Fascinating Education Script Fascinating Physics Lessons

Transcription

1 Fascinating Education Script Fascinating Physics Lessons Why Things Float Slide 1: The blue column of water Here is a lake. I want you to imagine a blue column of water extending from the bottom of the lake up to some point below the surface of the water. This blue column of water is supporting the red column of water sitting directly above it and extending all the way to the surface. In fact, though, this blue column of water could support anything so long as it has the same volume as the red column of water and doesn t weigh more than the red column of water. So if I exchange the red column of water with this column of metal that weighs the same or less, the blue column of water will hold it up. But if I replace the red column of water with something that weighs more than the red column of water, that something will sink because the blue column of water cannot hold up anything that weighs more than the red column of water. If we re trying to decide whether something will float, then, what do we have to measure? We know that the blue column of water will hold up anything that s the same weight and same size, or volume, as the red column of water. The two things we have to measure, then, are weight and volume. What are the units of weight and volume? Slide 2: The metric system The units for weight and volume, and also length, can be in expressed in either the metric system or the American system. Why the United States hasn t joined the rest of the world in

2 adopting the metric system is unclear. The metric system is a lot easier to work with than the American system. Take length. In the metric system, the unit of length is meter. If you have a thousand meters, you have a kilometer. If you only have one one-hundredth of a meter, you have a centimeter, and one-thousandth of a meter, a millimeter. In the American system, though, you have to know that 12 inches make a foot, and three feet make a yard, 1760 yards make a mile, and 5280 feet make a mile. The only unit of volume you have to know in the metric system is the liter. Again, a thousand liters is a kiloliter, and one-thousandth of a liter is a milliliter. But in the American system you start with a teaspoon. Three teaspoons make a tablespoon. Two tablespoons make a fluid ounce. There are eight ounces in a cup, two cups in a pint, two pints in a quart, and four quarts in a gallon. In the metric system, the units of weight are in grams, kilograms, and milligrams, but in the American system, we have ounces, pounds, and tons. There are 16 ounces to a pound and 2000 pounds in a ton. Because the metric system is so much easier to work with than the American system, from here on, we re going to describe length, area, volume, and weight in the metric system. We ll use units of meters for length, liters for volume, and grams for weight. Slide 3: Length and area So what is length? Length is simply how long a straight or a curved line is. Because we can only move along the line, either forward or backward, length is one dimension. Once we get off the line and spread out along a surface in two directions, we are making an area. An area is two dimensional. Simple areas are squares, rectangles, triangles, and circles. We can measure any area by adding up the number of squares, say, 1 meter on a side that we can fit into the area.

3 Here, for example, is a square that s 10 meters long and 10 meters wide. What s its area? How many squares 1 meter on a side can we fit into the big square? If we count them, we get 100. That s how many we would have gotten if we had multiplied the length by the width. Ten times ten is 100. Let s try that with a rectangle. This rectangle is 6 meters wide and 8 meters long. We could count the boxes and get 48, or we could just multiply 6 times 8 and get 48. Each little box was 1 square meter in area. In our two examples, we fit 100 of the square meters into the square and 48 of the square meters into the rectangle, so the size of the square is 100 square meters and the size of the rectangle is 48 square meters. Slide 4: Area of a triangle What s the area of a triangle? The area of a triangle is one-half the base, or width, of the triangle times its height. If you made a box around the triangle, the area of the box would be its base times its height. If the formula for the area of a triangle is onehalf base times height, what the formula is saying is that no matter what shape the triangle is, if you make a box around the triangle, the triangle will fill half the box. How can that be? Because every triangle can be split into two triangles: one to the left of the height line and one to the right.

