Ramps: Introduction

Hello.I'm Lou Bloomfield, and welcome to How Things Work at the University of Virginia.

Today's topic, ramps.

People have been using ramps for heavy lifting since long before the Great Pyramids were built.Whenever something is too heavy to lift straight up, the simplest solution is often a ramp.

As long as the slope of the ramp is gentle enough, and you have something like wheels to keep friction at bay, you can lift almost anything from here to there.

You use ramps without even thinking about it.Whenever you drive or bicycle up a hill, you're using a ramp to lift yourself to that hilltop.

Consider the alternative.Traveling straight up a cliff face to that hilltop.

Not for everyone.

Ramps are just as useful for lowering things as they are for lifting them.Suppose, for example, that you have a piano on a ledge and you want to lower it to the ground.Well, you can push the piano off the ledge and it will arrive at the ground, but don't expect it to be in tune when it gets there. You’d do a lot better to lower that piano much more delicately, more carefully, by taking it down a ramp.

Ramps, also known as inclined planes, are one of the six simple machines.The other simple machines are levers, wheels, pulleys, wedges, and screws.

In telling the story of ramps, however, I'll be laying the physics groundwork for all the simple machines. Namely, that they allow you to change the amount and or the direction of the force you're using to do something.

Doing something is of special significance in physics because it often involves the transfer of an important physical quantity, energy.

The term energy is familiar, but people use that term to describe a broad range of concepts, only some of which are the physical quantity.

One of my goals for this episode, then, is to explain what physicists mean when they talk about energy.

For now, you can think of energy as the capacity to do things.In other words, the more energy something has, the more it can do.

With that in mind, let's return to look at ramps. And I want to ask you a question to think about. That is, don't, I'm not going to ask you to answer it yet. But you should keep it in mind as we continue to look at how things work.

As background, ramps come in all shapes and sizes. There are ramps that are long, and there are ramps that are short. There are ramps that are low, and there are ramps that are high.

And with, with that as background, then, here is the question.

When does this wagon have the most energy?That is, the most capacity to do things.When it's at the bottom of a long ramp, the top of a long ramp, the bottom of a high ramp.And now, I want to end the ramp right around here so it is not long, it's high.So, the bottom of a high ramp or the top of a high ramp.

To guide us through the study of ramps, we'll pursue five how and why questions.

Why doesn't a wagon fall through a sidewalk?

Why does the sidewalk perfectly support the wagon's weight?

How does a wagon move as you let it roll freely down a ramp?

Why is it more exhausting to lift a wagon up than to lower it down?

Why is it easier to pull a wagon uphill on a ramp than to lift it up a ladder?

There's a video sequence for each of these questions, and a summary video at the end.And now, onto the first question.

Ramps: Part 1 - Why doesn't a wagon fall through the sidewalk?

The answer to that question is that the sidewalk pushes up on the wagon to prevent the two objects from occupying the same space at the same time.

The sidewalk exerts what's known as a support force on the wagon. Support forces appear whenever two surfaces try to occupy the same space. My hands, for example.As I push them together, trying to make them overlap, the atoms, molecules, and materials that

are my hands begin to push apart.

Well, support forces act perpendicular to surfaces. Perpendicular is the sort of universal right angles.This stick is perpendicular to the surface of this book, meaning it is at right angles at every respect.And the stick actually is experiencing a support force when I push it against the book.Again, I am trying to make the two of them occupy the same space and they do not like that.

The book pushes away, with a support force on the stick. And the stick is showing you the direction of the book's support force.

There's another kind of force that acts along surfaces. That type of force is known as a frictional force. And we're going to leave frictional forces for the episode on wheels.For now, we're going to ignore friction and look only at support forces.

And so, if we go back to the wagon, the sidewalk is pushing perpendicular to its surface on the wagon. And since the surface on the sidewalk is horizontal, its support force on the wagon is straight up. That upward force cancels the wagons downward weight leaving the wagon here inertial and motionless.

That brings us to a question.

If I push on a ball in which direction is the ball's support force on my finger?

Wherever I touch the ball, the ball pushes on my finger with a support force that's perpendicular to that local patch of ball surface. And that perpendicular direction, which I'm illustrating now with this stick instead of my finger. That perpendicular direction points from the centre of the ball, to the place where the stick is touching. And I'm just continuing that line with the rest of the stick. So you can see the direction of the support force that the ball exerts on the stick when the two try to overlap in space.

The wagon and sidewalk clearly push on one another with support forces but which one is pushing hardest on the other.

The answer to that question is surprisingly simple.They push equally hard on each other in exactly opposite directions.That's an example of what is known as Newton's Third Law of Motion.

And Newton's Third Law of Motion is an observation about our universe, which says that whenever one object pushes on a second object the second object pushes back on the first object with a force that's equal in amount, but opposite in direction, every time.

So if I push on, one finger on the other finger.

The second finger pushes back on the first finger, equally hard in the opposite direction. No matter what I'm doing.

In the case of the wagon on the sidewalk. The sidewalk is pushing up on the wagon to support the wagon and keep it from falling through the sidewalk but at the same time the wagon is pushing down on the sidewalk just as hard in exactly the opposite direction.

Well, Newton's Third Law of Motion, which is often just simplified as 'For every action there is an equal but opposite reaction,' is easy to say but not so simple to comprehend.

To show you all the ramifications of Newton's Third Law of Motion I need some help and some more room. So let's go outside and show you how Newton's Third Law works.

To show you just how general Newton's Third Law is, I've enlisted the help of Arris and Ryan, and they're going to push against each other using these spring scales. So Arris's spring scale will show you how hard she is pushing against Ryan. And Ryan's spring scale will show you how hard he is pushing against Arris. And your goal, guys, is to push differently against one another. See whether you can make it so that one spring scale reads differently than the other.

If you do, you violated Newton's third law and we have a Noble Prize to go earn.Okay, alas we're not going to earn it.

Watch, okay.Give it a try.Now you can do better than that.Come on.It's always reading the same.

The little secret is the universe is rigged against them.They can't do it no matter how hard they try.

Okay, so that's horizontal.Total failure.You can't do it, right.Now, let's try vertically.Up and down, okay?

You know, 70 and 70, 50 and 50.You can't beat the system.

So once again the universe demands that whatever force Arris exerts on Ryan, Ryan exerts the same amount of force on Arris in the opposite direction.

Okay, thanks.

