## The Power of Machines – Daedalus Style## OverviewOn a Saturday morning in April of 1988, Kanellos Kanellopoulos took off from the island of Crete in the Mediterranean Sea and flew his airplane 74 miles to the volcanic island of Santorini, skimming only 15 feet above the water. He tried to land his airplane on a beach, but crashed into the waves just before reaching ground. Luckily, he was able to swim to shore safely. Was his flight a failure? Not at all! Kanellos had just made history. So what was so special about this flight? Well, for starters, the airplane Kanellos was flying had no engine! He was providing the power himself - by pedalling just like you would on a bike. Kanellos was very good at pedalling, so good that he won 14 Greek national cycling championships. It's a good thing, too, because he wouldn't have made it without being a fantastic athlete. You see, even with Kanellos pedalling almost as hard as he could, he wasn't nearly as powerful as a normal airplane engine. In fact, it would take about 500 athletes as strong as him in order to equal one average airplane engine! Fortunately, his airplane was made to fly using only the power from one person's legs. This airplane was called the Daedalus, named after an ancient Greek hero who, legend has it, flew across the very same stretch of sea using wings built out of feathers and wax. We know that this didn't actually happen because there's no way a person could fly like a bird. Our arms just aren't strong enough. But the airplane Kanellos was flying used some special tricks that made it possible for it to fly with only the power of one human being. First of all, it was very light. That made it easier for Kanellos to get off the ground. Even though its wings were over 100 feet long, the airplane weighed less than 70 pounds - that's less than all the pillows on a 747! Another trick the airplane used is that it went very, very slow. It took Kanellos four hours to go 74 miles. That means he was going less than 20 miles per hour. Some people can run that fast! But Kanellos was willing to make a trade-off: he was willing to go slow if it meant he could fly. Just like with the Daedalus, we're going to use the Chaos toy to show how you can do a job that you think might be impossible, simply by going slow. We aren't going to build an airplane with the Chaos toy, but we will build something that lifts weight off the ground. The "engine" we're going to use is the Chaos motor unit, and it's going to lift weight off the ground using its chain. ## SetupHere are the materials we'll need: 19 long tubes 4 short tubes 12 five-way joints 1 accessory connector motor unit chain 1 ball carrier pulley 3 adjustable supports 4 short clips 4 tight, 90-degree turns balls a clock or stopwatch Assemble the tower as shown. Note that one long tube is missing on the middle level. This is because we don't want that tube getting in the way of the rising weight. Snap the motor unit onto the short tube as shown, and snap the accessory connector onto the other short tube as shown. Now we will make the weight that the motor unit is going to lift. Start by attaching the two grey clips to the sides of the pulley. Snap a short tube into each clip. Now put an adjustable support on each tube and slide two short clips onto each adjustable support. Make the circular track out of the four tight, 90-degree turns and snap the track onto the short clips. You now have a weight that can hang from the chain. You can make it heavier or lighter by adding or removing balls from the circular track. ## Stage IFirst, we'll see how much weight the motor can lift with the weight simply hanging from it. Snap a ball carrier onto one end of the chain. Now wrap this end around the pulley and hook the ball carrier onto the chain as shown. Feed the other end of the chain into the motor unit. Now turn on the motor and watch it lift the weight! It might be helpful to pull down a little on the free end of the chain so that it doesn't get wrapped around the motor pulley. Be sure to turn off the motor before the weight carrier gets to the very top! After the motor lifts the weight, feed the chain backwards through the hole in the motor unit so you can start over. OK, now that we know that our device works, why don't we give it a name? Daedalus sounds good... So let's see how powerful Daedalus really is! First, we'll see how fast it can go. Then we'll see how much weight it can lift. In order to see how fast it can go, we need to set a distance and then see how much time it takes for Daedalus to