Welcome back. At the end of the last

video, I left you with a bit of a question. We had a situation where we

had a 1 kilogram object. This is the 1 kilogram object,

which I’ve drawn neater in this video. That is 1 kilogram. And we’re on earth, and I need

to mention that because gravity is different from

planet to planet. But as I mentioned,

I’m holding it. Let’s say I’m holding it 10

meters above the ground. So this distance or this

height is 10 meters. And we’re assuming the

acceleration of gravity, which we also write as just g, let’s

assume it’s just 10 meters per second squared just for the

simplicity of the math instead of the 9.8. So what we learned in the last

video is that the potential energy in this situation, the

potential energy, which equals m times g times h is equal to

the mass is 1 kilogram times the acceleration of gravity,

which is 10 meters per second squared. I’m not going to write the units

down just to save space, although you should do this when

you do it on your test. And then the height

is 10 meters. And the units, if you work them

all out, it’s in newton meters or joules and so it’s

equal to 100 joules. That’s the potential energy when

I’m holding it up there. And I asked you, well when

I let go, what happens? Well the block obviously

will start falling. And not only falling, it will

start accelerating to the ground at 10 meters per second

squared roughly. And right before it hits the

ground– let me draw that in brown for ground– right before

the object hits the ground or actually right when it

hits the ground, what will be the potential energy

of the object? Well it has no height, right? Potential energy is mgh. The mass and the acceleration of

gravity stay the same, but the height is 0. So they’re all multiplied

by each other. So down here, the potential

energy is going to be equal to 0. And I told you in the last video

that we have the law of conservation of energy. That energy is conserved. It cannot be created

or destroyed. It can just be converted from

one form to another. But I’m just showing you, this

object had 100 joules of energy or, in this case, gravitational potential energy. And down here, it

has no energy. Or at least it has no

gravitational potential energy, and that’s the key. That gravitational potential

energy was converted into something else. And that something else

it was converted into is kinetic energy. And in this case, since it has

no potential energy, all of that previous potential energy,

all of this 100 joules that it has up here is now going

to be converted into kinetic energy. And we can use that information

to figure out its velocity right before

it hits the ground. So how do we do that? Well what’s the formula

for kinetic energy? And we solved it two videos

ago, and hopefully it shouldn’t be too much

of a mystery to you. It’s something good to memorize,

but it’s also good to know how we got it and go

back two videos if you forgot. So first we know that all the

potential energy was converted into kinetic energy. We had 100 joules of potential

energy, so we’re still going to have 100 joules, but now

all of it’s going to be kinetic energy. And kinetic energy is

1/2 mv squared. So we know that 1/2 mv squared,

or the kinetic energy, is now going to

equal 100 joules. What’s the mass? The mass is 1. And we can solve for v now. 1/2 v squared equals

100 joules, and v squared is equal to 200. And then we get v is equal to

square root of 200, which is something over 14. We can get the exact number. Let’s see, 200 square

root, 14.1 roughly. The velocity is going to

be 14.1 meters per second squared downwards. Right before the object

touches the ground. Right before it touches

the ground. And you might say, well Sal

that’s nice and everything. We learned a little

bit about energy. I could have solved that or

hopefully you could have solved that problem just using

your kinematics formula. So what’s the whole point

of introducing these concepts of energy? And I will now show you. So let’s say they have the same

1 kilogram object up here and it’s 10 meters in the air,

but I’m going to change things a little bit. Let me see if I can competently

erase all of this. Nope, that’s not what

I wanted to do. OK, there you go. I’m trying my best to erase

this, all of this stuff. OK. So I have the same object. It’s still 10 meters

in the air and I’ll write that in a second. And I’m just holding it there

and I’m still going to drop it, but something interesting

is going to happen. Instead of it going straight

down, it’s actually going to drop on this ramp of ice. The ice has lumps on it. And then this is the bottom. This is the ground down here. This is the ground. So what’s going to

happen this time? I’m still 10 meters in the

air, so let me draw that. That’s still 10 meters. I should switch colors just

so not everything is ice. So that’s still 10 meters, but

instead of the object going straight down now, it’s going to

go down here and then start sliding, right? It’s going to go sliding

along this hill. And then at this point it’s

going to be going really fast in the horizontal direction. And right now we don’t

