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36 |
37 |
41 | The key to understanding the behaviour of our tiny things is energy.
38 | 39 | 40 |
42 |
45 |
46 | The key to understanding the behaviour of our tiny things is energy.
38 | 39 | 40 |Let’s invent a new game: Billiards on ice or mud!
51 | 52 | 55 | 56 |Which one is the most fun?
57 | 58 | 59 |I added some more balls!
51 | 52 |You know what to do.
53 | 54 | 58 | 59 |Nice break shot!
60 | 61 |Wait, why are we playing billiards?
62 | 63 | 64 |Does friction make it easier or harder to spread out the particles?
52 | 53 | 56 | 57 | 58 | 59 |How would it be to play billiards without friction?
51 | 52 |You tell me.
53 | 54 | 58 | 59 |Madness!
60 | 61 |This is how the tiny, microscopic particles work. They keep bouncing all over and never stop.
62 | 63 | 64 |Did you expect them to vibrate forever?
58 | 59 |You were right! But they have to start close enough.
60 | 61 | 62 |How does the vibration change with friction?
58 | 59 |Snap them together with different amounts of friction.
60 | 61 | 64 | 65 | 66 | 67 |Let’s begin by playing some billiards.
51 | 52 |The impulse tool works sort of like a billiards cue.
53 | 54 |Hold down the mouse button and drag to aim, and when you release the button, you shoot!
55 | 56 |Try it out!
57 | 58 | 64 | 65 |Nice!
66 | 67 |It’s not really billiards with just one ball, though…
68 | 69 | 70 |Move these particles closer to each other.
58 | 59 | 67 | 68 |As they come together, they vibrate a bit.
69 | 70 | 71 |Back to billiards!
60 | 61 |Split the group-hugging triangle.
62 | 63 | 67 | 68 |It’s harder when they are sticking together, but with enough speed it’s possible.
69 | 70 | 71 |Normally, if you stop pushing or pulling something, it will eventually stop moving.
54 | 55 |Drag around the ball a bit and then look at what happens when you let go.
56 | 57 | 70 | 71 |When you let go, the ball starts slowing down and eventually stops.
72 | 73 | 74 |Make a break shot!
54 | 55 | 59 | 60 |If you shoot hard enough, the balls will split and end up spread out across the billiards table.
61 | 62 |This makes for new situations every game.
63 | 64 |Now, shoot a ball and try to predict where it will end up.
65 | 66 | 70 | 71 |Was your prediction correct?
72 | 73 | 76 | 77 |Being able to predict where particles end up is what makes billiards a fun and challenging game.
78 | 79 | 80 |One thousand particles!
61 | 62 |It might seem like a lot.
63 | 64 |It isn’t.
65 | 66 |You would need approximately
67 | 68 |10,000,000,000,000,000,000 (or 1019) boxes
69 | 70 |each with 1000 particles, just to get the amount of air particles in a single human breath.
71 | 72 | 73 |To the right is a ball.
57 | 58 |Pick up the ball and throw it!
59 | 60 | 67 | 68 |Well done!
69 | 70 |I will usually ask you to perform some simple task (like throwing the ball), just to get you started interacting with the simulations.
71 | 72 |You are of course free to keep playing with them for as long as you’d like!
73 | 74 |When you are ready to move on, click at the bottom of the page ↓ or in the right margin →.
75 | 76 | 77 |16 balls might be enough for billiards, but in the real world there are incredibly many more than 16 tiny particles.
56 | 57 | 72 | 73 |The more particles, the harder it becomes to track a single particle.
74 | 75 | 78 | 79 | 80 | 81 |The force that that causes the ball to slow down is called friction.
54 | 55 |Some things have more friction than others:
56 | 57 |Here is a slider that changes the friction of the billiards table to be more mud-like (more friction) or ice-like (less friction).
63 | 64 | 67 | 68 |Change the friction with the slider and drag around the ball to get a feel for how friction works.
69 | 70 | 71 |What do you think will happen when there is no friction?
56 | 57 |Move the particles together.
58 | 59 | 69 | 70 |They don’t want to stay together!
71 | 72 |Without friction, the speed they get from the attraction is too high to stay.
73 | 74 | 75 | 76 |Let’s try something else.
56 | 57 |What happens if the particles collide at high speed?
58 | 59 | 69 | 70 |They just bounce off each other!
71 | 72 |The force between the particles wants to keep them together, but the speed is too high for the attraction to take hold.
