Introduction to work and energy Introduction to work and energy
Introduction to work and energy
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- 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
- 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?
- 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.
- 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.
- 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
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