# Intro to springs and Hooke’s law | Work and energy | Physics | Khan Academy

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Let’s learn a little

bit about springs. So let’s say I have a spring. Let me draw the ground so that

we know what’s going on with the spring. So let me see, this

is the floor. That’s the floor, and

I have a spring. It’s along the floor. I’ll use a thicker one, just

to show it’s a spring. Let’s say the spring looks

something like this. Whoops, I’m still using

the line tool. So the spring looks like this. This is my spring, my amazingly

drawn spring. Let’s say at this end it’s

attached to a wall. That’s a wall. And so this is a spring when I

don’t have any force acting on it, this is just the natural

state of the spring. And we could call this, where it

just naturally rests, this tip of the spring. And let’s say that when I were

to apply a force of 5 Newtons into the spring, it looks

something like this. Redraw everything. So when I apply a force of 5

Newtons– I’ll draw the wall in magenta now. When I apply a force

of 5 Newtons, the spring looks like this. It compresses, right? We’re all familiar with this. We sit on a bed every

day or a sofa. So let’s say it compresses

to here. If this was the normal resting–

so this is where the spring was when I applied no

force, but when I applied 5 Newtons in that direction, let’s

say that this distance right here is 10 meters. And so a typical question that

you’ll see, and we’ll explain how to do it, is a spring

compresses or elongates when you apply a certain force

by some distance. How much will it compress when

you apply a different force? So my question is how much will

it compress when I apply a 10-Newton force? So your intuition that it’ll

compress more is correct, but is it linear to how much

I compress it? Is it a square of how

much I compress it? How does it relate? I think you probably

could guess. It’s actually worth

an experiment. Or you could just keep

watching the video. So let’s say I apply

a 10-Newton force. What will the spring

look like? Well, it’ll be more

compressed. Drop my force to 10 Newtons. And if this was the natural

place where the spring would rest, what is this distance? Well, it turns out that

it is linear. What do I mean by linear? Well, it means that the more

the force– it’s equally proportional to how much the

spring will compress. And it actually works

the other way. If you applied 5 Newtons in this

direction, to the right, you would have gone 10 meters

in this direction. So it goes whether you’re

elongating the spring or compressing the spring within

some reasonable tolerance. We’ve all had this experience. If you compress something too

much or you stretch it too much, it doesn’t really go back

to where it was before. But within some reasonable

tolerance, it’s proportional. So what does that mean? That means that the restoring

force of the spring is minus some number, times the

displacement of the spring. So what does this mean? So in this example right here,

what was the displacement of the spring? Well, if we take positive x to

the right and negative x to the left, the displacement

of the spring was what? The displacement, in this

example right here, x is equal to minus 10, right? Because I went 10 to the left. And so it says that the

restorative force is going to be equal to minus K times

how much it’s distorted times minus 10. So the minuses cancel out,

so it equals 10K. What’s the restorative force

in this example? Well, you might say, it’s 5

Newtons, just because that’s the only force I’ve drawn here,

and you would be to some degree correct. And actually, since we’re doing

positive and negative, and this 5 Newton is to the

left, so to the negative x-direction, actually, I should

call this minus 5 Newtons and I should call this

minus 10 Newtons, because obviously, these are vectors and

we’re going to the left. I picked the convention that

to the left means negative. So what’s the restorative

force? Well, in this example– and we

assume that K is a positive number for our purposes. In this example, the restorative

force is a positive number. So what is the restorative

force? So that’s actually the force,

the counteracting force, of the spring. That’s what this formula

gives us. So if this spring is stationary

when I apply this 5-Newton force, that means that

there must be another equal and opposite force that’s positive 5 Newtons, right? If there weren’t, the spring

would keep compressing. And if the force was more than 5

Newtons, the spring would go back this way. So the fact that I know that

when I apply a 5-Newton force to the left, or a negative

5-Newton force, the spring is no longer moving, it means that

there must be– or no longer accelerating, actually,

it means that there must be an equal and opposite force to

the right, and that’s the restorative force. Another way to think about it is

if I were to let– well, I won’t go in there now. So in this case, the restorative