Newton's third law works, not just when people are standing still. It works when they're moving as well. And this isn't all that intuitive.It sure seems like if you push on something that's moving toward you that well, you don't push the same as it pushes on you. Or if it's moving away from you, again, you don't quite push on it as it pushes on you. The secret is, though, you do push just as hard on it as it pushes on you.You can't beat Newton's third law.

And I'll show you that with Aris in a wagon and Ryan pushing on her. Both to push her to go faster and to go slower.It won't work.They push equally hard.

So here comes Aris, and you can now get ready to push on, get ready to push on Ryan.So, no matter that Aris is moving and Ryan is pushing her forward. They're still pushing equally.Now we'll go backward. Here we go.Same thing.

Isn't it nice to have a wagon?And how about if you, Ryan instead of pushing her that direction, come in front.Push her, push her back.

You gotta turn your scale around.There you go.Ready, okay?

So now I'm, Ry, Ryan is fighting me.Making it harder for me.I, I'm working harder now, right?And they still push equally hard.

And now, Ryan can actually make Aris accelerate.I'll stop pushing and let, you know, they still push equally.We can have all kinds of accidents here.But no matter what, the two forces in a Newton's third law pair are always exactly equal in amount and in exactly the opposite direction.I hope you’re convinced.

Suppose you reach out and push on a passing bus, with a force of five Newtons away from you.What force does the bus exert on you in return?

Regardless of what the bus is doing it will always exert an equal but opposite force on you.So if you push it away from you with a 5 Newton force, it will exert a 5 Newton force on you in

the direction opposite to your force namely towards you.

Evidently, the wagon and sidewalk push equally hard on one another. The sidewalk exerts an upward support force on the wagon, and the wagon pushes back exactly as hard on the sidewalk with a downward support force.

Well, the wagon is motionless here, which means that it's inertial. It's not accelerating at all.So the net force on it must be zero.

We know it has a weight, and yet it's not falling. So the support force from the sidewalk on the wagon must exactly cancel the wagon's weight.

And so it does. The sidewalk is perfectly supporting the wagon's weight.

Well, before we go on to look at why the sidewalk chooses exactly that amount of force to exert on the wagon, let's take a look at Newton's Third Law, one last look at it, and recognize that so far I've only talked about three forces.

The wagon’s downward force on the sidewalk, the sidewalks upward force on the wagon, and the wagon’s downward weight.That's three forces, that's an odd number.

And Newton's third law says that for every one force, there's an equal but opposite force around. We'll deal with the around in the next section.

We'll we’re missing a force.

The missing force is the gravitational attraction of the wagon on the earth.Recall that the wagon's weight is the earth's gravitational attraction on the wagon.

Lo and behold, the wagon exerts an equal but opposite force.A gravitational force that is on the earth.And that's the fourth force that is missing and we do have two pairs of Newton's Third Law Forces.

The one pair is the wagon's force on the sidewalk and the sidewalk's force on the wagon.

The other pair is the earth's gravitational force on the wagon and the wagon's gravitational force on the earth.

Well, that's enough, then, about just having the wagon and sidewalk push on one another.Now, in the next segment we'll look at why the sidewalk chooses to push on the wagon with just enough force to support the wagon's weight.

Ramps: Part 2 - Why does the sidewalk perfectly support the wagon's weight?

We know that the wagon is perfectly supported because it's not accelerating. Its weight downward must be perfectly cancelled by the upward support force that the sidewalk is exerting on the wagon.

But how does a sidewalk know how to exert that amount of force on the wagon?

The answer to the question is, the wagon and sidewalk negotiate until the sidewalk perfectly supports the wagon's weight.

That negotiation is real and it actually takes some time.

Underlying it is the fact that there's no such thing as a truly rigid object. Everything dents slightly when you push on it and when it's pushing back on you. So when I push on the sidewalk, it dents a little as it pushes on my hands. The more I push on it the more it dents.

Now the denting of a sidewalk is so minuscule it's hard to see. But it's a lot easier if I pick a softer object like this spring scale not only moves downward noticeably when it's pushing, when I'm pushing on it and it's pushing on me but there's the needle that shows you how much it is dented downward. So if I push gently on it, it dents a little. If I push hard on it, it dents a lot. And you can see everything in between.

Let's watch the negotiation when I set the wagon on the scale, as opposed to on a on the sidewalk.

Here I'm going to actually drop the wagon onto the scale and watch the negotiation occur.

That bouncing of the needle is real, that's the negotiation. Whenever the wagon is under supported as it is before it even touches the scale it's accelerating downward, and therefore tends to move toward the ground, down.

Whenever he wagon is denting the scale deeply, it's being pushed up so hard that it's accelerating upward and will soon move upward and so every time the dent is too deep the wagon accelerates up. Every time the dent is too small it's accelerating down. - It's negotiating with the scale to find just the right amount of dent and the right amount of upward force so that the wagon can be motionless, inertial, and here at rest.

And let's watch that negotiation again. Here it goes. Ready, get set, negotiate.

And when it all settles down, we have a motionless, perfectly supported wagon.

The same negotiation that occurs between the wagon and the spring scale also occurs between the wagon and the sidewalk. They negotiate briefly and, when the dust settles, the sidewalk is perfectly supporting the wagon's weight and the wagon is therefore inertial and motionless.

Actually that same negotiation occurs whenever you set an object on a horizontal surface.

For example, an egg, if I set the egg on the table, there's a brief negotiation, and then the table is perfectly supporting the egg's weight. So the net force on the egg is zero. The egg isn't accelerating. It’s at rest and staying at rest. Voila, but that brings us to a question.

Can the table ever exert and upward force on the egg that is greater an amount than the egg's weight?

Although the table is perfectly supporting the egg's weight right now during the negotiation that occurred when I set the egg down there were times when the egg was being pushed up harder than its own weight. The egg can take a little bit of extra force exerted on its surface, but not a whole lot. Watch what happens if I make that negotiation extreme by dropping the egg on the table.

That negotiation is an amazing thing. It ensures that the sidewalk perfectly supports the wagon. In fact it works when the wagon is motionless, or when the wagon is moving, or even when the wagon is accelerating back and forth. It's still perfectly supported because of the negotiation.

Actually, if the sidewalk is rough and bumpy, the negotiation is ongoing, and the wagon is still supported on average.

