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## Physics library

### Unit 5: Lesson 1

Work and energy- Introduction to work and energy
- Work and energy (part 2)
- Conservation of energy
- What are energy and work?
- What is kinetic energy?
- What is gravitational potential energy?
- What is conservation of energy?
- Work and the work-energy principle
- Work as the transfer of energy
- Work example problems
- Work as area under curve
- Thermal energy from friction
- What is thermal energy?
- Work/energy problem with friction
- Conservative forces
- Power
- What is power?

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# Introduction to work and energy

Introduction to work and energy. Created by Sal Khan.

## Want to join the conversation?

- I don't quite understand the difference between negative work and no work?(5 votes)
- Negative work can be understood this way:

Car breaks down while going uphill and it starts to roll downward. You, as a good samaritan, try to stop the car from rolling down the slope by pushing on it with all your might. The force you apply on the car is directed uphill but alas, it's not enough to stop the car. The car continues to move downhill, that is, it's displacement is in a direction opposite to the force you are applying. This means you are doing negative work on the car. If you draw the free body diagram for this car, rolling down the incline, you'll see that the component of gravity parallel to the incline is doing the*positive*work because both this component and the displacement are in the same direction.

Now suppose, more bystanders come along to help stop the car. Everyone pushes on the car uphill so that the car slows down and eventually stops. This happened because the negative work that each person was doing eventually became big enough to cancel out the work that gravity was doing. Once the car stops and the people continue to push it uphill, the car will start rolling*upward*, in the direction of the applied force and now you'll get*positive*work.

During this scenario, note that the normal force on the car from the incline is perpendicular to the surface and the car and it does zero work because there is no motion along its direction.

I hope this helps to assuage your doubts.(46 votes)

- Sal says that work = force . distance... how can a vector be multiplied with a scalar to yield a scalar?(13 votes)
- The actual formula for work is

W =**F**·**s**,

i.e. Work is the*scalar*product of the*vectors*Force and**displacement**, not necessarily distance.

Scalar product is so called because it returns a scalar, which in this case is Work. (It is also called "dot product" because of the "·" symbol between the vectors in the formula.) So in fact, Work does not equal Force times distance; Mr. Khan did a white lie there.

Why do I say he did a white lie? Well, in the case of moving in a straight line (with force in same direction as displacement),

the scalar product has the same effect as multiplying the magnitudes of the 2 vectors, and the magnitude of displacement vector**is equal to**distance:

||**s**||=d

so W=**F**·**s**=||**F**||*||**s**||=F*d.

So in this case, Mr. Khan's definition of Work is correct. But this obviously won't work for other cases (e.g. NOT moving in a straight line); Mr. Khan gave this definition for introduction's sake.(11 votes)

- what is the difference between work,energy and power？(5 votes)
- Hello Han,

If you are interested from an electrical perspective I made these videos that may help:

https://www.youtube.com/watch?v=XdgKqf4h0tQ

https://www.youtube.com/watch?v=EQxCkq4BFKQ

Regards,

APD(4 votes)

- the law said that the energy can neither be created nor be destroyed if its true and we need energy to move our body then where did the energy went for example before moving our hand the energy was stored there but after moving it the energy is used the question is where is the used energy after moving the hand ?(4 votes)
- So the energy associated with moving out hands is dissipated in several ways. One way is release as thermal energy within our actual body - so when we use our muscles, they actually heat up, because our bodies have to do a lot of exothermic (heat releasing) chemical reactions to actually create muscle contraction. We also interact with air molecules, kind of "swatting" them, which will vaguely increase their speed.

When we do small motions, like waving our hand once or twice at a friend, this isn't going to release a noticeable amount of heat... but if you run a marathon, I guarantee your legs will feel warm, and your body will heat up at the massive amount of work your body does over the course of the marathon!

Hope this helps.(5 votes)

- what is negative force?

what angle must me there between displacement and force in order to do negative work?(2 votes)- Negative force is force in the opposite direction from the direction you have defined as positive.(2 votes)

- So when it comes to a problem and we need to find velocity...and it isn't a projectile or impulse, should we use this instead of Newtons Laws? (i.e. vf=vi+at, etc. etc.)(2 votes)
- You should use the best approach for you.

Unless you are told to do it a certain way.(2 votes)

- Hi!

I had a doubt about this example.

If I am carrying a book in my hand ( till chest ) and then walk till 10 m then is it called work done? or not,

as 2 forces are acting to each other

- gravitational

- my hand's force to keep it upright(1 vote)- If you're holding the book completely horizontally, then you aren't doing work. Work, being the dot product of force and displacement, is zero when those two vectors are perpendicular to each other.(4 votes)

- At0:36, He says work is energy transferred by force, Using this definition shouldn't the formula be Work = Energy times Force ?(2 votes)
- No. Work IS energy. when you exert a force over a distance, you transfer energy to the object you are exerting the force on. The amount of energy you transfer is force*distance.(2 votes)

- In the equation work equals force times distance, but cant distance be replaced by displacement?(2 votes)
- Yes, It is actually force.displacement(dot product).(2 votes)

- Work is a scalar quantity and therefore negative work is only used to denote the direction.Right?(2 votes)
- Firstly, since it is scalar, the sign has nothing to do with the direction. Negative work is an indication that work is done against the object. For example, to stop a fast moving car (Vo), you need to apply work against it motion (V). The same goes for work done by friction which acts against the direction of motion.(1 vote)