lift the weight that distance (speed = distance / time). We'll mark the distance with one of the adjustable supports. Snap the adjustable support onto the tube below the motor. Start with the weight carrier on the ground and time how long it takes for the motor to pull it up to the adjustable support. Record this time. Now let's see how much weight Daedalus can lift. Try putting just one marble in it. Can it still lift the weight? How about with two marbles? Keep adding marbles until the motor unit can no longer lift it, and record this maximum number of marbles. Note: when the motor unit can no longer lift the weight, it will begin to make an ugly clicking noise. Once it starts to do this, turn it off. It's not good for the motor to be making this noise for too long. So now we know the maximum amount of marbles Daedalus can lift. Right? Wrong! We still have some tricks up our sleeve. Remember how Kanellos was able to fly if he was willing to go slow? Well, we can lift more weight with Daedalus if we're willing to do it a little slower. How can we make Daedalus lift the weight slower? First, remove the ball carrier from the chain. Now hook the chain onto the accessory connector at the top of the tower. The chain should now be hanging between this accessory connector and the Chaos motor. Now place the pulley on the lowest part of the chain. You have just built a pulley system, or a block and tackle. Remove all the balls from the weight carrier and turn the motor on. How long does it take to lift the weight carrier from the ground to the adjustable support? How does this compare to how long it took before? Now start adding marbles. What is the maximum number of marbles it can lift? Is it more or less than it could lift before? Can you explain why Daedalus took longer to lift the weight after we changed the pulley setup? And why was it able to lift more weight? There are a couple different ways to explain what happened here. These two ways are explained below. We'll call the first way "The Tension Argument", and the second way "The Power Argument." ## Stage IIThe Tension Argument The amount of force pulling on the chain is called tension. If you grab a rope hanging from the ceiling, then the amount of tension in the rope will be equal to your weight. What if you grab two ropes hanging from the ceiling? Well, in that case, the two ropes will work together to support your weight. So the tension in each rope will be equal to half of your weight. The same principle was at work with Daedalus. In the first setup, the tension in the chain was equal to the weight it was lifting. In the second setup, there were two strips of chain supporting the weight, so the tension in each strip of chain was equal to half the weight. What did this mean for the motor unit? Well, the motor unit could only lift a chain with a certain amount of tension in it. In other words, the harder you pull on the chain, the harder it is for the motor unit to reel it in. In the second setup, the tension in the chain was only half of what it was in the first setup. So the motor unit only had to support half of the weight. By the way, what was supporting the other half? (Answer: the accessory connector). ## Stage IIIThe Power Argument In physics, the word power means force times velocity. Power is measured in watts (or horsepower if you're talking about cars). P=F*V In this activity, the power was provided by Daedalus' motor unit. The force was gravity pulling down on the weight. And the velocity was the speed at which Daedalus lifted the weight. Daedalus is able to provide only a certain amount of power. When you added too much balls, the motor unit started clicking and not going anywhere because you were asking it to provide more power than it could. So why were we able to get it to lift more weight by changing the pulley setup? Let's look at the equation again: P=F*V We know that we can't change P. It is a constant which is determined by the motor unit. So the only things we can change are F and V. If we want to lift more weight, then F is going to increase (remember that F is the force of gravity on the weight, which goes up as more weight is added). If F increases and we can't increase P, then the only way to balance out the equation is to decrease V. To be exact, if we multiply F by two, we have to divide V by two. If we multiply F by three, we have to divide V by three. And so on. By changing the pulley setup, we were able to divide V by two. Can you see why this is? Let's say that the motor unit pulls in 100 links of the chain