force is 5 Newtons, so we can

solve for K. We could say 5 is

equal to 10K. Divide both sides by 10. You get K is equal to 1/2. So now we can use that

information to figure out what is the displacement

when I apply a negative 10-Newton force? When I push the spring

in with 10 Newtons in the leftward direction? So first of all, what’s the

restorative force here? Well, if the spring is no longer

accelerating in either direction, or the tip of

the spring is no longer accelerating in either

direction, we know that the restorative force must be

counterbalancing this force that I’m compressing

with, right? The force that the spring wants

to expand back with is 10 Newtons, positive

10 Newtons, right? And we know the spring constant,

this K for this spring, for this material,

whatever it might be, is 1/2. So we know the restorative force

is equal to 1/2 times the distance, right? And the formula is

minus K, right? And then, what is

the restorative force in this example? Well I said it’s 10 Newtons, so

we know that 10 Newtons is equal to minus 1/2x. And so what is x? Well, multiply both sides

by minus 1/2, and you get minus 20. I’m sorry, multiply both sides

by minus 2, you get minus 20 is equal to x. So x goes to the

left 20 units. So that’s all that

it’s telling us. And this law is called Hooke’s

Law, and it’s named after– I’ll read it– a physicist in

the 17th century, a British physicist. And he figured out

that the amount of force necessary to keep a spring

compressed is proportional to how much you’ve compressed it. And that’s all that

this formula says. And that negative number,

remember, this formula gives us the restorative force. So it says that the force is

always in the opposite direction of how much

you displace it. So, for example, if you were

to displace this spring in this direction, if you were to

apply a force and x were a positive and you were to go in

that direction, the force– no wait, sorry. This is where the

spring rests. If you were to apply some force

and take the spring out to here, this negative number

tells us that the spring will essentially try to pull back

with the restorative force in the other direction. Let’s do one more problem

and I think this will be clear to you. So let’s say I have a spring,

and all of these problems kind of go along. So let’s say when I apply a

force of 2 Newtons, so this is what I apply when I apply

a force of 2 Newtons. Well, let’s say it this way. Let’s say when I stretch

the spring. Let’s say this is the spring,

and when I apply a force of 2 Newtons to the right, the spring

gets stretched 1 meter. So first of all, let’s

figure out what K is. So if the spring is stretched

by 1 meter, out here, its restorative force will be 2

Newtons back this way, right? So its restorative force, this

2 Newtons, will equal minus K times how much I displaced it. Well I, displaced it by 1 meter,

so then we multiply both sides by negative 1, and we

get K is equal to minus 2. So then we can use Hooke’s Law

to note the equation for this– to figure out the

restorative force for this particular spring, and

it would be minus 2x. And then I said, well, how much

force would I have to apply to distort the

spring by 2 meters? Well, it’s 2 times

2, it would be 4. 4 Newtons to displace it by 2

meters, and, of course, the restorative force will then be

in the opposite direction, and that’s where we get the

negative number. Anyway, I’ve run out of time. I’ll see you in the

next video.

Tyler MarshPost authorIts a shame he goes into much more detail on other topics but he cover just the tip here.

Fuego FandangoPost authorWhy do ALL educational videos teach people more in 10 minutes than their teachers do in 10 days?

Sakir HossainPost authorWhen u pulled the spring 2N to the right the Resistance force is -2N. and since you move 1 meter,

F= – K X

-2N= -k * 1m

k= 2 not -2

momentlikethatPost authorwhat is the -K?!?!?

Alex WongPost authorits a predetermined constant

momentlikethatPost authoryeah I figured that out later

TheSpiderManuPost authorLet's see you do one of these lessons, you tool.

RadialEffectsPost authorthe force is strong in this one

kevinbs05Post author10 m for 1/6th the distance of the spring? That's one big ass spring.

ThenconvienttruthPost authorWhy watch the video just to down it jealous punks

bananianPost authorIs there a Springe's law for hook physics?