73 | 74 | 75 |So, we have now tried playing billiards on ice and in mud. Kinda weird.
54 | 55 |But the tiny billiard balls that make up everything are even weirder than that.
56 | 57 |They have no friction.
58 | 59 |What does that mean?
60 | 61 |Give the ball a kick.
62 | 63 | 69 | 70 |Wait for it to stop.
71 | 72 | 76 | 77 |It never stops!
78 | 79 |Without friction slowing things down, they never stop.
80 | 81 |They keep going forever.
82 | 83 | 84 |Uh-oh!
60 | 61 |There’s a third particle here!
62 | 63 |Will there be a fight?
64 | 65 | 75 | 76 |No, they all like each other equally!
77 | 78 |Move them around a bit and you’ll notice that they don’t just move towards the pointer. 79 | They also rotate around each other!
80 | 81 | 82 |I’ve put two billiards tables side-by-side.
66 | 67 |Make a hard shot in one.
68 | 69 |And a soft shot in the other.
70 | 71 |The soft shot takes a lot longer to spread all the particles out, as we saw before.
72 | 73 |But notice too that the strength of your shot is still visible. The particles in one table are a lot more energetic than the particles in the other.
74 | 75 | 76 |Move these particles closer to each other.
58 | 59 | 67 | 68 |They seem to like each other! As they come closer, they attract and snap together.
69 | 70 |Can you get them to let go?
71 | 72 | 79 | 80 |It takes some effort!
81 | 82 |There’s a force binding the particles together.
83 | 84 | 85 | 86 |To help us understand some of the more tricky concepts, we will use visualisations, mostly graphs.
57 | 58 |Here’s an example of a graph:
59 | 60 | 71 | 72 |Try figuring out what this graph is showing by throwing around the ball a bit.
73 | 74 |Does it show
75 | 76 |Figure it out yourself, I won’t give you the right answer!
83 | 84 | 85 |
74 | Temperature:
82 |
85 | 92 |
93 | 94 | 95 | 96 | 97 | -------------------------------------------------------------------------------- /kinetic_energy/2_multiple_particles.html: -------------------------------------------------------------------------------- 1 | 2 | 3 | 4 | 5 |I added some more balls in a conspicuous pattern. You know what to do!
59 | 60 | 67 | 68 |As the balls collide, they bounce off each other, transferring energy from one to the other.
69 | 70 |Below is a graph of the total energy, which is the energy for all particles combined.
71 | 72 | 82 | 83 |Note how, even when the particles are bumping into each other, the curve looks the same as it did with just one particle.
84 | 85 | 86 |In the bottom right corner of the simulation you can change tools.
57 | 58 |Having only one ball is a little dull, so let’s add more!
59 | 60 |Use the create tool to create more balls.
61 | 62 | 69 | 70 |(If you hold down the mouse button, you “paint” particles when moving the mouse.)
71 | 72 |Use the attract tool to lift all the balls off the ground.
73 | 74 | 87 | 88 |The tools will change from page to page, to suit the purpose of that page.
89 | 90 | 91 |In this chapter we started with the game of billiards, and modified it to be very many, attractive, frictionless particles.
56 | 57 |What we have done is create a model of how the tiny particles in the real world work. 58 | The model is not exactly like the real world – it’s simpler. 59 | But by being simpler, it makes it easier for us to explore and understand things about the real world.
60 | 61 | 70 | 71 | 72 |Without friction, billiards gets a lot messier.
62 | 63 |Turn off the friction.
64 | 65 | 78 | 79 |Take the shot.
80 | 81 | 85 | 86 |Try to put the balls back in a triangle now. It’s practically impossible! They keep bouncing around, and just making them slow down is a lot of work.
87 | 88 |With each shot you make, the particles spread out more and more.
52 | 53 |Get the particles to spread out evenly across the entire box.
54 | 55 | 85 | 86 |After a few shots, the particles are all spread out.
87 | 88 | 89 |Here is a billiard ball. Try throwing it!
55 | 56 | 63 | 64 |As you pick up and throw the ball, you give it speed, and in turn, energy. This kind of energy is called 65 | kinetic energy, or movement energy. This plot shows how the energy changes over time:
66 | 67 | 77 | 78 |Throw the ball around some more and see what happens in the plot.
79 | 80 | 95 | 96 |When you release the ball it starts to lose energy because of the friction in the table and air, which looks like a slope in the plot.
97 | 98 | 99 |Move these two closer.
