Welcome back. Welcome back.

Welcome back. I’ll now do another conservation

of energy problem, and this time I’ll

add another twist. So far, everything we’ve been doing,

energy was conserved by the law of conservation. But that’s because all of the

forces that were acting in these systems were conservative

forces. And now I’ll introduce you to

a problem that has a little bit of friction, and we’ll see

that some of that energy gets lost to friction. And we can think about

it a little bit. Well where does that

energy go? And I’m getting this problem

from the University of Oregon’s zebu.uoregon.edu. And they seem to have some nice

physics problems, so I’ll use theirs. And I just want to make

sure they get credit. So let’s see. They say a 90 kilogram

bike and rider. So the bike and rider combined

are 90 kilograms. So let’s just say the mass is 90

kilograms. Start at rest from the top of a 500 meter

long hill. OK, so I think they mean

that the hill is something like this. So if this is the hill, that

the hypotenuse here is 500 hundred meters long. So the length of that,

this is 500 meters. A 500 meter long hill with

a 5 degree incline. So this is 5 degrees. And we can kind of just view

it like a wedge, like we’ve done in other problems.

There you go. That’s pretty straight. OK. Assuming an average friction

force of 60 newtons. OK, so they’re not telling us

the coefficient of friction and then we have to figure

out the normal force and all of that. They’re just telling us, what

is the drag of friction? Or how much is actually friction

acting against this rider’s motion? We could think a little bit

about where that friction is coming from. So the force of friction is

equal to 60 newtons And of course, this is going to be

going against his motion or her motion. And the question asks us, find

the speed of the biker at the bottom of the hill. So the biker starts up

here, stationary. That’s the biker. My very artful rendition

of the biker. And we need to figure out the

velocity at the bottom. This to some degree is a

potential energy problem. It’s definitely a conservation

of mechanical energy problem. So let’s figure out what the

energy of the system is when the rider starts off. So the rider starts off at

the top of this hill. So definitely some

potential energy. And is stationary, so there’s

no kinetic energy. So all of the energy is

potential, and what is the potential energy? Well potential energy is equal

to mass times the acceleration of gravity times

height, right? Well that’s equal to, if the

mass is 90, the acceleration of gravity is 9.8 meters

per second squared. And then what’s the height? Well here we’re going to have

to break out a little trigonometry. We need to figure out this side

of this triangle, if you consider this whole

thing a triangle. Let’s see. We want to figure out

the opposite. We know the hypotenuse and

we know this angle here. So the sine of this angle is

equal to opposite over hypotenuse. So, SOH. Sine is opposite over

hypotenuse. So we know that the height–

so let me do a little work here– we know that sine of

5 degrees is equal to the height over 500. Or that the height is equal

to 500 sine of 5 degrees. And I calculated the sine of

5 degrees ahead of time. Let me make sure I

still have it. That’s cause I didn’t have my

calculator with me today. But you could do this

on your own. So this is equal to 500,

and the sine of 5 degrees is 0.087. So when you multiply these

out, what do I get? I’m using the calculator

on Google actually. 500 times sine. You get 43.6. So this is equal to 43.6. So the height of the hill

is 43.6 meters. So going back to the potential

energy, we have the mass times the acceleration of gravity

times the height. Times 43.6. And this is equal to, and then

I can use just my regular calculator since I don’t

have to figure out trig functions anymore. So 90– so you can see the whole

thing– times 9.8 times 43.6 is equal to, let’s

see, roughly 38,455. So this is equal to 38,455

joules or newton meters. And that’s a lot of

potential energy. So what happens? At the bottom of the hill–

sorry, I have to readjust my chair– at the bottom of the

hill, all of this gets converted to, or maybe I should pose that as a question. Does all of it get converted