4 The area of the triangle to the left of the height line is half the size of the red box, because the slanted side of the triangle stretches from the lower left corner of the red box to the upper right corner. That diagonal splits the box in half, so that the black triangle inside the red box is the same size as the light blue triangle. The same applies to the triangle to the right of the height line. Because the slanted side of the triangle splits the orange box, the black triangle inside the orange box has the same area as the light blue triangle. If the two light blue triangles, added together, are the same size as the two black triangles inside the green box, then the light blue triangle occupies half the area of the green box. The area of the green box is the base times the height, and the area of the light blue triangle inside the box is one-half the base times the height. Slide 5: Area of a circle How about a circle? The radius of a circle is the distance between the center of the circle and any point along the circumference, the line forming the outside of the circle. The diameter of a circle is a straight line that passes from any point on the circumference through the center of the circle to another point on the circumference. In other words, the diameter is twice the length of the radius. What s interesting about a circle is that no matter how big the circle, the circumference around the circle is always 3.14 times as long as the diameter of the circle. That number, 3.14, is called π, which is a Greek letter. Regardless of the size of the circle, π never changes; π is constant, always If I multiply the diameter by π, 3.14, I get the circumference. If I happen to have the radius instead of the diameter, I multiply π by twice the radius to get the circumference. What s the area of a circle? First, cut up the circle into 6 triangular slices. The area of each triangular slice is one-half the height, which in this case is the radius, times the base, which is 1/6 of the circumference of the circle.

5 When we add up the area of all six triangular slices, we get one-half the radius times the entire circumference. But what is the circumference? The circumference, we said, is π times twice the radius. So if the area of all the triangles is ½ the radius times the circumference, since the circumference is π times 2 times the radius, the area of all the triangles which is the area of the circle is ½ the radius times π times 2 times the radius. One half of two is 1, so the area of a circle is π times the radius times the radius again, which π times the radius squared, or πr 2. The area of a circle is πr 2. Slide 6: Volume in cubic meters Does this sphere represent area or volume? It depends. If you re talking about the surface of the sphere, that s area, or better yet, surface area. If you re talking about the inside of the sphere, you re talking about volume. So what s the difference between area and volume? Volume is when you have three lengths, and therefore, three dimensions. The first two lengths describe the cross-sectional area. The third length is the height. So if the length, width, and height of this cube are each 10 meters, what s the volume? 10 times 10 is 100 and 100 times 10 is 1000, but what are the units? Since we multiplied meters three times, the units are meters with a raised 3, which we call an exponent. The word meters with an exponent of 3 is pronounced, meters cubed, or cubic meters. The box is 1000 cubic meters.

6 Slide 7: Volume in liters Instead of using cubic meters to describe volume, we can also express volume with units of volume. In the metric system, the unit of volume is liter. A thousand liters is a kiloliter and onethousandth of a liter is a milliliter. A centimeter is one one-hundredth of a meter, just as 1 cent is one one-hundredth of a dollar. A centimeter is about the width of your baby finger. 1 cubic centimeter has a volume of 1 milliliter, which is one one-thousandth of a liter. A sugar cube 1.7 centimeters on a side, and a teaspoon, are both about 5 cubic centimeters or 5 milliliters. If a cubic centimeter and a milliliter are both one one-thousandth of a liter, then 1000 cubic centimeters and 1000 milliliters make 1 liter. A cube 10 centimeters on a side is 1000 cubic centimeters, or 1000 milliliters, or 1 liter, in volume. Here s the really great thing about the metric system. 1 liter of water weighs 1 kilogram. Length, volume, and weight in the metric system are connected! So when you buy a two liter bottle of soda, you know immediately how much it weighs. How much is that? 1 liter of water or soda weighs 1 kilogram, so a 2 liter bottle weighs 2 kilograms. Slide 8: Volume of a cylinder Here is a cube with a length, width, and height of 10 centimeters. What s its volume? Volume is length times width times height. Length times width is the cross-sectional area of the cube, so we could say that volume is the cross-sectional area times the height. The cross-sectional area of this cube is 10 centimeters times 10 centimeters, or 100 square centimeters. Its volume, then, is 100 square centimeters times 10 centimeters, or 1000 cubic centimeters, which is 1 liter. If I took two of these cubes and stacked them one on top of the other, the total volume would be 2 liters.