55 | 56 | 64 | 65 |They still like each other!
66 | 67 |What if there were more than two particles?
68 | 69 |Add more particles using the create tool.
70 | 71 | 81 | 82 |A group hug! How cute!
83 | 84 |The attraction between each pair of particles holds them together, and together they now make up a bigger object.
85 | 86 |Try moving the object around with the move tool.
87 | 88 | 94 | 95 |The tiny, microscopic particles move together as one.
96 | 97 |One big, macroscopic thing.
98 | 99 | 100 |With no friction, it should be even easier to break the triangle than on ice.
52 | 53 |Shoot the ball very carefully.
54 | 55 | 81 | 82 |The triangle will break, and the particles will spread out evenly.
83 | 84 |You just need to have patience.
85 | 86 |(Psst! If you get bored, use this slider to speed up time.)
87 | 88 | 103 | 104 | 105 | 106 |Let’s try a simpler scenario.
74 | 75 |Try putting all the particles in the left half of the box.
76 | 77 | 94 | 95 |It’s pretty hard, isn’t it? And they keep wanting to escape!
96 | 97 |This isn’t that many particles, but it’s already quite hard to predict where any single particle will end up when you shoot.
68 | 69 |Use your pool cue a few times.
70 | 71 | 94 | 95 |Do you see the waves?
96 | 97 |When you shoot, you start a chain reaction of particles bumping into each other. A wave of motion spreading.
98 | 99 |This is a phenomenon that only appears when there are enough particles.
100 | 101 | 102 |Let’s now put it all together!
56 | 57 |We start with a single particle that you can move around.
58 | 59 | 66 | 67 |We add many more particles (with the create tool).
68 | 69 | 79 | 80 |They attract each other and form a bigger object.
81 | 82 |Now turn off the friction.
83 | 84 | 101 | 102 |Gently bump the object into a wall.
103 | 104 | 115 | 116 |As the object bumps into the wall, the particles start vibrating.
117 | 118 |What happens if you keep bumping it into walls?
119 | 120 | 121 |When playing billiards, it’s easy to make a mess.
65 | 66 |Take the shot.
67 | 68 | 72 | 73 |The particles bounce all over the place, and end up in a random pattern. This makes for new situations in each game of billiards. If the balls always started spread out in a predictable pattern, it would be quite a different game.
74 | 75 |Now try putting the balls back the way they were.
76 | 77 | 108 | 109 |It’s a bit tricky, but doable.
110 | 111 |Things get more interesting when the particles attract each other. The potential still has a steep hill that prevents the particles from overlapping too much, but there is now also a valley.
64 | 65 |Drag the red particle toward the blue.
66 | 67 | 75 | 76 |If you give the particle a lot of speed it will roll into the valley, up the other side, turn around and go back out. With less speed, the particle will roll back and forth in the valley before settling at the bottom.
77 | 78 |The back-and-forth rolling is why the particles vibrate a bit when they snap together. Without friction, they will keep vibrating forever.
79 | 80 | 88 | 89 |Remember the many tiny things I was talking about earlier?
34 | 35 |We call them particles and they are sort of like tiny billiard balls. 36 | They move like billiard balls, and bounce like billiard balls.
37 | 38 |There are three big differences, though. The tiny particles …
39 | 40 |… never stop moving.
45 | 46 | 71 | 72 |… can attract each other.
77 | 78 | 100 | 101 |… are very many.
106 | 107 | 127 | 128 |Click on each difference to explore it.
133 | 134 |When you are done, go to the next page by clicking down there ↓ or over there →.
135 | 136 |To better understand the attraction, let’s first look at two non-attracting particles.
42 | 43 |I have put the particles on a narrow track, so they can only move back and forth (and not around each other). Imagine the camera rotating with the particles so that they are always on a horizontal line.
44 | 45 |Try moving the blue particle on the left.
68 | 69 | 76 | 77 |I’ve glued the blue particle to the wall so that only the red one can move. Imagine the camera following the blue particle, always keeping it on the same place on the screen.
78 | 79 |Below the particles I have added the potential for the interaction between the two particles. Think of it as an “interaction landscape”, where the red particle can be thought of as a ball rolling in the landscape.
80 | 81 |Drag the right particle towards the left one and see what happens to the ball in the potential.
82 | 83 | 91 | 92 |The ball in the potential landscape rolls up the hill, and then rolls back down again – it bounces off the other one!
93 | 94 |We have looked at each difference separately.