to kinetic energy? Almost. We have a force

of friction here. And friction, you can kind of

view friction as something that eats up mechanical

energy. These are also called

nonconservative forces because when you have these forces

at play, all of the force is not conserved. So a way to think about it is,

is that the energy, let’s just call it total energy. So let’s say total energy

initial, well let me just write initial energy is equal

to the energy wasted in friction– I should have written

just letters– from friction plus final energy. So we know what the initial

energy is in this system. That’s the potential energy

of this bicyclist and this roughly 38 and 1/2 kilojoules

or 38,500 joules, roughly. And now let’s figure out the

energy wasted from friction, and the energy wasted from

friction is the negative work that friction does. And what does negative

work mean? Well the bicyclist is moving 500

meters in this direction. So distance is 500 meters. But friction isn’t acting

along the same direction as distance. The whole time, friction is

acting against the distance. So when the force is going in

the opposite direction as the distance, your work

is negative. So another way of thinking of

this problem is energy initial is equal to, or you could say

the energy initial plus the negative work of friction,

right? If we say that this is a

negative quantity, then this is equal to the final energy. And here, I took the friction

and put it on the other side because I said this is going to

be a negative quantity in the system. And so you should always just

make sure that if you have friction in the system, just as

a reality check, that your final energy is less than

your initial energy. Our initial energy is, let’s

just say 38.5 kilojoules. What is the negative work

that friction is doing? Well it’s 500 meters. And the entire 500 meters, it’s

always pushing back on the rider with a force

of 60 newtons. So force times distance. So it’s minus 60 newtons,

cause it’s going in the opposite direction of the

motion, times 500. And this is going to equal

the ending, oh, no. This is going to equal the

final energy, right? And what is this? 60 times 500, that’s 3,000. No, 30,000, right. So let’s subtract 30,000

from 38,500. So let’s see. Minus 30. I didn’t have to do that. I could have done

that in my head. So that gives us 8,455 joules is

equal to the final energy. And what is all the

final energy? Well by this time, the rider’s

gotten back to, I guess we could call the sea level. So all of the energy

is now going to be kinetic energy, right? What’s the formula for

kinetic energy? It’s 1/2 mv squared. And we know what m is. The mass of the rider is 90. So we have this is 90. So if we divide both sides. So the 1/2 times 90. That’s 45. So 8,455 divided by 45. So we get v squared

is equal to 187.9. And let’s take the square root

of that and we get the velocity, 13.7. So if we take the square root of

both sides of this, so the final velocity is 13.7. I know you can’t read that. 13.7 meters per second. And this was a slightly more

interesting problem because here we had the energy wasn’t

completely conserved. Some of the energy, you could

say, was eaten by friction. And actually that energy

just didn’t disappear into a vacuum. It was actually generated

into heat. And it makes sense. If you slid down a slide of

sandpaper, your pants would feel very warm by the time you

got to the bottom of that. But the friction of this, they

weren’t specific on where the friction came from, but it

could have come from the gearing within the bike. It could have come

from the wind. Maybe the bike actually

skidded a little bit on the way down. I don’t know. But hopefully you found that

a little bit interesting. And now you can not only work

with conservation of mechanical energy, but you can

work problems where there’s a little bit of friction

involved as well. Anyway, I’ll see you

in the next video.

@Oneill9293 haha oh well, I was the one who signed up for it – thinking anything's possible as long as you put ur mind to it. xP And still believing! hehe 🙂 Best of luck to u too m8.

Wanted to say you saved me from failing my midterm! Thanks a lot keep it up

U r awesome man. Good explanation.

@stiffz thanks your way is quicker in exam! However I agree this video is helpful and helped me understand!

am feeling you sir hear in nigeria,r u a professor of physo

@TheRick309

friction?

Dear Mr. Khan

Please stop doing Physics explanations. Indeed, energy is ALWAYS conserved. For this problem should talk only about Mechanical energy or kinetic energy. This idea of ''energy wasted by friction'' etc is not correct. The answer is correct but the explanation is wrong, You are a great explainer ,but if you provide misleading explanations, we professors in engineering have to spend a vast amount of time correcting these misconceptions with only limited success. Prof Arun Srinivasa

These video make my understanding better

isn't Wf equal to F∆rcosø? because W=F•r which is a dot product…

energy IS conserved its just converted into heat, that iswhy you don't get the total KE equal to PE at the beginning. you should've stressed on that

u just need that pen that writes on the screen to accomplish the perfectness of teaching physics online, (+a calculator in all vids :P) , other than that ur (y)

@ArunSrinivasa ….if the majority of college professors were actually effective at explaining concepts like this, then Mr. Khan would have no need to do these videos. I'm definitely not judging you (because I have no idea what type of teacher you are), but the truth is, many professors are TERRIBLE at explaining things and care more about showing off their knowledge than they do about the students actually learning.