7 Here is a 2 liter bottle of soda. If this 2 liter bottle of soda had a diameter of 10 centimeters, and you slipped the bottle of soda into the 2 liter container, would the soda bottle stick up out of the container, and if so, by how much? Yes, the bottle of soda would stick up out of the container, because the cross-sectional area of the bottle is smaller than the cross-sectional area of the container. The circle will have to be taller than the square if they are to contain the same volume. So how tall will the 2 liter bottle of soda have to be? We already know that the container has a crosssectional area of 100 square centimeters and a height of 20 cm for a volume of 2000 cubic centimeters, or 2 liters. A 2 liter bottle with a diameter of 10 cm has a crosssectional area of πr 2. πr 2 is 3.14 times the radius, 5 cm, squared, which turns out to be 78.5 square centimeters, considerably smaller than the crosssectional area of the square container, which was 100 square centimeters. The volume of the bottle is the cross-sectional area times the height. What we don t know is the height of the soda bottle. How high does it have to be to make the volume of the cylinder 2000 cubic centimeters? We know that the cross-sectional area, 78.5 square centimeters, times the height of the bottle will end up with a volume of 2 liters, or 2000 cubic centimeters. Because we have an equal sign, mathematics allows us to change the left side of the equation so long as we do the same thing to the right side of the equation. So if we divide the left side of the equation by 78.5 cm 2, we have to divide the right side of the equation by 78.5 cm 2. Whenever something is divided by itself, or something equal to itself, the answer is always 1. So 78.5 cm 2 divided by 78.5 cm 2 is 1. 1 times the height of the bottle is just the height of the bottle.

8 On the other side of the equal sign is 2000 cm 3 divided by 78.5 cm cm 3 divided by 78.5 cm 2 is 25.5 centimeters. The height of the bottle has to be 25.5, or 25 and a half centimeters high to contain 2000 cubic centimeters. That s 5.5 cm, or 5 and a half centimeters, higher than the square container. We can check this answer by multiplying the area of the circle, 78.5 cm 2, by the height, 25.5 cm times 25.5 is 2002, close enough. Slide 9: Density We did all this math so we could understand what volume is. We said before that if we re trying to decide whether something will float, the two things we have to measure are weight and volume. We can combine weight and volume by saying weight per volume. How do you translate weight per volume into mathematics? The word per means draw a line and make a fraction with whatever came before the per in the numerator and whatever came after the per in the denominator. So weight per volume is weight divided by volume. What is weight divided by volume? Weight divided by volume in English is density. When I say that sugar has a density of 0.8 grams per cubic centimeter, or 0.8 grams per milliliter, I m simply saying that a cubic centimeter, or 1 milliliter, of sugar weighs 0.8 grams. Which ones of the following are measures of density: kilograms per liter, grams per cubic centimeter, molecules per milliliter, grams per cup, milligrams per square centimeter? Kilograms per liter and grams per cubic centimeter are both density, because they both measure weight per volume. But, molecules per milliliter is not density, because molecules is not a measure of weight. Grams per cup is weight per volume, so grams per cup is measuring density, but milligrams per square centimeter is not, because square centimeters is a measure of area, not weight. Slide 10: Will it float?

9 What does density have to do with whether something will float? Let s see. Here is a rectangular wooden box that s 5 meters long, 2 meters wide, and 2 meters deep. One meter is a little less than a yard. The box, when empty, weighs 50 kilograms. The box is used to carry supplies from one side of a fresh water lake to the other. How much weight can the box carry without sinking? If the lake is calm so there s no worry about waves splashing over the sides of the box, how many kilograms of supplies can be loaded into the box? The more supplies we load into the box, the deeper the box sinks into the water until finally no more supplies can be added because the box has sunk right to the top of its side walls. The water that was pushed aside, or as we say, displaced by the box, is of course exactly the same volume as the box. Before the box was even put in the water, the column of water that s now below the box was holding up the water that s now been displaced by the box. So long as the box and its supplies don t weigh more than the water being displaced, the blue column of water beneath the box will hold up the box, because it doesn t care what it s supporting, so long as it doesn t weigh more than the water being displaced. Mathematically, the blue column of water will support the box if two conditions are met. First the volume of the box submerged in the water has to be the same volume as the water pushed aside, or displaced, by the box. That s an easy condition to meet because no matter how much of the box is submerged, the volume of the submerged part will always equal the volume of water displaced. The second condition is that the weight of the box cannot exceed the weight of the displaced water. If the volumes are equal and their weights are equal, then by drawing a line between them, whether something will float depends on whether the thing trying to float has the same density as the water it s displacing. If it does, it will float. If the density is greater than the displaced water, however, it will sink.

