have to count up the amount of force you applied over each tiny little bit of distance. And if you’ve watched our episodes on calculus,

then you know that there’s a faster way to add together infinitely tiny increments:

integration. So, to find the work done by a varying force,

you just have to integrate that force relative to the distance the object moved. Which would

look like this. But force-times-distance is only one of the

ways that physicists measure work. Because, you know how we just said that Joules are

the units of work? Well, Joules are often used as the units for

something else: energy. And work uses the same units as energy,

because work is just a change in energy. It’s what happens when an external force is applied

to a system and changes the energy of that system. In fact, that’s one of the ways to define

energy — it’s the ability to do work. There are all different kinds of energy, but in this episode, we’ll mainly be talking about two of them: kinetic energy and potential energy.

Kinetic energy is the energy of motion. When the box was resting on the ground, we’d

say that it had no kinetic energy. But once you applied a force and it started

moving, it did have kinetic energy. And the energy of the box changed, which means

that you did work on it. More specifically, the kinetic energy of an object is equal to half of its mass, times its velocity squared. If this looks familiar, that’s because it

comes from applying both Newton’s second law and the kinematic equations to the idea

that work is equal to force times distance. So, if the box had a mass of 20 kilograms,

and at some point while you were dragging it, it reached a velocity of 4 meters per

second, we’d say that its kinetic energy at that moment was 160 Joules. Then there’s potential energy, which actually

isn’t what it sounds like. Potential energy isn’t potentially energy

— it’s potentially work. In other words, potential energy is energy

that could be used to do work. One common type of potential energy is gravitational

potential energy – – basically, the potential energy that comes

from the fact that gravity exists. If I hold this book a meter above the ground,

we’d say that it has gravitational potential energy. Because if you let it go, then gravity is

going to do work on the book. Gravity exerted a force that moves it to the ground. Once the book hits the ground, though, we’d

say that its gravitational potential energy is zero, because gravity can’t do work on

it anymore. Calculating gravitational potential energy

is easy enough: it’s just the force of gravity on the object

— so, the object’s mass times small g — multiplied by the object’s height.

Or mgh for short. Which means that, just by knowing that this

book’s mass is about a kilogram, and that it’s a meter above the ground, we can calculate

its potential energy: which is 9.8 Joules. Another type of potential energy that shows

up a lot is spring potential energy. Despite its name, this is not a seasonal thing —

and yes, I really made that joke. Rather, it’s the type of potential energy that’s

specific to springs! The force of a spring is equal to the distance

by which it’s either compressed or stretched, times a constant that we write as k. This equation is known as Hooke’s law, after British physicist Robert Hooke, who came up with it in 1660. Now, the constant, k — also called the spring

constant — is different for each spring, and it’s a measure of the spring’s stiffness. And the equation makes total sense, if you

think about it: The further you push on the spring, and the

stiffer it is, the harder it will resist. You even can test this out for yourself by taking apart a clicky pen and playing with the spring inside. By combining Hooke’s law, with the idea

that work equals force times distance, we can find the potential energy from a spring: it’s half times k times the distance squared. For example: if you have a spring with a spring

constant of 200 Newtons per meter, and a block is compressing it by half a meter, then the

potential energy of the block would be 25 Joules. So, when something does work on a system,

its energy changes. But how that energy changes depends on the

system. Some systems can lose energy. These are known

as a non-conservative systems. Now, that doesn’t mean that the energy that’s

lost is literally disappearing from the universe… And it doesn’t have anything to do with

the system’s personal politics, either. It just relates to one of the most

fundamental principles of science: that energy can neither be created or destroyed. But systems can lose energy, like when friction

from the box dragging on the floor generates heat. For non-conservative systems, you can still talk about their kinetic energy or potential energy at any given moment. But conservative systems let you do much more

than that. A conservative system is one that doesn’t

lose energy through work. Say, a simple pendulum. When the pendulum is at the top of its swing,

it stops moving for a brief moment as it changes direction — meaning that its kinetic energy, at that point, is zero. But it has lots of potential energy, because

the gravitational force can do work on the pendulum, pulling it down until it reaches

the bottom of its swing. At the bottom of the swing, that potential

energy becomes zero, because gravity can’t pull the pendulum down anymore. But now the pendulum has lots of kinetic energy,

because it’s moving through the swing. And it turns out that, at any given point

in the pendulum’s motion, its kinetic energy and its potential energy will add up to the

same number. If its potential energy increases? Its kinetic energy will decrease by the exact same amount, and vice versa. So, now that we know how to define work, we

can use that definition to help explain another common term that physicists have a very specific meaning for: power. Or, more specifically, average power. Average power is defined as work over

time, and it’s measured in Watts, which is just another way of saying Joules per second. Basically, it’s used to measure how much energy is converted from one type to another over time. So, remember that box you were pulling? We figured out that you did 250 Joules of

work on the box when you moved it 5 meters. If it took you 2 seconds to move the box,

then your average power output was 125 Watts. You’re basically a lightbulb! Now, we can also describe power in another

way, by putting two different facts together: One, that work is equal to force times distance. And two, that average velocity is equal to

distance over time Knowing this, we can say that power is the net force applied to something with a particular average velocity. If you moved the box 5 meters in 2 seconds,

then its average velocity was 2.5 meters per second. And we already said that you were pulling

the box along with a force of 50 Newtons. So, the force you were using to pull the box,

times the box’s average velocity, would also give you an average power output of 125

Watts. The two equations for average power are

really describing the same relationship; they’re just using different qualities to do it. We’re going to be talking about power a

lot when we discuss electricity in later episodes. It’s the best way to calculate how

energy moves around in a circuit. But that’s a story for another day. For

now, our work is done. Today, you learned the two equations we can use to describe work, and that energy is the ability to do work. We also talked about kinetic and potential

energy, and how they play into non-conservative and

conservative systems. Finally, we found two different equations

for power. Crash Course Physics is produced in association

with PBS Digital Studios. You can head over to their channel to check

out amazing shows like The Art Assignment, PBS Idea Channel, and PBS Game Show. This episode of Crash Course was filmed in

the Doctor Cheryl C. Kinney Crash Course Studio with the help of these amazing people and

our equally amazing graphics team is Thought Cafe.

