Expanding Your Energy and Momentum Demo Toolbox
Aside from the Newton’s Cradle and the Faith in Physics pendulum, there are not very many well-known energy and momentum demonstrations. In this video and article, I aim to resolve this. I have especially focused on energy because those demonstrations are usually very hard to find.
Energy as Water Analogy
Young children are often confused as to whether the amount of water is changed when it is poured from a short glass to a tall glass. But adults know better because we understand measurement. In this demo, I like to show how energy is often converted between kinetic and potential, but the total MECHANICAL energy (the sum of these) is a constant.
Of course, spilling would change the amount of water that is kinetic or potential, but the total volume is still constant, although some is no longer MECHANICAL, it is now HEAT or some other unusable form such as sound and light.
When I did this demonstration, I started with very little blue food dye and poured it into a second container that had a drop of red food dye in the bottom. This accounts for the first color change. I then used “movie magic” to reverse the color back – in this case digital compositing of two very similar scenes. If I was performing this demonstration live I would use an acid-base indicator, such as methyl red, for the second case and have a few drips of acid in the second container. Then sneak a few drops of ammonia into the first container when I switched back.
Figure 1: Pouring water back and forth illustrates conservation of energy. Spilling some or letting some evaporate can illustrate this still further. The water color change is optional.
The point is, the total volume of water is a constant, even if it evaporates and we can never get it back. Energy cannot be created or destroyed. Richard Feynman used a child’s wood blocks that keep getting lost in a messy room for his analogy. I think that water is a better choice however because we have the same intuitive challenges with mistakenly feeling that the water is “gone” when it evaporates.
Racing Marbles Lab
One of the best energy demos is the racing marbles lab. Two marbles are released at the same time and travel these different paths, but which one will reach the end first?
The results of this experiment are usually quite a surprise. In the video I pause to have those watching explain to their neighbor their predictions.
After the results, which lets the low marble win, we now must allow the students a second chance to explain what has happened. This technique is consistent with learning theory that explains that learning is a social process. Often, students are much more interested with what their neighbors think than with what their teacher actually thinks.
The marble that was allowed to dip lower converted its potential energy into kinetic energy, which resulted in a higher velocity. The higher-ramp marble moved at pretty much a constant speed. By the end of the race, they both finish at the same speed, just not the same time.
Figure 2: The Racing Marbles Lab is one of the best energy demos. Be sure to stop and let the students thing about what might happen before you perform the solution.
This experiment can be made quantitative by the use of photogates, you can verify that the final speeds are pretty much the same, which makes sense because the change in potential energy is the same for both. However, if you wish to calculate the speed with which these marbles are rolling you must also consider rotational kinetic energy, rather than simply using potential energy lost becomes kinetic energy gained.
Galileo performed many experiments to investigate motion. At least he said he did. It is much more likely that he was only claiming many of these, such as his Leaning Tower of Pisa demonstration. But this one seems easy enough to do, so he may have actually performed it.
A pendulum is swung and always seems to remember how high you released it from. Not only does it come back to the point it was released from, it will return even if interrupted. In my example, it is interrupted by a peg in the middle of its path. This shows that whatever it loses on its journey toward the bottom is not actually lost, but only converted from the possibility of falling into actual falling. The pendulum not only returns to the original height, but swings out to the same height, even when there is a peg.
When you perform this experiment, you should ask your students the following questions:
“We see that if a pendulum is swung from a specific height, it somehow always remembers the height it was released from. Very strange, how does it remember?”
Figure 3: Galileo's Pendulum is a good way to start off an energy unit. It's amazing that the peg doesn't interfere with the ball as it rises to the same height as it was released
“What if we put a barrier in the way? Somehow it still remembers. Where is this memory stored?” [in the motion]
“What is it that the mass has that helps it remember, what carries it to this height?”
Newton’s Cradle as an Energy Demo?
Many people use the Newton’s Cradle to teach momentum, but it is also possible to use it to teach energy concepts – perhaps this is its best application! Of course, Newton himself used it to explain and demonstrate his third law. For example, when ball A swings to hit ball B, then ball a will stop and ball b will go. They hit each other with equal and opposite forces or with equal and opposite impulses.
Yes, momentum is conserved in the collision, and in fact it is conserved in all collisions. The motion mv, of the first ball is transferred to the second, but are we giving Newton too much credit?
Couldn’t two balls come out of the collision and not just one?
This would NOT violate the conservation of momentum! If the two come out at half of the speed! Then the momentum mv would be equal to 2m x ½ v which is an acceptable result. WHY DOESN’T THIS HAPPEN?!
The answer is energy. Specifically, energy would have to be lost for that to happen, and what makes this toy so fun to watch is that very little energy is lost in each collision.