10 So what information do I need to decide if the weight of the box equals the weight of the water pushed aside by the box? I need to know how much water is pushed aside and how much that water weighs. That will tell me how much the box and the supplies, together, can weigh. How much water is pushed aside by the box? The most water that the box can push aside is when the box sinks right up to the top of the box. How much water will that be? Lowering our box into the water is like digging a hole in the ground. Our hole in the water will be 5 meters long, 2 meters wide, and 2 meters deep. What s the volume of the hole? The volume of the hole will be the volume of the box. The amount of water pushed aside, or displaced by the box will be 5 meters long by 2 meters wide and 2 meters deep, or a volume of 20 cubic meters. What do we need to know to determine how much 20 cubic meters of water weighs? We need to know how much 1 cubic meter of water weighs, because our 20 cubic meters of water will weigh 20 times that. It s known that 1 cubic meter of water weighs 1000 kilograms. If 1 cubic meter of water weighs 1000 kilograms, 20 cubic meters of water must weigh 20 times that, or 20,000 kilograms. Since the box itself weighs 50 kilograms, the most cargo that the box can carry without sinking is 19,950 kilograms. Slide 11: Archimedes Measuring the volume of a box was pretty easy, but what if the object isn t a box, but a crown? How do you measure its volume? Archimedes figured it out around 250 B.C. What he did was simply drop the crown in a glass of water and measure how much the water rose. The cross-sectional area of the glass times the increase in water level is the volume of water displaced by the crown.

11 The reason Archimedes wanted to measure the volume of the crown was that the king has asked him if the crown was pure gold or whether some other cheaper metal had been mixed in with the gold. Archimedes knew that gold was very dense. A single cubic centimeter of gold weighs 19.3 grams while a cubic centimeter of silver weighs only 10.5 grams, nickel 8.9 grams, iron 7.9 grams, and even lead only 11.3 grams. Aluminum is very light, weighing only 2.7 gram per cubic centimeter. Archimedes had already weighed the crown before dropping it into the glass of water. After measuring how much the water rose in the glass, what do you suppose he did then? He divided the weight of the crown by its volume to get the crown s density. He found that the density of the crown was 16.1 grams per cubic centimeter. What conclusion did he draw? Archimedes concluded that because the density of the crown at 16.1 grams per cubic centimeter was less than the density of gold, which is 19.3 grams per cubic centimeter, the maker of the crown had mixed in some cheaper, less dense metal when he made the crown, and was now claiming, falsely, that the crown was pure gold. Slide 12: What is the density of something only partially submerged? Archimedes measured the density of the crown by dividing the weight of the crown by the volume of the crown. The volume of the crown was the volume of the completely submerged crown. When measuring the density of something only partially submerged, what is its weight divided by its volume? It makes sense that the volume is the volume of submerged part of the swan, because that s the volume of water pushed aside by the swan, but is the weight the weight of the entire swan or just the weight of the submerged part?

12 What is the density of this boat? The volume is the volume of the submerged part, but is the weight the weight of submerged part of the boat or the whole boat? The weight is the weight of the whole boat. So things float when the density of whatever is submerged equals the density of the surrounding water, but the density of a partially submerged object is the weight of the entire object above and below the water divided by the volume of the displaced water. Moreover, things that are denser than the surrounding water will continue to sink until they reach a level where their density does equals the density of the surrounding water. And conversely, lighter things will float upward until their density equals the density of the surrounding water. So when this ball was first lowered into the water, how far into the water did it settle before it began to float? The ball sank until its weight equaled the weight of the water displaced by the ball, because at that point, the weight of the entire ball equaled the weight of the water displaced by the ball, and the volume of submerged part of the ball equaled the volume of water displaced by the ball. In other words, the density of the submerged part of the ball equaled the density of the surrounding water. Slide 13: Will this rock sink, and if so, how far? If you were standing at the railing of an ocean liner and tossed this 125 gram rock overboard, how far down would the rock sink? The volume of the rock is 100 milliliters. The density of the rock is 125 grams divided by 100 ml. When you actually divide the fraction, you get a density of 1.25 grams per milliliter. The rock will sink until it reaches a level where the density of the surrounding water is also 1.25 gm/ml.