Well, before putting the wagon on a ramp, I have one more question to look at regarding the support of objects by surfaces. If I put a ball on the sidewalk or on the table here, the ball's pushing down on the table, the table's pushing up on the ball. Those two forces are equal in amount but opposite in direction. Do they ever cancel?

Although the two forces are equal in amount in opposite directions, they act on different objects and therefore never cancel. Only one of those forces acts on the ball, namely the force that the table exerts on the ball. That affects the ball and it can easily cause the ball to accelerate. For example, now, the ball is accelerating. It leaps right off the table, because the table is pushing up on the ball so hard during that impact that the ball is accelerating upward. And off it goes.

The table is experiencing things as well. It's attached to the whole world, so you don't notice it very much. But the bottom line is, the 2 forces in a Newton's Third Law pair never cancel because they're always on different objects.

I asked that question to call attention to an important misconception people have about Newton's Third Law.

While it’s true forces always occur in pairs, that are equal in amount but opposite in direction, those forces never cancel because each of the forces acts on a different object.

For example if I push on this wagon one of the forces acts on the wagon and causes it to accelerate. The other force in that Newton's third law pair, namely the force that wagon exerts on my finger acts on me. And in principle it would cause me to accelerate. In fact, if I were on slippery ice, I would accelerate. Off I'd go in that direction, the wagon would go off to the right.

Well, that's it for wagons on sidewalks.

Now it's time to tip the sidewalk up to make it a ramp.

Ramps: Part 3 - How does a wagon move as you let it roll freely on a ramp?

The answer to that question, is that the wagon accelerates downhill.

Now, it's tempting to think that the wagon moves downhill. But that's not necessarily true.

If I start the wagon heading up hill watch what happens to it.

It initially is moving up hill. It comes to a stop and then it rolls downhill. So it's not necessarily moving downhill while it's rolling freely. What you can say, though, is that it's always accelerating downhill.

So if I let go of it from rest it starts from rest and develops more and more downhill speed, and that's indicative of downhill acceleration.

And if I start it from moving uphill, it initially is heading uphill, that's its velocity, but its acceleration is still downhill. It's losing its uphill speed. It's going slower and slower. It momentarily comes to a stop but it's still accelerating downhill. And then it continues its travels downhill, going faster and faster.

So the long and short of it is, a wagon that's rolling freely on a ramp is accelerating downhill,

and we can't say anything specific about its velocity without more information.

Well, that brings us to the issue, where does this downhill acceleration come from?Why does a wagon on a ramp accelerate in that particular direction?

And the answer to that, is, the net force on the wagon, once I let go of it, is downhill. And it's accelerating in the direction of the net force on it. Like anything else.

Well, that just passes the buck.

Why is there a downhill force on the wagon?

That turns out to come from the, the Interaction of two separate forces.One is the wagon's weight which is straight down as always toward the centre of the earth.The second force acting on the wagon is the support force from the ramp.

Now if you recall support forces act perpendicular to the surfaces that exert them.For example when the ramp wasn't a ramp at all but rather a sidewalk.It is a horizontal surface and the support force it exerts is therefore vertical.

I can show you the direction again with my little stick.

So, this is a horizontal surface and it exerts vertical support forces on the things that sit on it, that touch it, that try to penetrate into its surface.

But when we tip this sidewalk into a ramp, it's not horizontal anymore.And the support forces it exert aren't vertical anymore. They're up and to your right.

So the support force on the wagon is now up and to the right.It's in this direction.

And a force that's up and to the right can't cancel a force that's straight down the weight of the wagon.Those 2 forces. Add up to something. They don't add up to 0. They can't cancel.Instead the downward weight and up and to the right support force add together to become a very small net force that is downhill. That is exactly along the surface, parallel to that ramp surface.

And it's that net force in the downhill direction that causes the wagon to accelerate downhill when I let go of it.

Now, I call the net force on the wagon that points downhill, the ramp force.

And the ramp force isn't a new kind of force.

Rather, it's the sum of two separate forces that don't quite cancel, the wagon's downward weight and the not quite upward support force exerted by the ramp on the wagon.Those two forces, when you sum them together, produce this downhill net force, this ramp force, which causes the wagon to accelerate.

The amount of downhill ramp force depends on the steepness of the ramp.

To show you that I will start with no ramp at all.Go back to our horizontal surface and now the downhill ramp force is 0.That's because the cancellation is perfect between the wagon's downward weight and the vertically upward support force from the horizontal ramp.

But as I start to tilt the ramp just a little bit, now there's a downhill ramp force and that ramp force is equal to the wagon's weight times a number that's smaller than one.

That number turns out to be the height of the ramp, which in this case is about 10 centimetres, or 4 inches, divided by the length of the ramp, which is 4 feet, or a bit over a meter. So it's about a 10 to 1 ratio. And that means that the downhill ramp force on this wagon is about a tenth of the wagon's weight, and aimed along the ramp.

If I tip the ramp still further you've got more downhill ramp force.That's because the height's larger, the length is the same.The ratio now is more like 5 to 1.

I can keep going.

I don't have the reflexes to keep going without some help.

So now bigger ramp force and the extreme case is when I take the ramp up to full vertical. In this case the ramp force, which is straight down, is the full weight of the wagon.

So the ramp force evolves perfectly. From zero, the ramp is horizontal and I've got no spacers here.

It evolves continuously to larger and larger ramp forces all the way to the full weight of the wagon.

The steeper the slope, the bigger the downhill ramp force.

This slope on the grass is a whole lot steeper than a handicap access ramp, so the downhill force will be big and so will my acceleration.Don't try this at home, professional driver here.

And off we go.

Big downhill force, fast acceleration.

It's pretty clear now, that if you let a wagon roll freely on ramp, it accelerates downhill.

But what if you intervene and you exert an uphill force that is equal an amount to the downhill ramp force.How does the wagon move?

If you exert an uphill force on the wagon that exactly cancels the downhill ramp force the wagon is inertial and it moves as an inertial object. It coasts. If it happens to be motionless as, as it is now, it remains motionless. But if it's moving, it keeps moving at constant velocity.So let me get it moving.

Here we go.Now.It's inertial.I'm balancing ramp force.

I ran out of ramp.But that's the idea.It can coast uphill.But there it is.Or it can coast downhill.Let me get started.There we go.

Those are all possible situations where you've perfectly cancelled the downhill ramp force by exerting your own uphill force. Of an equal amount.