She is so beautiful

I looove this…. Well, it's alot of information in a few minutes, probably this explains the name of the channel, Crash course. Thanks though team crash course…. This z great work, great set up, great illustrations…. Keep it up. As an owner of a tutorials YouTube channel, I'm greatly inspired to up my game too…..

0:04 for a moment i heard wack…

Had to slow this down

3:06 I just realised this is above my IQ level

..what?

You're too fast to catch…๐ฒ๐ฒ

I have a test over rotation, work energy power, forces, impulse/momentum, and kinematics in a few hours. Physics is satisfying and difficult at the same time.

I demand an unattractive teacher for I cannot focus!!๐

i got a physics test in 45 minutes,,,,,lets goooo

This made the whole pendulum thing easier

is there arabic?? plaese

hi

Sheโs hot

You're basically a lightbulb

Discusting add

I was distracted by her hair, I just wanna touch it.

what happened to John Green? I like him better he is more elaborate and better to understand.

ALL MY GUYZ ARE BALLERS

(Yawns.) 2 ez. Next.

God I love this channel. It's a great review, but being out of school for a while I now have a genuine interest in learning as much as I can.

I heard Wack ๐ ๐ D

I donโt understand half of the things she says

Whenever I see a video with her I sigh in relief. I'm saved

what is the meaning of plowing afriend?

0:03 —– Shwing!

could you find the tension in the rope that's pulling it at an angle?

Iron man disliked the video

What if the angel is 360 ???

Plz somebody help me

too fast

hello

Too fast. Annoying. Adds to scatter-brain.

Thank you so much I've got an exam tomorrow and didn't have a single clue about this stuff

You've taught me this in 10 mins I've been going to school for the past 10 months and I didn't get a single word.

you talk way too fast I can't understand anything you are saying

slow down

Hagrid: harry your the sympol of power

Harry: i am a watt??

Thataaaaaaaaaa

Use Avg instead of Ave for Average

This is one of the videos listed to watch by my online summer physics professor and I am sorry, but you clearly you know your stuff but you go waaaay too fast for me to learn anything.

Im so very confused

<3 <3 <3 <3

Final exam is in 4 minutes and here I am

Omagoiid! I DO have a history exam tomorrow!!!

…and my physics final exam an hour from now. Haha

Bless you CrashCourse! <3

เฎ

omg I love you

My university linked me this video, that's quite cool ๐

I learned physics in German

Now I have to translate everything in my head to follow

4:51 ME: my bible

I didn't understand ๐

Theeeta

She's so funny, makes it nice and clear. Really helpful

I slow down crash course videos and replay the 10 times so i could surely understand. I tired.

too confusing…

too confusing…

ุดูุฑุงโฆโค๏ธโฉ

Thank you โค

when I sAy wHaCkk

Can you make a video about momentum and friction?

Bad one star

I feel personally attacked from the quote of "that history exam that's coming up soon", the history exam that's tomorrow rIGHT AFTER MY SCIENCE EXAM

Anyone still here in 2019 because they need to study for physics?

I therefore conclude that you can't crashcourse physics.

When I say wak

So you mean that work is defined as how much force recieved on the object

Awesome for review of chapter ๐๐

Hah gayyyy

Day after tomorrow is my physics exam like and wish me

Thank you

you guys are awesome!! could you make a crash course calculus?

i love the name of JESUS AND I DONT WANT IT TO BE USED IN VAIN' so please be sensetive in such issues

Fair to say conservative systems are unrealistic? A small amount of energy is always lost as heat or something…

3:08 iight imma head out

Work is not always just force ร displacement

Q

you idiots have to watch a video on physics, i know everything there is to know about humans and physics, math,science, even minecraft and terraria but not fortnite that game sucks. i am on a higher plane of existence than you neanderthals. also, you've been gnomed

This the the sixth chapter of physics plus one in ncert

Thanks to explain

anyone will understand power well if the teacher will be so beautiful and smart.

You know, if you used proper units, you would eliminate ambiguity with calories for energy and BTUs for work.

6:40 LOL.

I definitely understood everything

I like my theta to be bae. That's why I pronounce it thAEta

Yup, 100% wish she was my physics professor instead of the one I have. For many many reasons lol.

Bravo!!!!! My concept of energy is finally clear

i've gotta put in more work this is getting harder

I wonder how many of us are here because we've got a Physics exam soon lol.

when she says wAcK the first thing that comes to my mind is that the british are so wAcK

What is the difference between energy and Force ??

4:18 I am suddenly completely lost..

You single?

Now there is british girl ?

Too faaaaast

If energy can neither be created nor destroyed how it came into existence

Itโs nice to see you simply use fdcos theta instead of f dot d which is less intuitive

boring

You're hot! and it's too distrusting to pay attention on the study part. I'm screwed in tomorrow's exam๐ญ

So nicely explained. Thank u

–

hello sir homko Pura information energy me bare m chahea

book named einstentein.

rip

Thank you mam you cleared all my problems.