34 | 35 |Let’s now put them together and see what happens!
36 | 37 |The particles attract each other and never stop.
42 | 43 | 64 | 65 |The particles never stop and are very many.
70 | 71 | 97 | 98 |The particles are very many and attract each other.
103 | 104 | 134 | 135 |Bumping stuff into walls is not a very precise method of investigation.
75 | 76 |Instead, here is a slider that controls how much the particles move.
77 | 78 | 92 | 93 |Slowly increase the amount of movement.
94 | 95 | 102 | 103 |The particles jiggle in place.
104 | 105 |Keep increasing.
106 | 107 | 114 | 115 |The particles start “walking” around the other particles. Sometimes, a single particle breaks free from the object.
116 | 117 |Keep increasing.
118 | 119 | 126 | 127 |The particles start to lose their connections and break off into separate groups.
128 | 129 |Keep increasing.
130 | 131 | 138 | 139 |The particles are bouncing around, alone or in small groups, almost as if there was no attraction at all.
140 | 141 | 142 | 143 |#### A study in static
36 | 37 |Thermodynamics is the study of heat. What is heat? That’s like temperature, right? Hot and cold and so on. And thermodynamics has something to do with entropy, whatever that is (disorder something something). You might also have heard something about energy loss becoming heat somehow. All this is actually pretty easy if you look at it right. Let’s take a closer look, literally.
38 | 39 |Top of each page: “This page assumes you are familiar with the following concepts (click on them to read more)”
97 |We see that Energy is conserved, which should be true for elastic collisions. [Is momentum conserved? Why/why not?]
100 |[If something is in brackets, it is meant as an exercise]
104 | 105 |
106 |
107 |
108 |
109 |
110 |
111 | Math changes when radio button changes
If you leave a glass of water somewhere and come back a few days later, some or all of the water will be gone. Here is a timelapse of the water slowly disappearing.
38 | 39 | 40 | 41 |The water is turning from liquid to gas form, which is called evaporating.
42 | 43 |Here is a model of a glass. Fill it with particles!
89 | 90 | 104 | 105 |I’ve put the thermostat on really cold, so the “water” is now frozen solid. Heat it up!
106 | 107 | 123 | 124 |As the contents of the glass melts, the particles start tumbling around. Sometimes, this random tumbling will give one of the surface particles a lot of kinetic energy. If the energy, and therefore the speed, is great enough, the particle will escape the glass! (You might have to wait a little while for this to happen.)
125 | 126 |This also means that the rest of the particles will lose energy and get a little colder. But the temperature difference with the rest of the room will soon even out again.
127 | 128 |We now have some more understanding of how two particles interact. Now let’s see what happens when there are more than two!
73 | 74 |Let’s add some more particles! (select the create tool and use the mouse)
79 | 80 | 86 | 87 |They group together and form a larger shape, a solid, if you will.
88 | 89 |Try moving the solid around.
90 | 91 | 97 | 98 |The particles collectively behave like the macroscopic objects we are used to, moving and rotating as a unit.
99 | 100 |So far, we’ve have had friction, but there is no friction in the microscopic world.
101 | 102 |Turn off the friction.
103 | 104 | 115 | 116 |Give the particles some energy.
117 | 118 | 124 | 125 |Let’s try amplifying the speed of each particle, in turn increasing the jiggling.
126 | 127 |The random jiggling kicks the particles out of their positions, and what was a neat shape becomes something less ordered and more random. We have melted the solid into a liquid.
128 | 129 |If we increase the temperature (and thus the jiggling) even further, the speed is to great to keep the particles together, and they start bouncing around randomly. The heat of the system is too high for the attraction to matter much, and we’ve vaporized our liquid into gas.
130 |I’ve installed force measurement devices in the walls here. They detect whenever a particle bounces off the wall, and how hard.
54 | 55 | 65 | 66 |Carefully throw the ball at a wall.
67 | 68 | 74 | 75 |Throw the ball with a lot of force.
76 | 77 | 84 | 85 |Since the particles only collides with the wall for an instant, the collisions show up as narrow spikes in the graph. Short impacts like these are called impulses.
86 | 87 |Drag the ball toward the edge of the box, and keep dragging even as the mouse is outside the box.
88 | 89 | 107 | 108 |This simulates you pushing the ball toward the wall, which puts pressure on the wall. And not just a short spike, but continuous pressure that doesn’t let up until you let go.