We've seen that when you pull uphill just enough to cancel the wagon's downhill ramp force that the wagon becomes inertial, and it can be motionless or coasting.

But what if you pull a little too hard or a little too soft? In that case, the wagon does accelerate. For example if I pull a little too weakly in the uphill direction. The wagon accelerates gently downhill. And if I pull a little too hard in the uphill direction, the wagon accelerates gently uphill.

That allows us to control the wagons motion.For example, how do I get the wagon to go from the bottom of the hill to the top of the hill?What's the whole process?

The whole process has three parts.Let's start with the wagon at the bottom of the hill and motionless. And my goal is to get it to

the top of the hill and motionless.

Here are the three steps I've gotta do.First, I've gotta make the wagon accelerate uphill by pulling it uphill a little extra hard.So I'm going to do that just a little and get it moving.Here we go.A little extra strong pull, a little upward hill acceleration.I'm good to go now.

Now the wagon is coasting.I'm no longer pulling extra hard.I'm simply balancing the downhill force.

And now I'm getting to the top of the hill.Now I've gotta bring the wagon to a stop.How I do that?

Pull a little less hard, and under support the wagon, so that it accelerates downhill opposite its uphill velocity and it slows to a stop.

So just to make sure you can follow that let me do it again. Let me go to the bottom of the hill.

A miracle occurs and we are at the bottom of the hill again.

And now, I pull a little extra hard to get it started, now I just pull enough to keep it coasting, and now I pull a little extra weak to let it slow to a stop. And we're done.

This actually works in reverse to go downhill. Suppose I got the wagon at the top of the hill?Which I do and I want to get it to the bottom of the hill.From stopped, to moving, to stopped.

Well I under support the wagon at first, so that it accelerates in the downhill direction, it gets moving.There, I've done it.

Now, I let it coast. I simply support the downhill ramp force.

And now I want to stop it, so I pull uphill a little extra hard and slow it to a stop.

You use processes like these to move objects up and down ramps all the time, without even thinking about it. Most of the time, you simply support the object against its downhill ramp force to let it coast.But you use subtle adjustments in your uphill force to cause the object to start or stop.

Well, the trip uphill, simple, the trip downhill, simple.

They sure look similar in terms of physics, up to this point, but they feel very different.You know from experience that dragging something uphill is a lot more fatiguing, in many ways, than lowering it downhill.

In the next segment, we'll talk about what distinguishes the trip up from the trip down.

Ramps: Part 4 - Why is it more exhausting to lift a wagon up than to lower a wagon down?

The answer to that question lies in the fact that you transfer energy to the wagon as you lift it and you receive energy from the wagon as you lower it.

Energy is an intangible physical quantity that can move from object to object. And people generally find it more exhausting to give energy away than to receive it.

Energy is what's known as a conserved physical quantity. Meaning, that you can't create it or destroy it. You can only move it from object to object.Conserved quantities are very rare in nature and energy is one of them.It's analogous to money.In a society with law abiding citizens, money is pretty much a conserved quantity as well.You can't create it or destroy it. Usually, without going to jail.

And, it's the conservation of that quantity that makes it so interesting. If people could print money at will, why, money wouldn't be very interesting anymore.

Similarly, if you could create or destroy energy at will, no one would care about it anymore.

Well, society decided to make money a conserved quantity.Society had no choice in making energy a conserved quantity.

That's the way our universe works.In any civil, civilization that's sophisticated enough to have discovered the laws of physics will have found the concept of energy and will have exactly the same quantity in their minds.

Just as you can learn a lot about how a community or an economy works by watching how money moves through it, you can learn a lot about how something works by watching how energy moves through it.

We'll do just that with ramps in a few minutes.

But first, I need to talk a little bit about what energy is and how it moves between objects.

Since we are going to encounter several other conserved physical quantity in later episodes, I want to distinguish energy from those other conservative quantities.

Energy is the conserved quantity of doing.

The more energy you have, the more you can do.

The doing that I have in mind is what physicists call work. Work is a common word that has many meanings, only one of which is what physicists refer to as work.That, physicist work is the mechanical means of transferring energy.Doing work is analogous to spending money.When you spend money, you're transferring money from you to someone else.

The total amount of money present in the world doesn't change, it just moves from one place to another.Overall, it's conserved.

When you do work on something, you transfer energy from yourself to something else. The total amount in the world doesn't change. It just moves from one thing to another.

Energy, which I've described as the conserved quantity of doing is defined as the capacity to do work.And work is defined as the mechanical means for transferring energy.

That circular pair of definitions isn't very satisfying at the moment. But, as we begin to play with work and energy, it'll all begin to make clearer and clearer sense.

So bear with me.Even though I've defined energy as a capacity to work, and work, as the means of transferring energy, it's all going to work out in the end.But first, I've gotta take a look at what work is.

So let me show you, work. Work according to a physicist.

To do work on the wagon, there are two requirements. I have to push on the wagon and the wagon has to move a distance in the direction of my push.For example, if I put my hand under the wagon, push up on it, and cause it to move upward, I'm doing work on the wagon.

I'm following the rules. I'm exerting an upward force on the wagon, you know this from experience, and you saw that the wagon moved a distance in the direction of my force.Therefore, I did work on the wagon and that means I transferred my energy to the wagon.The total amount of energy around in the world didn't change, but it did move in part from me to the wagon.

Now, this is analogous to what you do when you spend money, right? So, so this is my money and I'm going to give it to the wagon.

Don't spend it in one place. So, the total amount of money in the world didn't change, but it moved from me, in part, from me to the wagon. Same thing when I do work on it, energy moves from me to the wagon.

Now, if I don't follow the full rules, I don't do work.For example, if I don't push on the wagon, I do no work on it.

On the other hand, if I push on the wagon, but it doesn't move a distance in the direction of my push, I do no work again. So, I am pushing, or let me, hold, don't watch for a second, let me get this up here.Okay, now watch.

Now, I'm still pushing up on the wagon, but it's not moving, so I'm doing no work on it.

And, actually, I don't have to make sure that it's not moving all together.

I just have to make sure that it's not moving in the direction of my force.So since my force is upward, if it moves horizontally, that's not in the direction of my force.I do no work.So let me get it started.

But now, now, as it coasts to your right, I'm doing no work on it. Now let me get it going to the left. Again, it's coasting to the left, my force is straight up.But it's moving horizontally. It goes at right angles to each other. I'm doing no work on it.