2 people couldn't do it in their head…

A great man once said, "If you slid down a slide of sandpaper your pants would feel very warm"

Who in the fuck would slide down a sandpaper ?

@goldensilverstar its called an example, asshole

This really helped me figure this stuff out, Thanks!

damn friction is a bitch, ate up 30,000 and now he's just left with 8.5k :

this was made 4 years ago…now he uses a pen on a mat to write instead of his mouse

so if they asked you to calculate the work done, what would your answer be?

dont you also have to consider the work done by the mass naturally moving down the inclined plane?

SMARTER THAN 100% of all teachers at school.

Knowing the height of the hill (43.6m), couldn't you just say that the Square root of 2gh = v? I'm confused…

he use Wacom Bamboo Tablet and SmoothDraw Painy Program!!

no matter what hes using to show us this info, im gonna finnaly pass physics!!!! 😀

i think that way it's easier to stream for those with weaker internet connections. otherwise that kinda opposes the 'knowledge for all' purpose. yes it is harder to see but you still get the concept if you listen along as he writes.

stop confusing people in here, he has explained you what to do with pretty good details. plz stop

im just trying to help… if you're familiar with the E=(mv^2)/2 you'd know that v=the square root of 2gh… much easier and much less time-consuming than the way that the great Khan demonstrated.

I'm NOT bashing his videos or way of thinking, he's a genius, just saying.

khanservation of energy, very punny sir

i can't thank you enough for these!!

hahahaha xD

How can the friction (kinetic friction) be in the opposite direction of the motion or distance ? Think about it we are not pushing a box where the friction is in the opposite side of the motion. Friction comes from the sliding of the two surface in contact with each other. Here while the wheel is rolling, friction will be in the same direction as the distance or motion. This was one question I missed in MCAT! Like if you agree 🙂 so the comment can stay on the top!

I think it's because these are older videos (i.e. he did the earlier concepts again later on). However, I'm not sure if I heard him say something like that once, or if I'm just guessing.

Static friction is in the direction of motion if you have a wheel (that's how we are propelled forward, e.g. walking, bicycling). Therefore, this problem is wrong. The non-conservative force should be added instead of subtracted. Very good problem nonetheless. Thanks Sal.

@7.44 why doesn't he do 60(500)(cosof angle)

isn't it Fdcosangle ?

He does that because force is given with respect to the incline plane. If force was in the horizontal direction then you'd be correct.

@toorbabray No if you push an object then you wood be pushing it in a given direction. Friction is a vector quantity so the friction would have to be opposite the direction you push because the friction would be a retarding force (sllowing the box down) . Of iit went in the same direction then relative to the box it would be adding force not taking it away which isn't possible because friction generates heat from converted energy.

@crazyboy33398 *lost

Very extreme helpful! Thanks

Extremely**. Lol still doesn't make sense anyway but idgaf

lol no longer? look at the date first

lol ok ok i got it you're the 5th person to comment on that 😛

i wasn't paying attention as I was studying for an exam at that time lol

not very effective for serious students

theses are the older videos , the newer ones are in hd i believe

if you dot want anyone replying then remove the comment and people will stop answering you.

These are earlier videos from the 2011 ones. ANd I know it's hard but they're just as helpful

why dont you work out what youre going to say and write before making the video? It makes it hard to follow the process when youre continually scrubbing things out and making it messy

what to do if the force of friction is not given but friction is there….

Anyway, I'll see you in the next video ♫

hmmm… very unrealistic… as the speed increases, the air drag increases as well.. it would be interesting to calculate it as well

it may be my computer..but his drawings are going off of the bottom?anyone else?