MadCarbonPost author00.26. That's what he said

lawlgirl97Post authorhe doesn't need to prepare he's amazing

Rayne DeermanPost authorvery unprofessional… didnt learn the material in class and now has to cover up his dumbass with youtube videos. stfu

Shubham ShahPost authorIts not he video ……we need practical

Alex Van NoordPost authorWouldn't k in the second equation be 2 and not -2? Since he's applying the force in the positive direction, the restorative force would be negative, so -2=k*1, so k=-2? Isn't that what he did in the first example?

ShujeePost authorYou're right. K should be 2 in the last equation.

Julie AlmerPost authorThese people actually know how to teach, verses others that attempt to teach.

David KimPost authorwell his subscribers and like ratios tell otherwise….therefore your comment is invalid.

David KimPost author…that..was a terrible comparison.

IVIichaelDPost authorHaha. 1 year later and that guy is still getting shit. He must regret posting that comment so much 🙂

David KimPost authorhis comment was bad and he should feel bad >:]

MitchellPost authorThank you so much! I was feeling a little shaky about a few things for my Physics exam that I forgot to ask my teacher, and these videos have really cleared things up!

Dianacat777Post authorAll of my yes D:

John HorakPost authorI think the people who go out of their way to put videos up on youtube for free generally have an enthusiasm that not all teachers have (some anyway)

Agassi TranPost authorWhen I am in class, I'm like, "GOD WHAT CAN'T THIS PHYSICS CLASS BE SHORTER…" When I am watching this video, I'm like, "GOD WHY CANT THIS VIDEO BE LONGER…" 😉

ECGTheConduitPost authornewton must feel like such a badass, forget a building or even a species or a star, he has a force of nature named after him.

iieeKateyPost authorWhy wasn't the restorative force in the last example -2N instead of 2N since it was acting to the left?

Joshua Daly ManocchioPost authorDat spring

Nastascia BrownPost authorI bet he has a higher pass rate than your "professional and organized" teacher who prepares for classes

Nastascia BrownPost authoryes i think he created another video to correct this

rgorjon9Post authoryou explain things too slowly

Ben LewisPost authorI can tell you as a student that often students don't want to be in lessons or don't care about what their teacher is saying, but if a student stays around long enough to watch a video then they definitely care enough about the topic or like way it's taught and it's a convenient time for them. Hence students always find educational videos more convenient and hence better.

LaurelindoPost authorI believe the typical flaw of many physics teachers is that they don't really explain things in-depth, they just shove formulas into your face and tell you to calculate something.

Anyone can put numbers into formulas, the real challenge in physics is to actually understand what's going on and WHY the formulas look the way they do.

Khan is very good at explaining those kinds of things, and it gives you a much better intuition.

nopenismanPost authorBecause teachers get paid by the hour.

Darth WaderPost authorShouldn't the value of K in the last example be positive due to the fact that the force isn't put to compress? In that way it's negative from the beginning, -2N to counteract the positive force of 2N?

Anish BachanPost authorya

Anish BachanPost authorikr

karan handaPost authorRobert Hooke?

Adam WojtczakPost authorBecause lots of teachers don't fully understand what they are teaching. They know how to get the right answer, in terms of using the formulas correctly, but I bet you they couldn't break down what that formula is actually doing… They don't understand WHY the formula works essentially. Don't get me wrong there a lots of awesome teachers (from my experience at least), but there are also too many that simply teach the curriculum, without an in-depth understanding of what they teach.

Namrata ChauhanPost authorthanks Mr. Khan.

Eric DalrymplePost authorKHAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAN!!!!!!!!

maquis tomPost authorYou would have to watch Khan for a month or so without a break in order to watch all their videos. I just calculated it assuming the videos average 10 min in length. Better start somewhere…;)

Benjamin NeufeldPost authorhow does the 1/2 part come into play in the restoring force =-kx formula

Frida WesterberghPost authorBut if the spring is at rest the restoring force must be zero?

Matt SiegelPost author20 metres? that is a lonnnnng spring

Doreen StanleyPost authorRestorative force for the last example is NEGATIVE 2; I think Khan put positive 2 by mistake

mastercj90Post authorclick the little settings cog and above quality change the speed to 1.5. exams are too soooon

c flynnPost authorI don't understand why k is negative…. isn't the equation F = (k)(x)?