Now, you wonder, why is it tiring to sit here holding up a wagon?

That's because, human beings are not statues and we burn calories just trying to hold a pose.So, I'm not transferring any energy to the wagon, but I'm getting tired nonetheless, because I'm turning my own chemical energy into thermal energy. I'm getting hot, holding this here all day. That doesn't affect the wagon. The wagon is just minding its own business with the same amount of energy now, as now, as now. Because I'm doing no work on it.

Now that you've seen how work works in the context of wagons, let's apply it to another situation.

Rubber bands.

So here is a question for you.

If I hold one end of the rubber band motionless with my left hand, and I take my right hand, and stretch the rubber band outward like this, which of my hands is transferring energy to the rubber band?

Your right hand, the one that holds a piece of rubber band that moves does work on the rubber band. The other hand, the one that stays still, doesn't move, and therefore, it does no work. So, as I move the rubber band to, to your left with my right hand, sorry for the complexity here.This hand is doing work. It's pushing the rubber band to your left as the rubber band moves to your left. Goes in the same direction. My, my hand here is doing work on the rubber band. The other hand doesn't move, does no work.

We've seen that when you push on an object and it moves in the direction of your push that you do work on it. And that means you transfer your energy to it.

But what if it moves in the direction opposite your force? Like this.

I'm pushing up on the wagon but it's moving downward. What then?In that case, you do negative work on the object. That is, you transfer less than zero energy to it. And you reduce its overall amount of energy.

Is there a money analogy to this?Sure.

We've seen that the money analogy to doing work is to give money.So, doing work on the wagon and increasing its energy is analogous to giving money to the wagon and increasing its money.Okay?

Doing negative work on the wagon is equivalent or analogous to giving the wagon debts. To giving it less than no amounts of money.For example, my car loan, it's weighing me down. If I give it to the wagon, I weigh it down.My money just increased. I'm happy.The wagon suddenly saddled with, with debt it didn't expect, is impoverished. I can give it my, my mortgage. I can give it another mortgage, on the summer house, and, hey, maybe a loan for college. So, I have passed along negative money to the wagon. It's poor and I'm richer. This is great.

That's analogous to negative work. Whenever you do negative work on something, you lower its energy, and amazingly enough, you increase your own.

Well, how did I increase my energy by doing negative work on the wagon? I'll show you.I'm about to do it.

The wagon right now has some energy, and as I lower it, and therefore do negative work on it,

watch what it does to me. It's pushing down on my hand and my hand is moving downward.It's doing work on me.So, at the same time I do negative work on the wagon, the wagon does an equal amount of positive, that is work, on me. And that's how the energy moves. Whenever one object does positive work on the other, the second object does negative work on the, on the first. There's a perfect transfer of energy from one to the other.And overall, the total amount of energy doesn't change. It just moves.

That brings me to one last point.

I've talked about doing work and doing negative work. Shouldn't the word positive show up in here? Shouldn't this be positive work and negative work? Maybe.

But physicists have adopted the convention that if you don't specify negative or positive, we assume positive.And, that just simplifies the language.So, doing work always refers to doing a positive amount. If you're going to do a negative amount of work, say it, use the word negative. And you might think, well, that's a silly convention, no one ever adopts that convention outside of physicists. Well, think about charity.When you give money to charity, we're assuming you're giving a positive amount of money.

Don't you go giving your loans and your mortgages to a charitable organization, they're not going to be happy about that.

I've been talking a lot about work and letting energy come along for the ride. But it's time to reverse that arrangement.

Let's talk about energy.And to do that, let's revisit the rubber band problem.

When I stretch a rubber band, the rubber band changes.

When it's unstretched, okay, it can't do anything.But once I stretch it, it has something it didn't have before. Not more mass, not more weight, not more speed, more ability to do things. And energy after all, is the conserved quantity of doing. This rubber band, now that I've stretched it, is capable of doing work and making things happen.

Energy takes two principle forms, kinetic energy and potential energy.

Kinetic energy is the energy associated with the motion in objects.Now, energy itself is the conserved quantity of doing, not of moving. So energy isn't inherently

about motion, but there is energy in moving objects.

For example, this ball.When the ball is at rest, it has no energy associated motion, because it's not moving. But if do work on it, I will push it toward your right, and it will move toward your right. And during that brief period while it was passing quickly to the right, it was chock full of kinetic energy. That is, it had energy that was in the form of this energy of motion, kinetic energy.So the whole act of throwing the ball from one hand to the other, involves investment of energy in the ball, so I'm transferring energy to the ball by way of work. It then moves, it's carrying its energy with it as kinetic energy, and when I catch it, I take the energy back out by doing negative work on it.

So, long story, simple action, but there's energy going in and coming out.

So, moving objects have energy associated with their motion that is called kinetic energy.

But even objects that are at rest can have another form of energy.Potential energy is energy stored in the forces between, or among, within objects.So forces can store energy.For example, there is a gravitational force or traction between this ball and the earth.You know that because we've talked about dropping, you drop the ball and it falls.So, the ball is being attracted to the earth, the earth is being attracted to the ball. And if I pull them apart, something that takes work to do, I invest energy in the ball in the form of gravitational potential energy. That is, an energy stored in the forces of gravity. In this case, between the ball and the earth.

So, when the ball is down low, it has relatively little of this gravitational potential energy. And as I lift it upward, and do work on it in the process, I'm pushing it upwards, it moves upward, I'm increasing its, its total energy. And that energy is going primarily into the form of gravitational potential energy, the energy stored in the forces of gravity.

I tend to identify the forces involved in a potential energy.Some, in some cases, people simply refer to potential energy generically.

But if we can, it, it makes sense to identify the forces that are doing the storing.So that's gravitational potential energy.

Let me show you elastic potential energy, energy stored in the forces of an elastic object.

I hope you had one of these cans of mixed nuts when you were young and you would go up to your, to your favourite aunt or uncle and say. You know?

Uncle Richard, would you like some nuts? I have them, hear them rattling? And then you would open the can and out would jump a snake, right?

And then you would laugh.Everyone would laugh.You would stick it back in the can.

And five minutes later, Uncle Richard, want some nuts again?And you would be surprised yet again.

Well, okay, so fun and games.

But that energy that caused this snake to leap out of the container and attack my, my magnets down there on the table. That's energy stored in the elastic forces within this snake and I'm doing work pushing the snake back in as it moves inward. I'm packing it full of elastic potential energy and it's ready to attack another relative.