know how fast. And just using our kinematics

formula, this would have been a really tough formula. This would have been

difficult. I mean you could have attempted

it and it actually would have taken calculus

because the angle of the slope changes continuously. We don’t even know the formula

for the angle of the slope. You would have had to break

it out into vectors. You would have to do all sorts

of complicated things. This would have been a nearly

impossible problem. But using energy, we can

actually figure out what the velocity of this object

is at this point. And we use the same idea. Here we have 100 joules

of potential energy. We just figured that out. Down here, what’s the height

above the ground? Well the height is 0. So all the potential energy

has disappeared. And just like in the previous

situation, all of the potential energy is now

converted into kinetic energy. And so what is that kinetic

energy going to equal? It’s going to be equal to the

initial potential energy. So here the kinetic energy

is equal to 100 joules. And that equals 1/2

mv squared, just like we just solved. And if you solve for v, the

mass is 1 kilogram. So the velocity in the

horizontal direction will be, if you solve for it, 14.1

meters per second. Instead of going straight down,

now it’s going to be going in the horizontal

to the right. And the reason why I said it

was ice is because I wanted this to be frictionless and I

didn’t want any energy lost to heat or anything like that. And you might say OK Sal, that’s

kind of interesting. And you kind of got the same

number for the velocity than if I just dropped the object

straight down. And that’s interesting. But what else can

this do for me? And this is where it’s

really cool. Not only can I figure out the

velocity when all of the potential energy has

disappeared, but I can figure out the velocity of any

point– and this is fascinating– along

this slide. So let’s say when the box is

sliding down here, so let’s say the box is at this point. It changes colors

too as it falls. So this is the 1 kilogram

box, right? It falls and it slides

down here. And let’s say at this point it’s

height above the ground is 5 meters. So what’s its potential

energy here? So let’s just write something. All of the energy is

conserved, right? So the initial potential

energy plus the initial kinetic energy is equal to the

final potential energy plus the final kinetic energy. I’m just saying energy

is conserved here. Up here, what’s the initial

total energy in the system? Well the potential energy is 100

and the kinetic energy is 0 because it’s stationary. I haven’t dropped it. I haven’t let go of it yet. It’s just stationary. So the initial energy is going

to be equal to 100 joules. That’s cause this is

0 and this is 100. So the initial energy

is 100 joules. At this point right here, what’s

the potential energy? Well we’re 5 meters

up, so mass times gravity times height. Mass is 1, times gravity, 10

meters per second squared. Times height, times 5. So it’s 50 joules. That’s our potential energy

at this point. And then we must have some

kinetic energy with the velocity going roughly

in that direction. Plus our kinetic energy

at this point. And we know that no energy

was destroyed. It’s just converted. So we know the total energy

still has to be 100 joules. So essentially what happened,

and if we solve for this– it’s very easy, subtract 50 from

both sides– we know that the kinetic energy is

now also going to be equal to 50 joules. So what happened? Halfway down, essentially half

of the potential energy got converted to kinetic energy. And we can use this information

that the kinetic energy is 50 joules

to figure out the velocity at this point. 1/2 mv squared is equal to 50. The mass is 1. Multiply both sides by 2. You get v squared

is equal to 100. The velocity is 10 meters

per second along this crazy, icy slide. And that is something that I

would have challenged you to solve using traditional

kinematics formulas, especially considering that we

don’t know really much about the surface of this slide. And even if we did, that would

have been a million times harder than just using the law

of conservation of energy and realizing that at this point,

half the potential energy is now kinetic energy and

it’s going along the direction of the slide. I will see you in

the next video.

how does the value of P.E became 200 from 100?

I love your vidoes! They are helping me so much.

Thanks so much man, I have an ETA this week and I never really understood this process. This helped me so much!

Thanks a alot …

can you explain the formula or P.E+K.E+U?. which is change on potential E and change in kinetic E added to change in internal energy? what does the internal energy change, and how to solve for it?