Figure 4: Perhaps the Newton's cradle demonstration has more to say about energy than it does about momentum.
There is of course the exciting possibility that we could force the coupling of two balls of the Newton’s Cradle. I usually do this experiment with a hair tie, and I like to film it in slow motion. When the collision does occur, the two balls scream in protest. We not only witness that momentum is conserved in all collisions, but that energy is not! The mechanism of energy loss is twisting, vibration, and sound.
This is an important demonstration because most people are unaware that energy is almost completely conserved in the newton’s cradle’s collisions. They usually only discuss momentum, but this is just as much a demonstration of energy.
Regarding energy, when in normal operation – without hair ties – the newton’s cradle also demonstrates that it wears down to a lower energy state of five moving at once, the most boring of all situations.
Happy and Sad Ball Collisions
Momentum is transferred by collisions, but an interesting questions is, "Will more energy be lost in sticking or bouncing?" For example when a ball that doesn’t bounce hits a block, is it more or less likely to knock it over than a ball that sticks to the block?
Make your prediction. This is a demonstration that can help us understand the idea that momentum is a vector, and that change in momentum is larger when the momentum is reverse. As many teachers will have correctly guessed, the bouncing transfers more momentum because it bounces backwards with negative momentum, the total change is larger than just coming to a stop. The sticking is only losing the momentum it brought into the situation.
Rigging up your happy sad balls demonstration is a bit tricky. Be sure to practice before hand. The block must tip over decisively. Many people will be surprised by the results, even if they guess correctly!
Figure 5: Energy is conserved in both cases, but why doesn't the sad ball knock over the block?
Colliding Steel Spheres
The collision of heavy metal spheres transforms a lot of kinetic energy into heat. That energy has to go somewhere. It is cool that we can use this collision to singe paper and cause ripples in aluminum foil. We expect that momentum might be discussed when we think of wrecking balls, but more relevant is the discussion of energy imparted when motion is brought to a halt. Just think of slamming on the brakes–those tires will be hot! In the case of the spheres, most of if will be in this one tiny spot.
Colliding Steel Spheres can illustrate the idea of energy being "lost" in a collision. Of course it is not lost, but only converted, and yet the conversion is into forms that are no longer available to us for anything useful.
Figure 6: Colliding steel spheres are a great demonstration of how energy converts from one form to another.
Relative Potential Energy and Relative Kinetic Energy
Most people will immediately get the idea that potential energy is RELATIVE to some arbitrary zero-point energy. For example, a mass might fall off a stack of books to the table top, but it could also fall all the way off the floor, or even further out the window onto the ground, then it might fall down a down a well which allows it to fall down a cavern all the way to the center of the earth, and maybe the earth will fall into the sun or the sun could fall all the way to the center of the milky way galaxy!
Most people do not know that it is possible to show that Kinetic energy is also relative. Here is a way, if we take a swinging pendulum and I let it swing back and forth, it has its highest kinetic energy at the lowest moment.
Figure 7: Relative to the table, the mass has no potential energy after it falls off the stack of books. But it does have potential energy relative to the floor.
But if I walk with it then I see from my perspective that it looks as though it has zero kinetic energy. My relative motion affects my calculation of the kinetic energy of this object. Kinetic energy depends on the relative motion of two objects. Usually it is an object relative to the laboratory. That is, we assume that the laboratory is not moving but everything else inside could be. This is not a very truthful assumption because we are on a rotating planet orbiting a star that is itself moving sinusoidally in an orbital plane of the galaxy.
But this demo can serve as a discussion for the idea of center of mass motions and collisions. For example, if it is just one proton hitting another in an atom smasher, such as the Large hadron Collider at CERN. It would be completely arbitrary which proton is the one that is stationary. However, there is kinetic energy relative to the center of mass, which will also be the point of collision, or nearly so, as the proton has a finite radius.
The Proof of Potential and Kinetic Energy
One of the purposes of this video is to illustrate that energy is not momentum. Far too often I feel that we do momentum demonstrations that are very similar to our energy demonstrations and vice versa. Therefore, for the final demo, I like to show a simple lab that shows that kinetic energy is connected to height. Specifically, height lost will result in new kinetic energy being gained. ½ mv2.
This experiment can be done with a marble, a car, or a rolling can, and the height of fall is not proportional to velocity, but velocity squared. This is true even if we take into account rotational kinetic energy. This lab shows it immediately.
I have chosen an opaque marble which can immediately reveal the translational velocity as it passes through a photogate. As I move up the ramp, the vertical height gives me a faster translational velocity at the end. Twice the height does not however give twice the velocity. Rather only radical-two times as much.
Figure 8: If I want to double the speed, I have to start from four times the height… which is 2 squared. The height to which an object will rise or fall corresponds with the square of the velocity.