Okay.

Another familiar situation with elastic potential energy is an elastic balloon.If I inflate this balloon with air, an action which requires work, I push the skin outward by way of my air, and it moved outwards so I did work on it. It now has energy stored in the elastic forces in the balloon surface. And if I let go, off it goes. It uses the energy I put in to do something, fly around the room.

Other forces.The forces between magnets, we can store energy, as magnetic potential energy. These magnets are attracted strongly to one another. There's as close as they can get.I have to pull them apart. Something that's not easy to do. I'll get 'em apart.

There, they're apart.And that action took work.

I pulled them apart, and they moved apart.So I've invested energy. They now have it in the forces, the magnetic forces between them.So magnetic potential energy.And if I let them come near each other, off they go. They release that energy, leap at each other, the energy transforms spontaneously from magnetic potential energy to kinetic energy.Because suddenly, we had we had some fast moving magnets and then into sound and other forms of energy.

How about the forces between electric charges?

So that's the force between magnets, magnetic poles, something for the future.

How about the forces between electric charges?

Well, this is a device that stores separated positive charge and negative charge. And I'm going to, right now the charges are evenly distributed here. There's nothing special going on.

But I'm going to separate positive and negative charges from one another and if you remember the, the old opposites attract well opposite charges attract. And I'm going to separate them with the help of this collection of batteries. Batteries can do work on electric charges and that's what I'm going to let them do, so, here they go. The batteries are now doing work, pulling apart positive and negative charges, accumulating negative charges on this side, accumulating positive charges on that side.

It's an arduous process, because this stores a lot of separated charge.

Here we go. It's pretty well separated at this point.And I'm going to stop that process, and I'm going to let them get back together.They're, the energy is stored as electrostatic potential energy. So frequently this would be called magneto-static potential energy. That's full of electrostatic potential energy. I'm going to let that get together.

Ready, get set, got together, and, energy was released.

Last form of energy to, to talk about here, because I'm going to leave nuclear potential energy for some other situation. I can show it to you, but I, then I'd have to do something.So, ready?Chemical potential energy.

Must be a dud.Okay.So you get the idea.

Energy can take two principal forms. That is, kinetic energy, the energy of a moving object. And it can take potential energy, that is, energy stored in the forces between, within, among objects.There are a variety of forces to work with, we've worked with several of them, and, those forces can store energy. Often, when the energy is being stored in potential form, there's no motion at all. When there's kinetic energy, of course, there is motion.

And the last observation to say about energy is, energy as a whole, is a conserved quantity. You cannot create total energy, you cannot destroy total energy.But the individual types of energy, they're not conserved.So, kinetic energy can change as long as potential energy changes correspondingly in the opposite direction.

Similarly, you can turn chemical potential energy into kinetic energy. You can turn kinetic

energy into gravitational potential energy, like that and so on.

Don't try to conserve the individual pieces of energy, the types. It's total energy that is truly the conserve quantity in nature.

Like any object, a wagon has kinetic energy when it's moving and it has gravitational potential energy when it's elevated.Now, in the context of ramps, we are doing a lot of lifting of wagons. And so knowing how much gravitational potential energy the wagon has at various heights is going to be useful to us in understanding what ramps do. How they make life easier?

So, let's figure out how much gravitational potential energy the wagon has at various heights.To do that, I have to start by making sure it's clear exactly how much work you're doing when you lift that wagon.

Work, I've told you, is force and distance. That is, to do work on this wagon, I have to exert force on it and it has to move a distance at the direction of my force.

The exact amount of work I do is the product of the force I exert on the wagon times the distance it moves in the direction of that force.

Now, in this case, it's moving exactly in the direction of my force. My force is straight up and it's moving straight up. Life is simple.

But if I push the wagon upward, and it moves up at an angle, the overall distance the wagon moves isn't the issue. What matters is the component of its motion, that is in the direction of my force.Since my force is straight up, the only part of the wagon's motion that counts is its motion in the upward direction. Its motion horizontally doesn't matter, it doesn't contribute to the work.

So, the amount of work I do in lifting this, this wagon is the force I exert on it, times the distance it travels upward. Its increase in elevation or altitude.

That's interesting, because, in order to lift this wagon upward at constant velocity, I have to push up with a force that exactly cancels the wagon's weight. So as it goes up, steadily, I am pushing up with a force equal in amount to the wagon's weight, although in the upward direction and it's moving upward directly in line with my force. So the work I'm doing is the product of the wagon's weight times the upward distance it moves.

That's very simple. I'm doing that work and that work is becoming entirely gravitational potential energy in the wagon.

So starting with a clear understanding of work, that it is the force you exert on the wagon,

times the distance the wagon moves in the direction of your force, we can then figure out how much gravitational potential energy the wagon has at any given height. It's simply the wagon's weight times its increase in altitude.

So, it turns out we have to set a zero of gravitational potential energy. Because, this, we might call this zero, but actually, if I drop the wagon on the floor, I can release a little bit of gravitational potential energy that's even there at zero. So we choose a zero and if you really want to, you can go into the negative values by coming off the table.

But this is a perfectly good zero right here. We don't have to worry about going to the floor or going to the basement and so on.

Start at zero here.

If I increase the height of the wagon by 1 meter, then, and I suppose I've had to push up on this wagon with the force of, let's say 10 newtons.So, a 10 newton force upward times 1 meter of upward motion, that is 10 newton meters of work that I did on it.

Now, the newton meter has a name. It is the unit of energy. It's got a name to make life simple, it's called the joule.

So in lifting this, this wagon, 1 meter upward using a 10 newton force, I did 10 joules of work on the wagon and they are now present in the wagon as gravitational potential energy. The gravitational potential energy of the wagon increased by 10 joules going from here to here.

It's time for the question I asked you to think about in the introduction to this episode,

When does the wagon have the most energy?When it's at the bottom of a long ramp?The top of a long ramp?The bottom of a tall ramp, so the ramp ends here?Or the top of a tall ramp?

By being at the top of a tall ramp, the wagon has as much gravitational potential energy as it can have among the choices I offered. So by getting here to the top of the tall ramp, it's accumulated as much energy as it can accumulate.