Thank you so much for your help.

sal you forgot to that mgh is 1*10*10 when you removed the m for the 0.5mv2 you made it no 100 but 10 joule the v is equile to squire 20

Question: Why would you use this formula if you could use V^2=Vi^2+2ax? V^2=0+2(9.8)10, V=14m/s Seems easier. Could You show me another example where it might make more sense to choose an energy formula instead of velocity?

Question, once the object hits the ground, its not moving, so K=0. But, energy needs to be conserved, and it isnt transferred into potentional because PE=0 at h=0. Where does the 100J go?

Amazing , you saved me : )

old but gold

Dos IT actuly chnge colers wen it fals? M Cunfused :/, Plz expln why? hve fysics tes tmrw???

I WANT TO NOMINATE YOU FOR THE NOBEL PEACE PRIZE, for your excellence in education. Providing free, accurate and thorough education to millions of individuals online.

that speck left at is really bothering me…

thnk u so much

I don't care about the topic, I just find his voice so soothing.

saved me in my computer class, the class is so boring

At 3:51 he said the velocity was in m/s^2, is this true?

Nice, don't get why people dislike your videos. Great work

I love this. It was looking impossible in class, thanks so much man.

If you're travelling through a series of hills in an automobile will you conserve fuel by accelerating through the downhill then coasting through the uphill or by maintaining a constant speed limit?

K so where can I practice questions.. Any sites?

I still don't get how you can't find the V (before the ice comes in, when it's free falling) by simply calculating through the acceleration. Like this

V_initial = 0, a=g=10m/s, d=10m, what is V_final?

V_final should be 10m/s and it should take the object 1 second to hit the ground.

I would also like to ask a follow-up question please. Imagine the same premise before the ice (when 1kg free falls 10m). Instead of just having ground at the bottom, you have a scale (in Newtons let's say). If the object would be just standing on it (F=ma) the scale would show 10N. Ok… But the object is falling from 10 meters directly on the scale. QUESTION: what would be the MAX value that the scale would show on impact? (in Newtons). Is there a way for that KE to tell us or do we use some other formula?

how did you make The velocity units sudenly from Jules Into M/s on 3:30 ??? that doesnt seems right

And then on 3:48 you say m/s^2 like acceleration even if you write m/s which still i didnt get how you got them from the Jules…

Really improved my understanding on this topic!

Just want to let you know that you are AWESOME and HIGHLY APPRECIATED! 😀

Thanks for the videos! I was really lost on my homework so I decided to look for help and this is exactly what I needed.

I LOST IT AT "IT CHANGES COLORS, TOO, AS IT FALLS!" OH MY GOSH

7:30

I honestly love Sal so much. Thank you!!! Wouldn't have gotten through class without your help

even I dont speak English very well , I got it

thanks a lot

I think there is a miscalculation while he was calculating the kinetic energy the formula is (KE=1/2*G*H)

so what he did is that he multiplied 2 both sides to get rid of the denominator and didn't multiply it by the mass which is (1KG) and the answer he got is (14.2). while I was working it out i multiplied 1/2 times 1kg then divided( .5) by both sides then i did the sqr. root to get v by it self, so I ended up with 7.5 (half of what he got). Somebody correct me if I am wrong.

Thank you!!

hmmm better than a teacher,, well i guess teachers get bored kind of doing the same thing over and over again for 10 years,, im so unlucky we only have one physics teacher,, if your facing a teacher and cant understand him and he dorsnt even help properly do it yourself,, thats what smart people do if you want to ace the test,, study on your own

this guy should get paid,,, is he getting paid

isn't there a zeno's paradox with the definition of "right before touching the ground"?

Any body believe that energy can not be created or destroyed. I don't think so. If so, why does it exist? It means that energy can be created right?. If energy can not be created, then it will not be there. Think about it…..

I will change the definition of Conservation of Energy to a better understanding by saying that " Energy can not be added or subtracted ". It makes more sense maybe.

Very informative. thanks <3

Conservative force/energy = Equal force/energy (before=after)..Its bcoz

(i)before the motion the object at rest i.e zero

(ii)after the motion the is also at rest i.e zero

how was ur velocity 200?

