Buoyancy: activity (written in 2003 by Don Yost) Why do some things float and others sink? Here are a group of materials and their densities. Arrange them in groups of floating and non-floating based on your own experience or educated guess. Steel Lead Aluminum Cork Salad Oil Gold Zinc 7.8 gm/cc 11.3 gm/cc 2.7 gm/cc 0.2 gm/cc 0.9 gm/cc 19.3 gm/cc 6.9 gm/cc Brass Balsa wood Wood (fir) Gasoline Ice Mercury Platinum 8.4 gm/cc 0.13 gm/cc 0.45 gm/cc 0.75 gm/cc 0.92 gm/cc 13.6 gm/cc 21.4 gm/cc 1. The density of water is 1.0 gm/cc. How do the densities of floaters and sinkers compare to the density of water? 2. Mercury is a liquid metal. A block of Aluminum will float on a pool of mercury, but a block of gold will sink. Would a block of Steel float or sink in mercury? Why? 3. The density of alcohol is 0.8 gm/cc. Would an ice cube sink or float in alcohol? So objects with densities lower than the liquid float and objects with densities higher than the liquid sink. This is true for solid objects, but it can’t be the entire story, or how would steel ships float? A Greek named Archimedes can help us out with this. Construct a group 10 plastic 1cc cubes so they will fit into a graduate cylinder. Pour enough water into the graduate so that you can completely submerge the plastic blocks. You may have to push it under with a straightened paper clip. 1. What is the water level in the cylinder before you put in the cubes? 2. What is the water level after you submerge the 10 cc plastic figure? 3. How much did the water level move up? Did you notice that a 10 cc volume pushes the water up 10 cc? Check this with a few other volumes. Another way to do this is to use an overflow can. It is a good way to measure objects that will not fit into the cylinder. Fill an overflow can so it stops overflowing. Submerge your 10 cc. plastic figure in the overflow can and catch the water in the graduate cylinder. Since a 10 cc. object should shove 10 cc. of water aside, you should have caught about 10 cc. of water in the graduate cylinder. This makes a very convenient way to measure volumes. Just measure the volume of water which spills into an overflow can. Now that we have a way to measure the amount of water pushed aside by an object, let’s look at some weights in and out of water. Place a weight on a spring scale. Take a reading in and out of water and measure all the overflow water. How does the difference in the spring scale readings compare to the overflow volume? Try this with several different weights. Did you notice that if the spring scale read 20 grams less, there was 20 1 cc’s of overflow water? Since 1cc of water weighs 1 gram, 20 cc’s of water would have a mass of 20 grams. In other words, the spring scale reads 20 gm. less when you shove aside 2 gm of water. To sum it up then, if you dunk an object in water, its spring scale reading decreases by the same amount of water overflow. If a spring scale goes down by 50 grams, you must have pushed 50 grams of water out of the overflow cup. Archimedes would have said the “ objects weigh less in water by the weight of water they displace (push aside)” 4. What is the density of aluminum? 5. What would be the mass of a 1cc block of aluminum? 6. If you placed a 1cc block of aluminum in water, how much water would be pushed aside? What would be the mass of that water? 7. Using the results from #5 and #6, how much lighter would the spring balance read connected to the block of aluminum in the water? 8. Would the aluminum sink of float? Why? We can’t change the density of aluminum. So is there any way we could get 2.7gm of aluminum to float? 9. How much water must the aluminum push aside so that the difference in the balance would be 2.7 gm? 10. If you could make the aluminum push aside 2.7 gm of water, then the spring difference would be 2.7 gm. and there would be no net downward force on the aluminum. Would it sink or float? 11. There is no way a 2.7 gm block of aluminum can be made to push aside more than 1cc. of water, however, what about aluminum foil? If we pound that 2.7 gms of aluminum out flat, is there a way to make it displace more than 1cc of water? Can you bend some aluminum foil so it will displace as much water as its mass? 12. You will find that you can even add more mass to your “boat.” Load some weights in you boat. Mass your boat. Float the boat, collecting the overflow. How does the mass of your boat compare to the amount of overflow? 13. Try another heavy boat. How does the mass of the boat compare with the amount of overflow? 14. Make up a rule for floating objects and overflow. Extra: What would happen if an object displaced more water than its mass? Find the mass of a wood block. Using a paper clip, force it under the water and collect the overflow. 15. How does the mass of the wood compare with the amount of overflow? 16. Is the wood actually floating? 17. What happens when you take the paper clip away? 2