The work you do in lifting a wagon depends only on how much you increase its altitude and not on the specifics of how you did that lifting process. Whether you go up the ramp or you go straight up, doesn't matter, it's just the increase of altitude that matters. And the work you do is the weight of the wagon times the increase in altitude.That means that, as you go up the ramp, you must be doing work on the wagon, because you're increasing the wagon's altitude, and therefore, its gravitational potential energy.

As you lower the wagon down the ramp, you must be doing negative work on it, because you're decreasing its altitude, and therefore, decreasing its gravitational potential energy.

We're now in a position to answer the question I asked at the beginning of this video segment.

As you take the wagon up the ramp, you're doing work on it, increasing its gravitational potential energy. And doing work on a heavy load involves transferring a lot of your energy to the wagon. And so, we're, you're using chemical potential energy in your body energy that you receive from your food. You're consuming that. You're transferring it mechanically into the wagon and that transfer, is tiring. It wears us out. It fatigues our muscles. It consumes our energy.

As you lower the wagon down the ramp, it actually requires negative work. You're taking energy out of the wagon and receiving it yourself, it's coming into you.

Now, human beings, like most animals, cannot store energy well, so the work is really being done on us. We are receiving energy as we lower the wagon down the, down the ramp, and what we do with that energy is to waste it.We turn it into the waste version of energy, the most degraded useless form of energy, which is known as thermal energy. Thermal energy is, we'll deal with in the near future in other episodes, is ordinary energy chopped up into little pieces. And scrambled and sprinkled among all the particles that make up your body in this case. And thermal energy is hard to do anything useful with. It's energy, but it's disordered energy. And you can't get it ordered together to do work, or not easily.

So taking the wagon up the ramp involves you transferring energy to the wagon and that's tiring.Taking the wagon down the ramp involves the wagon transferring energy to you that has some tiring aspects to it, but at least, it's not consuming the same amount of, your stored chemical food energy. And it's, it's less exhausting, it's a little nerve-racking, cause you can get injured as that energy rushes into you but it is not as fatiguing.

Ramps: Part 5 - Why is it easier to pull a wagon up a ramp than it is to lift it up a ladder?

The answer to that question is that the ramp allows you to lift the wagon using a smaller force exerted over a longer distance.Regardless of how you lift the wagon you have to do work on it, to raise its altitude from this to this.That increase in altitude comes with an increase in gravitational potential energy in the wagon.So you have to transfer a specific amount of energy to the wagon to pay for that increase in altitude and therefore increase in gravitational potential energy.

Well if you go up the ladder, you do that work, you transfer the energy by exerting a large upward force on the wagon as it moves a short distance, the minimum possible distance in the direction of your force. That involves a big upward force, which may or may not be practical.

Okay.

In going up the ramp, however, you increase the wagon's altitude gradually. It goes from the low level, to the high level, while traveling quite a long distance. Now, the distance it travels is in the direction of your force. You are pulling the wagon uphill in order to cancel the downhill ramp force. But that's a gentle uphill force and the wagon moves uphill.

So you're doing work on it.

But it takes a much longer travel along that ramp to do the work involved in lifting the wagon from low to high.So while you do the same amount of work whether you go up the ladder or up the ramp, the ramp version of this trip involves a small force exerted over a long distance, whereas the ladder version involved a large force exerted over a short distance.

Well, it's all very well to do this in my laboratory with a dinky little wagon. But we can do better. Let's head on outside and do the trick with a real wagon and a real handicap access ramp.

Suppose I want to lift this wagon from ground level to building entry level. I have two options.

On the right I can go up to that ledge and lift the wagon straight up. In a very short distance I can manage to elevate the wagon from ground level to entry level.

On the left I can go up the ramp. It's a much longer trip. I'll be pulling the wagon up the ramp, but I can still do the job of lifting the wagon from ground level to entry level.

Let's start with the first option, the ledge. I'll roll the wagon out to the ledge. And now to lift the wagon up I have to support its entire weight so that it can coast upward constant velocity and go from ground level to building entry level. So big upward force as the wagon moves a short upward distance in the direction of that force.

Job done.

I did a certain amount of work on the wagon.That amount was the weight of the wagon times the distance upward the wagon moved. Its increase in altitude.

Okay.

Let's try the second option.

Back to the starting point and this time I'm going to go up the ramp. As I go up the ramp, I have to pull uphill gently just enough to balance the downhill ramp force so the wagon can coast upward. I am doing work on the wagon though, this entire trip, because I am pulling it uphill as it moves uphill. That means I'm doing work, it's moving in the direction of my force on it.

I'm almost there, almost there, I'm there.So I have managed to lift the wagon from ground level to building entry level, this time using a small force exerted on the wagon, as the wagon moved a long distance in the direction of my force. I did a certain amount of work on the wagon in that process and lo and behold, it's the same amount of work that I did in lifting the wagon from ground to ledge. All that mattered was the increase in elevation or increase in altitude of the wagon. That's the increase in the wagon's gravitational potential energy. The only form of energy that increased.

It went from motionless to motionless so it has the same kinetic energy it had at the beginning, zero.And the only other form of energy that it has is gravitational potential, and that went from the value at ground level to the higher value at building entry level.

And whether I went up the ledge or whether I went up the ramp, makes no difference.The wagon has no memory of which approach I took. It doesn't matter at all.

But there's a difference to me.

In going up the ledge I had to exert a large force on the wagon as the wagon moved a short distance in the direction of that force.In going up the ramp I had to exert a gentle force on the wagon as the wagon moved a very long distance in the direction of that force.The product of those two, force x distance, was the same in each case, but if this wagon were a little more heavily occupied than it is going up that ledge would have been very difficult if this were full of bricks. There is no way I can lift it up the ledge. So I could still pull it up the ramp.

So, I get mechanical advantage. The mechanical advantage of a simple machine known as a ramp, or inclined plane.What that ramp is doing for me is allowing me to do something. To rearrange the force and direction of force. The amount of force and the direction of force that I need to use to do some particular activity.

Instead of using a very large upward force to do the activity, in this case I was able to use a small uphill force to do that same activity namely lifting the wagon.

Now that the wagon is full of energy I can release that energy by riding it back downhill.

And here we go.

The gravitational potential energy is becoming kinetic energy.

And off I go. In case you're jealous and wanted to make the trip yourself, here's your opportunity.You get to go down the ramp also.Ready?Off we go.

It's time for a question.