Friction wastes energy. Please tell that to the GOP.

you have to walk before you can run

Thanks

Its intro level physics, you have to learn this before you can take air resistance into account.

beautiful job done.God bless u sir

Now I am studying to my Physics Final Exam from these videos which are very useful and clear to understand. I want to say a BIG THANK YOU! I can understand physics with these videos easily rather than 1600 pages of PHYSICS BOOKS. I am very happy to see people who are making good works to help people. From other side of the world with respects!

Thanks a billion! have an exam 2mao

how he got 8455J ??? (posiitive num??)

It's too bad the resolution is so low, and the scribe writer is poor, the writing is sometime illegible.

negative work of friction? 60? where did he get 60?please explain! thank you!

Why are most of your videos only in 240p? The content is great, but the quality is unbearable.

WOW WORDS CANNOT EXPLAIN MY LOVE FOR YOU u helped me so much

How did you get that drawing thing i want it plz tell@Khan AcademyCould anyone explain how he got 38500-30000=8455? Thank You!

These videos actually help a whole lot. 🙂

Im failing pls heLp

shouldnt the initial energy be in joules?

@7:45 The Work done by friction = force * displacement * cosine(angle) ? But why did he skip the cosine part? I was thinking it shouuld be Wfric = (60N)(-500m)(cos5degrees) ? Can anybody explain this to me? Big thanks 🙂

I don't get it, shouldn't the gravity acting on the bicyclist be 9.81m/s^2*Cos(5) because its at an angle?!?! Please help.

Is typing on a computer keyboard consider doing work in physics sense?

Its so hard to read these. Would you upload this video with higher resolution?

I love the hilarity put in your videos 🙂

you killed me at 2:08 XD but thanks for the great explanation !!

Love that interesting problem. Great explanation as usual !

what is up with the quality

An electric motor takes a car weighing 800kg up to point A 140m above the ground. If the total resistive forces = 0.25MJ, how much energy does the electric motor use to get the car to point A?how will you work this out?

will it be (800)(0.25)(140)

Sal I don't know if you're still reading these but man I have been learning so much from you- Trig, Pre-Calc, Calc, and now Physics. You're a huge inspiration, man. I'm considering becoming a teacher and I just wanted to acknowledge and thank you. Thanks for all of the hard work you do, day in and day out.

when you have mgh+1/2mv^2=mgh2+1/2mv^2 how do you know which side of the formula the friction goes on?

is the friction of rolling maximum static friction ?

and why it is static friction why the velocity of contact surface is equal zero?

I really want to know why.

i had no interest in maths and physics i used to waste a lot of my time on the internet but now cause of khan academy i have started liking and understanding these subjects a lot better and it becomes very interesting. thnx a lot man

I have learn so much, words are not enough to express my gratitudes .I pray may GOD blessed you all the Tutors whom have put their effort here.

haha who would dare to slid down on a slide of sandpaper ? 😀

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

Another well made video!

For record you can still use your computer calculator by doing alt+2 and it will open it as a scientific calc

ill think ill pass the test tomorrow

I don't know why but I get all the problems here but my exam problems are much harder and I get stuck.

Why doesn't force due to gravity in the x direction put work in?

Can someone help me out on how he got 8455J please. thanks

All these smart people in the comments. I need help 🙁

I never took this in HS, I took maths I needed to graduate :'(

please upload in 1080p or at least 720, i cant read half of what u wrote in 240p

What a terrible mess, Sal.

I didn't take last year of physics in high school and the introductory physics course at my university is way harder than a high school class would've been lol. My final is tomorrow…. and your videos are perfect for reviewing!! How do you know so much!?

Hm. Dat's strange, but seems with friction byke moves faster???? O_o

conservative forcesHow can we support Khan academy? Youve done us good for so long!

Where does the extra energy come from after it is wasted by friction

Can someone please explain to me why we aren't including the work done by gravity? Thank you so much.

give this man a nobel peace prize in education