These videos are an amazing help, but that pen!!! If he wasn't talking, I'd be lost! I do have a much better understanding though!

This is very pixelated

Thank god for khan academy !

U do not know how much u have helped me, the a lot

Pour mes fils Stéphane et Antoine…musiciens…

I'm getting really fed up with this poor resolution. Why didn't you fix your system before recording so many bad quality videos? It's nearly impossible to learn anything when the handwriting is inscrutable.

can u make them to a better quality

If energy cannot be created, from where did the energy of the Big Bang came into existence??

You made it so simple, and I'm able to apply this underlying knowledge to more complex problems. Thank you for helping me.

good

You make physics so much easier and understandable. I am starting to like physics.

ترجمة الى العربي

really helpfull

Can't read half the graphics ffs.

Great!!

This vid is bullsit the velocity component needs a direction which isn't the same for the second icy slide

Is this not false after all the universe was created in the big bang so matter and energy can be created from nothing

Gave this video a like because why not

My 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

I want to buy him a writing board for his computer like seriously he needs one

Gravity 9.8m/s squared btw not 10 just saying

I thought g was 9.8 m/s?

I thought g was 9.8 m/s?

I ALWAYS LOVE your videos, you speak well and have exceptional penmanship. BUT in the last few videos I have watched you are using a thicker font which makes everything hard to read, follow and understand.. PLEASE go back the the thinner font when writing so that it is easier to follow along and read!! Thanks

Wow!

plz give real life examples. i can not get you. plz simplify your explanation.

very difficult explanation.

after watching this video my concept has been destroyed.

so going down the ice it accelerates at freefall due to gravity?.. but has to overcome gravity twice on the way down? and still at freefall speed? also if its traveling a longer distance wouldnt the energy be converted from velocity to distance? im so confused. youre using gravity to accelerate it, but not to decelerate it on the ice as it has to travel upwards?

man's really tryna save my semester eh

Plz see my videos

Do the reverse thinking and you will obtain antigravity.

Uhhh… I found about 3 videos on YouTube with over 100k Views that talked about the conservation of energy. This is bizarre. The law of energy conservation is by far the most important physical law. How are there not more videos on this?

write clear !!!

✋

thank you sir, you are 100 times better than my professor 🙂

sal khan is my religion

½ X 100 = 50

Thanks bro

At 1:21, I'm getting 100 kJ? Not 100 J. Did anyone else?

So useful

Ehm, isn’t the acceleration of gravity 9.81?!

Something here I didn't get, how is the final velocity of a free falling object when it hits the ground is equal to the final velocity of the same object when it slides the ice mountain, even when H is the same, this path it took is longer, and there is an X component and a Y component.

Please someone tills me what I missed(other than the friction-less surface) cause the difference I feel isn't only from friction.

m per second*

i like that concept thanks sir

When gravitational potential energy is given to an object during work to some height and the object is dropped, gpe gets converted to ke. If there is no air resistance, where does the ke go after the object hits the ground? The earth? How if a great enough force wasn’t applied over a distance to the earth to transfer such amount of energy?

is good thank you

I missed class for a field trip today. You’re a life saver

what r u even saying. i am brain dead. pls dummify it

this video is 11 years old…….. feel old yet?

i love you. so much.

Thank you ☺️

How about using pounds and feet? As far as I can remember 10 meters could be 10 houses long

such a good teacher!

If energy can not be created ,then since the population is rising ,will there be enough energy for all of us?

2019 anyone?

Thank you for your effort for teaching sir

because of these videos i'm gonna get an A on my exam bet

How did you get V*2 = 200?

Wow this video actually taught me, unlike the one hour lecture I attended from a dweeb with a PHD

This was helpful thanks.

I'll even send this to my friend william.

He thinks that the derivation is easy but personally, I am still a bit confused as to how to derive to the final from initial.

Its like you think they are rivets but they are actually nuts. I'd throw in The Washers atleast. But the added number of components, sure complicates assembly. Double check, triple check everything. Making sure they dont have a nut lose. usually they are all lose. From the vibrations. Re-tightening them just takes more time..