G3 mintPost authorVideo won't load…

ClevverPost authorvideo doesnt load for me, tried it on both youtube and khanacademy site, doesnt work

John GomesPost authorlove you KHAN

UNBASHDubPost authorWhy isn't the video loading?

Viiz VenomZzPost authorgo to settings put the graphics to 240p and it will surely work :}

ed grovesPost authorskip forward a few seconds if it isnt loading

Essam CreamPost authorIts fine now

denzelPost authorwhat exactly is K?

Dhiraj KhanalPost authorWow

Muhammad Haziq HafizuddinPost authorIn the last example, why the sign of restoring force is positive?

AnastasiaPost authorWatching your videos always makes me envy the kind of education developed countries get, where i'm from physics might as well be math with different units ..

m1h2al3Post authorhe's really good at explaining, but he spends tooooo much time drawing and wasting time over silly things

Colton ClarkPost authorthats a big spring

fairlylocal TØPPost authori can always rely on you

Amarysti KardiPost authorisnt it supposed to be f=-(-2)x for the 2nd question? anyone?

Meckro 1203Post author240p This is HD YouTube quality right here!

101chorochoroPost authorx is displacement, a vector unit, so shouldn't 10m also have a negative sign on it?

Érchegyi DávidPost author-5N to the left direction (as drawn) means 5N to the right

ZnNlove EfilPost authorGood ol' days of 240p Khan Academy

asparwhite86Post authorYou totally kick my professor's ass.

Rahul RoyPost authortoo slow u should use another way to teach (dont use those painting apps or whatever)

AntonyPost authorhelped me alot thanku so much

AntonyPost authorin the last question isn't restorative force -2 Newton cause it's acting towards the left?

Hani HashemiPost authorQUALITY ;(

Equay GamingPost authorGetting this on my test 😉

Equay GamingPost authorHooke's law states that the extension of a spring is directly proportionate to the force applied.

Hazem AlsoweedPost authorThanks khan academy

Sidney ReedPost authorSurely the signs for the last question would have to change??

FaZe AdaptPost authorWHAT IS K!

ⒽⓐⓝⓐPost authorThanks for the great expanation! May the FORCE be with you 🙂

Khiem LuongPost authorso F is not the applied force?

Bhuvanesh NPost authorSo even if I move a car by distance x or if I move a pin by the same distance X then the force applied by me is the same for both cases ??

Steven SosaPost authorThank you!

Abhishek BhattacharjeePost authoryou have come a long way sal

sumit kumarPost authorMy new PHYSICS SOLVING APP.More then 150+ formulas,Solves for any variable you want,Covers up all physics.download now.https://play.google.com/store/apps/details?id=com.physics.lenovo.myapplication

Jesus and Mary, Inseparable - Flat Earth CatholicPost authornot very good

BennethpPost authorI wish they would redevelop these videos

BeequoofiusPost authorIB Physics where u at

TPlus GamingPost authorwho dislikes this video

West KoreaPost authorHe used the force applied force instead of the restorative force so k should be 2 instead of -2. He should have known something was wrong as soon as k was negative which is impossible

Hussain AladwanPost authordude doesnt know simple math

Jason JosephPost authori dont get it

daddy coolPost authorWho doesn't understand physics like me?

Alex HarrisonPost authorthe quality of the video looks like it was recorded using a calculator

jobless indianPost authorWhy dnt u draw dia in advance

SWETA SHAWPost authorCannot understand simple harmonic motion of horizontal elastic string and mass system. Mind it it's string not spring

eh6794Post authorI think Sal was one of the first people to do these types of videos, but man, they are hard to watch today. Too much nonsense with the colors and pictures.

bagya AluthgePost authorTy

Arman GrigoryanPost authorSal, don't stammer please, I'm getting confused 🙁

Jesus From HyrulePost authorWouldn’t F=2x in the last example ? Since u had k = -2 therefore -(-2)x would be the function

Light33 NightshadePost authorIf I take positive X to right and negative to left since force is also a vector quantity shouldn't it b negative to left as well?