109 | 110 |I’ve installed force measurement devices in the walls here. They detect whenever a particle bounces off the wall, and how hard. Try throwing the particle at the wall at different speeds.
155 | 156 | 164 | 165 |Friction is what makes things stop. For example, if you drop a ball, you expect it to bounce a bit and then stop.
57 | 58 |Drag and drop the ball from a reasonable height.
59 | 60 | 72 | 73 |There are two things at play here: air drag and inelastic collisions. Let me show you!
74 |Friction is what makes things stop. For example, if you drop a ball, you expect it to bounce a bit and then stop.
130 | 131 |Drag and drop the ball from a reasonable height.
132 | 133 | 145 | 146 |There are two things at play here: air drag and inelastic collisions. Let me show you!
147 |To understand what happens to the energy as the particles collide, I have colored each particle in a unique color.
63 | 64 |Play with the particles and look at how their energy changes over time in the graph below.
65 | 66 | 115 | 116 |We can now see how the total energy is made up of the individual energy of each particle. And while the total energy always has the same shape, the energy of the individual particles vary wildly.
117 | 118 |Balls knocking each other around is actually a pretty good model of how the world works at the atomic level. 119 | One big difference: there is no friction.
120 | 121 |Lower the friction using the slider below.
122 | 123 | 134 | 135 |Then give the particles a little bit of energy.
136 | 137 | 145 | 146 |Without friction, the particles never stop bouncing! The total energy stays the same, even though each individual particle changes its speed often. Because the energy keeps steady, the particles will on the whole neither speed up nor slow down.
147 | 148 | 149 | 150 |This is a model of a ball, made of up small atoms. We cannot simulate millions of atoms, so we make do with about a hundred.
100 | 101 |Drag and drop the ball from the top of the box.
102 | 103 | 112 | 113 |Observe how it bounces. This helpful graph shows how the ball’s height changes over time:
114 | 115 | 141 | 142 |It keeps losing height, so at first glance it seems to be losing energy. But look at the energy graph:
143 | 144 | 153 | 154 |The energy doesn’t change at all! So where is the energy going?
155 | 156 |Part of the energy goes into the rotation of the ball.
157 | 158 |Figure with stacked gravitational potential + rotational energy. Or perhaps skip rotational.
159 | 160 |The rest of the energy becomes heat! As the ball bounces into a wall, some of the energy will cause the atoms to randomly bump into each other and start jiggling.
161 | 162 |So when you bounce a ball on the ground and it loses height, that lost height is actually heating up the ball (and also the ground, but we didn’t include that in the model).
163 | 164 |Many familiar physical phenomena can be explained by looking through the many-tiny-things lens. Here are the ones we’ll be focusing on here, with some related questions to give you a feel for what each concept is about.
33 | 34 |Heat is the many tiny things jiggling randomly
75 | 76 | 129 | 130 |Pressure is many tiny things bouncing on a surface
134 | 135 | 166 | 167 |Every big thing in the world is made up of many tiny things.
31 | 32 |Air is many tiny things bouncing around everywhere
36 | 37 | 68 | 69 |Water is many tiny things sloshing around
73 | 74 | 113 | 114 |Normal-sized things are many tiny things stuck together
119 | 120 | 167 | 168 |But we can’t see the tiny things without a microscope. They are too small, microscopic. 173 | We can only see the macroscopic objects the tiny things make up 174 | (and in the case of air, we can’t see it at all!).
175 | 176 |This website is a series of explanations on how the tiny, microscopic things are connected to the big, macroscopic things that we can see, hear and feel. We will ask the question:
177 | 178 |What are the macroscopic consequences of being made up of many microscopic things?
179 | 180 |The explanations will include simulations of many tiny things, as you can see above. Not only are these simulations running in real time, they are also interactive. Try clicking, holding and dragging in the simulations above and see what happens!
181 | 182 |When you are ready, click here for an introduction!
187 | 188 | 209 | 210 |Then continue here, with billiards!
215 | 216 | 234 | 235 |To a person like you and me, heat is very important. We heat our food, get hot in the sun, feel the body heat when hugging someone, avoid touching things that are too hot and with too little heat we start freezing.
38 | 39 |But what is heat?
40 | 41 |Turn off the friction.
67 | 68 | 79 | 80 |Give the particles a shove.
81 | 82 | 90 | 91 |This is heat.
92 | 93 |Particles moving around randomly, endlessly.
94 | 95 |Links to heat energy
122 |