## Video transcript

Welcome back. I'm now going to introduce
you to the concepts of work and energy. And these are two words that
are-- I'm sure you use in your everyday life already and
you have some notion of what they mean. But maybe just not in the
physics context, although they're not completely
unrelated. So work, you know
what work is. Work is when you do something. You go to work, you
make a living. In physics, work is-- and I'm
going to use a lot of words and they actually end up being
kind of circular in their definitions. But I think when we start doing
the math, you'll start to get at least a slightly more
intuitive notion of what they all are. So work is energy transferred
by a force. So I'll write that down, energy
transferred-- and I got this from Wikipedia because
I wanted a good, I guess, relatively intuitive
definition. Energy transferred by a force. And that makes reasonable
sense to me. But then you're wondering, well,
I know what a force is, you know, force is mass
times acceleration. But what is energy? And then I looked up energy on
Wikipedia and I found this, well, entertaining. But it also I think tells you
something that these are just concepts that we use to, I
guess, work with what we perceive as motion and force
and work and all of these types of things. But they really aren't
independent notions. They're related. So Wikipedia defines energy
as the ability to do work. So they kind of use each other
to define each other. Ability to do work. Which is frankly, as good of a
definition as I could find. And so, with just the words,
these kind of don't give you much information. So what I'm going to do is move
onto the equations, and this'll give you a more
quantitative feel of what these words mean. So the definition of work in
mechanics, work is equal to force times distance. So let's say that I have a block
and-- let me do it in a different color just
because this yellow might be getting tedious. And I apply a force of--
let's say I apply a force of 10 Newtons. And I move that block
by applying a force of 10 Newtons. I move that block, let's
say I move it-- I don't know-- 7 meters. So the work that I applied to
that block, or the energy that I've transferred to that block,
the work is equal to the force, which is 10 Newtons,
times the distance, times 7 meters. And that would equal 70-- 10
times 7-- Newton meters. So Newton meters is one, I
guess, way of describing work. And this is also defined
as one joule. And I'll do another presentation
on all of the things that soon. Joule did. But joule is the unit
of work and it's also the unit of energy. And they're kind of
transferrable. Because if you look at the
definitions that Wikipedia gave us, work is energy
transferred by a force and energy is the ability to work. So I'll leave this relatively
circular definition alone now. But we'll use this definition,
which I think helps us a little bit more to understand
the types of work we can do. And then, what kind of energy
we actually are transferring to an object when we do
that type of work. So let me do some examples. Let's say I have a block. I have a block of mass m. I have a block of mass m and it
starts at rest. And then I apply force. Let's say I apply a force, F,
for a distance of, I think, you can guess what the distance
I'm going to apply it is, for a distance of d. So I'm pushing on this block
with a force of F for a distance of d. And what I want to figure
out is-- well, we know what the work is. I mean, by definition, work is
equal to this force times this distance that I'm applying
the block-- that I'm pushing the block. But what is the velocity going
to be of this block over here? Right? It's going to be something
somewhat faster. Because force isn't-- and I'm
assuming that this is frictionless on here. So force isn't just moving
the block with a constant velocity, force is equal to
mass times acceleration. So I'm actually going to be
accelerating the block. So even though it's stationary
here, by the time we get to this point over here,
that block is going to have some velocity. We don't know what it is
because we're using all variables, we're not
using numbers. But let's figure out what
it is in terms of v. So if you remember your
kinematics equations, and if you don't, you might
want to go back. Or if you've never seen the
videos, there's a whole set of videos on projectile motion
and kinematics. But we figured out that when
we're accelerating an object over a distance, that the final
velocity-- let me change colors just for variety-- the
final velocity squared is equal to the initial velocity
squared plus 2 times the acceleration times
the distance. And we proved this back then,
so I won't redo it now. But in this situation, what's
the initial velocity? Well the initial
velocity was 0. Right? So the equation becomes vf
squared is equal to 2 times the acceleration times
the distance. And then, we could rewrite
the acceleration in terms of, what? The force and the mass, right? So what is the acceleration? Well F equals ma. Or, acceleration is equal to
force divided by you mass. So we get vf squared is equal
to 2 times the force divided by the mass times
the distance. And then we could take the
square root of both sides if we want, and we get the final
velocity of this block, at this point, is going to be equal
to the square root of 2 times force times distance
divided by mass. And so that's how we could
figure it out. And there's something
interesting going on here. There's something interesting
in what we did just now. Do you see something that looks
a little bit like work? Well sure. You have this force
times distance expression right here. Force times distance
right here. So let's write another
equation. If we know the given amount of
velocity something has, if we can figure out how much work
needed to be put into the system to get to
that velocity. Well we can just replace force
times distance with work. Right? Because work is equal to
force times distance. So let's go straight from this
equation because we don't have to re-square it. So we get vf squared
is equal to 2 times force times distance. That's work. Took that definition
right here. 2 times work divided
by the mass. Let's multiply both sides of
this equation times the mass. So you get mass times
the velocity. And we don't have to write-- I'm
going to get rid of this f because we know that we started
at rest and that the velocity is going to be--
let's just call it v. So m times V squared is equal
to 2 times the work. Divide both sides by 2. Or that the work is equal
to mv squared over 2. Just divided both sides by 2. And of course, the unit
here is joules. So this is interesting. Now if I know the velocity of
an object, I can figure out, using this formula, which
hopefully wasn't too complicated to derive. I can figure out how much work
was imputed into that object to get it to that velocity. And this, by definition, is
called kinetic energy. This is kinetic energy. And once again, the definition
that Wikipedia gives us is the energy due to motion, or the
work needed to accelerate from an object from being stationary to its current velocity. And I'm actually almost out of
time, but what I will do is I will leave you with this
formula, that kinetic energy is mass times velocity
squared divided by 2, or 1/2 mv squared. It's a very common formula. And I'll leave you with
that and that is one form of energy. And I'll leave you
with that idea. And in the next video,
I will show you another form of energy. And then, I will introduce
you to the law of conservation of energy. And that's where things become
useful, because you can see how one form of energy can be
converted to another to figure out what happens to an object. I'll see