every minute. With the first setup, since the weight was attached directly to the chain, this meant that the velocity of the weight was 100 links per minute, going straight up. Now let's look at the second setup. Perhaps it would be best to turn on Daedalus again to get a closer look at what's happening. We have said that the motor is pulling in 100 links a minute. Where do these 100 links come from? Well, if you look to the left of the motor unit, you see two strips of chain: one running from the pulley to the accessory connector, and one running from the pulley to the motor unit. The chain on the left is always as long as the chain on the right, even as Daedalus is lifting the weight. The links of chain that the motor unit pulls in are coming from these two strips of chain. If the motor unit pulls in 100 links a minute, then you can see that 50 of these links come from the strip of chain to the left of the pulley and 50 come from the strip of chain to the right. So the chains supporting the pulley each get shorter by 50 links a minute. How fast is the weight moving then? 50 links a minute straight up, which is half as fast as it was in the first setup. So by changing the pulley setup, we were able to divide the velocity by two. This allowed us to multiply the force by two. That's why Daedalus could lift more weight the second time around. In fact, it should have lifted exactly double the amount of weight. You can verify this with a scale (remember that you have to weigh all parts of the weight, including the pulley, tubes, adjustable connectors, track, and balls). What if we were to make Daedalus lift the weight so slowly that it took an hour? Or a day? Or a year? Is there any limit to how much weight it could lift? The answer is no! It could lift a car or a house or an aircraft carrier. It's just a matter of time. Can you figure out how to make Daedalus lift its weight even slower? Hint: you would need at least two more pulleys. ## Exercises## Stage I1.Why are the gears on a bicycle toothed wheels of different sizes? How does this relate to pulleys? This is very similar to a pulley. By changing the gears on your bike you are able to change the difficulty of pedaling. Basically, the gear selects how far you are going to travel each time you push the pedals in a complete circle. Different gears make you go farther or shorter distances, letting you do the work all at once or a little at a time. ## Stage II1. We doubled the amount of weight Daedalus could lift by using a pulley to suspend the weight by two strips of chain instead of just one. Draw a pulley setup that would allow Daedalus to quadruple its lifting power (hint: you can use more pulleys if you want). Answer: ## Stage III1. A rocket ship is shooting straight up at 40 meters per second. Its mass is 1,000,000 kilograms. How much power are the engines producing? Assume that the rocketship is near the surface of the earth and ignore air friction. Answer: Use the formula P=F*V. The velocity (V) is 200 m/s. The force (F) is found by using F=MA, where M= 1,000,000 kg and A=g=9.8 m/s² (near the surface of the earth). P=(1,000,000)*(9.8)*(40). P=392,000,000 watts. That's equal to about 500,000 microwave ovens all on full power! 2. Let's say that our contraption Daedalus can produce 2 watts of power. We're going to try to lift a 200-gram weight using the first setup (with the weight simply hanging from the motor unit). The motor unit reels in 100 links per minute. Each link is 2.5 centimeters long. Is it going to be able to lift the weight? What is the maximum it can lift with the first setup? What is the maximum weight it can lift with the second setup? Method: Figure out how much power is required to lift 200 grams at 100 links per minute. P=F*V. F=M*A M=200 grams=0.2 kg A=g=9.8 m/s² F=(0.2)*(9.8)=1.96 N V=100 links/minute 1 link = 2.5 cm =.025 m. V=(100)*(.025) m/minute=(100)*(.025)/60 m/s= 0.0417 m/s P=(1.96)*(0.0417)=0.08 watts. 0.08<2.0, so it can indeed lift 200 grams! To find the maximum it can lift, make P=2 and use the same velocity. P=F*V 2=F*(.0417) F=(2)/(0.0417)=47.9 N F=MA 47.9=M*(9.8) M=(47.9)/(9.8)=4.9 kg=490 grams The maximum weight it can lift using the first setup is 490 grams. To find the maximum weight it can lift with the second setup, make P=2 again and V equal to half as much as it was before. P=F*V P=2 V=.0417/2=.021 2=F*(0.021) F=(2)/(.021)=95.8 N F=M*A 95.8=M*(9.8) M=(95.8)/(9.8)=.98 kg=980 grams The maximum weight it can lift using the second setup is 980 grams, twice the amount it could using the first setup. |