Suppose you have two ramps with the same height.That is, both ramps lift the wagon that rides them vertically upward the same amount, in this case, about that much height. But one ramp is long, and the other ramp is short.In fact, the long ramp is twice as long along its surface as the short ramp.In that case those two ramps look like this, this is the long ramp and the short ramp looks like, ignore this part of the board, like this, its steeper obviously because its only half as long as the long ramp.

The question then is this: If it takes 100 newtons of uphill force to pull the wagon up the longer ramp, how much uphill force does it take to pull the wagon up the steeper, shorter ramp.

If it took 100 Newtons of uphill force, to pull the wagon up the long ramp at constant of velocity, when you halve the length of the ramp while keeping its height constant, you must do the same amount of work in half for distance. So now you have to pull uphill with twice the uphill force.The product of the two, force times distance travelled by the wagon remains the same.But now instead of a 100 Newton force exerted over a long ramp, it's a 200 Newton force exerted over the short, half-length ramp.

It's clear that ramps make it easier to lift and lower heavy objects.For example, when you're moving something, or delivering something, or taking something back out; if you're using a ramp that's gradual enough, you can lift a very heavy load using a relatively gentle force.

One of the most important uses for ramps is for handicap access. An access ramp allows a disabled person to change elevations, to move up or down, with relative ease.But in order to be usable as an access ramp, the ramp has to be very gradually sloped.In fact, the United States regulates access ramps and will only approve them if their slope is 1 unit of rise to 12 units of run.Rise is defined as the vertical movement that occurs in going up a ramp. And run is defined as the horizontal movement that occurs in going up the ramp.

Now, I've been talking about rise all along, although I haven't called it that, I've talked about the altitude increase that occurs when going up a ramp; but I've been talking not about run, but about the length along the surface of the ramp because that's the one that's most useful to us in calculating work. That is, after all, the distance moved by an object rolling along the ramp.Fortunately for these very shallow angle ramps, very gradual ramps, there's almost no difference between the length of the ramp's surface and the run, the horizontal extent of the ramp.This is a trigonometry problem that basically for very small angles the difference between this hypotenuse and this horizontal component, there's almost no difference between them. It's a simple problem in trigonometry. You can do it as homework if you like.

So, the bottom line is that ramps, access ramps, can be no steeper than, ramps in which you move up 1 unit for every 12 units you go along the surface of the ramp. And, if you recall, the uphill force that you have to exert on an object coming up this ramp at constant velocity is 1 12th its weight.If it's a 1 to 12 ramp, 1 unit of rise to 12 units of length, then the force you have to exert in the uphill direction Is 1 12th of the weight of the object.That means that a disabled person coming up one of these access ramps at the maximum slope, needs an uphill force of approximately 1 12th their weight. And that was deemed to be all you can expect of the disabled person themselves or of their helpers in going up the ramp, 1 12 th

their weight is enough.

In addition to limiting the slope of an access ramp, US regulations limit the extent of that ramp as well. And the extent that they limit is its vertical extent. That is, what altitude change you go through in riding that ramp.

To be approved, an access ramp may have no uninterrupted inclines that take you through an altitude change of more than about this much.There's a sound physics basis for that requirement. Gravitational potential energy is related to altitude. And in going from this height to this height, your gravitational potential energy increases by your weight times that distance.So, in going up an access ramp the person responsible for doing the work necessary to increase your gravitational potential energy from this value to this value has to do the work necessary to increase that gravitational potential energy. And evidently, this much increase in altitude is enough. The person who's doing the work, whether it's the helper of the disabled person or the disabled person themselves needs a break. So don't make that person go through an altitude change of more than this without giving them a flat area to re-gather their energy.

On the way down similar problems are avoided, by having periodic breaks. In going from this altitude, to this altitude, the person descending releases gravitational potential energy and that energy takes some other form.If this occurs in an uncontrolled roll in a wheel chair, it becomes kinetic energy.If it's done in a controlled fashion, it becomes typically thermal energy in the people involved

and maybe the equipment if wheelchair brakes are involved.

So, evidently, this much decrease in altitude and the gravitational potential energy that's released in that process is considered to be enough.

And it's time for another pause.

So in descending what would otherwise be a very long, uninterrupted ramp, there are periodic flat spots put in to allow the people descending that ramp to pause, get ready for the next descent, and then continue on their way.

Ramps: SummaryIn this episode, we looked at the physics issues that make ramps so useful.

Ramps are simple machines that allow you to use gentle forces to lift and lower heavy loads. You exert those forces uphill as the heavy loads move long distances along the ramp.

The story of ramps is also the story of energy and work.It's the story of energy because energy is a conserved quantity that depends only on the situation. So that, in this case, the wagon has a certain amount of energy. And now, it has more energy, the energy increase in going from here to here, is all in the form of gravitational potential energy, the energy stored in the force of gravity.

The story of ramps is also a story of work because, in going from this position to this position, you have to do a certain amount of work on the wagon, to increase its gravitational potential energy from its low value to its high value. You're responsible for that increase in energy and you can do the work necessary to increase the wagon's energy, either by lifting it straight up with a large force exerted as the wagon moves a small distance, or with a gentle force as the wagon moves a long distance.

So, the work you do via either of these two approaches is and has to be the same because the wagon's increase in energy is the same.

In addition to looking at energy and work in this episode, we also looked at a new force, support forces.Support forces appear whenever two surfaces try to occupy the same space at the same time. And those support forces are exerted perpendicular to the surfaces involved.For example, when the surface involved is horizontal as the end of the sidewalk, the support forces that a horizontal surface exerts are vertical, as indicated by this stick.But if the surface that you're looking to obtain support forces from, is tilted as it is with our ramp, the support forces are no longer vertical. They are still perpendicular to the surface, but that's no longer straight up and down.

That up and, in this case, to the right, support force from this ramp cannot cancel, in this case, the wagon's downward weight, there is a residual left. When the two forces act on the wagon, the residual that is left is the downhill ramp force. And that ramp force, left unchecked, will cause the wagon to accelerate downhill.

We also talked about the third of Newton's Laws, Newton's Third Law of Motion, which observes that: for every force that one object exerts on a second object, the second object exerts a force back on the first object that is exactly equal to the amount and exactly the opposite direction.If my, what you see, this hand pushes on this hand, this hand pushes back on this hand equally hard in the opposite direction every time. It does not depend on whether the hands are accelerating or moving in any way they like.

Newton's Third Law works.

That's it for ramps.Do your homework, study hard, and I'll see you next time, as we continue to look at how things work.