13 The density of fresh water is 100 grams per 100 ml of water, or, after dividing, 1.00 gm/ml. The density of sea water is a little higher at grams per 100 ml of sea water, or gm/ml. Why is sea water denser than fresh water? Because sea water also contains salt which adds to its weight. So how far will the rock sink? What information do you need to answer this question? You need to know how much the density of water increases the deeper down you go in the ocean. Slide 14: A graph of ocean water density The best way to see how the density of sea water increases as you descend in the ocean is with a graph. This graph looks complicated but as soon as I explain how graphs work, you ll see how easy they are. A graph has two straight lines, one horizontal along the bottom, called the X axis, and another vertical line over to the left called the Y axis. The horizontal X axis down below represents the how far down in the ocean we go in miles, and as you can see below, the X axis is marked off every half mile. So if you start off where the X and Y axis meet and move along the X axis, you go deeper and deeper in the ocean, finally reaching a depth of 3 miles. The Y axis represents the density of water. Beginning again where the X and Y axes meet, and moving up the Y axis, the water gets denser and denser. The red line is the actual density of sea water at every depth. For example, if we go half a mile down in the ocean along the X axis, imagine a line moving up from that point to the red line directly overhead. Now go horizontally to the left over to the Y axis. That point along the Y axis tells you the density of sea water at half a mile below the surface of the water, in this case, just about grams per cubic centimeter. A cubic centimeter is the same size as a milliliter.

14 The graph displays how ocean water density increases as we descend to the bottom of the ocean 3 miles down. At the surface, the density of sea water is grams per 100 ml of sea water, or gm/ml. A half a mile below the surface, sea water density is grams per 100 ml, or gm/ml. From a half a mile below the surface to the bottom of the ocean, the density of sea water remains at gm/ml. Why doesn t all that weight of water squeeze water molecules together and increase the number of water molecules packed into 100 ml of water, and thereby increase its density? Because water molecules are already so densely packed that there s barely any room between them. Water is incompressible. That s why we can use water in heavy plastic road barriers. Because water doesn t give, water is like concrete, or steel, and works as well as concrete or steel to stop a car that s out of control. So what happens to the rock? How far does it sink? All the way to bottom of the ocean, because it remains denser than the surrounding water all the way to the bottom of the ocean. What would happen if I chipped off a small piece of the stone and tossed in the ocean? Would it sink all the way to the bottom of the ocean, too, or, being lighter, would it descend to some point and remain suspended there? The small chip would also sink to the bottom of the ocean, because even though the small chip is lighter, its density is the same as the rock it was chipped from. Density, not weight, is what determines the depth to which an object will sink. By the way, why isn t this picture a picture of the bottom of the ocean? Because no sunlight reaches the bottom of the ocean, and no fish live 3 miles down at the bottom of the ocean.

15 Slide 15: Making metal float Here is a ball of metal also weighing 125 grams and also 100 milliliters in volume. How can I make it float? Right now the piece of metal displaces only 100 ml of water. In order to make its density equal to the density of fresh water, which is 1 gram per milliliter, we need to expand the volume of the ball. We can do this by shaping it into a hollow sphere with a volume of 125 milliliters, or by shaping it into half a sphere, a hemisphere, with a volume of 125 milliliters. Because they are both 125 milliliters in volume, when either one is placed in the water, each one will displace 125 ml of water. And since each one weighs 125 grams, its density will be 125 grams divided by 125 milliliters, which is exactly the density of fresh water, 1 gram per milliliter. This same principle applies to building a steel battleship. You can t make the battleship too narrow or it won t displace enough water. But the wider you make it, the slower it travels in the water. Slide 16: Buoyancy Force We ve learned that things float when their density, that is, their weight per volume, equals the density of the surrounding water. When things sink, what force is pulling them downward? Gravity! When a boat floats on water, it s obviously not sinking. Is the force of gravity no longer exerting a downward force on the boat? No, gravity is still working but Sir Isaac Newton said that whenever something is experiencing a force in one direction, but isn t moving, it must be experiencing an equal force in the opposite direction. So if gravity is acting on a boat floating on the surface of a lake, what force is pushing up on the boat equal in strength to the force of gravity? Buoyancy force. Buoyancy force is the upward force of water.

16 Do we really need to conjure up buoyancy to explain why things float? Maybe we re looking at it backwards. Maybe the reason things float is simply because heavier things sink. If you shook a jar mixed with ping-pong balls and metal ball bearings, the ping-pong balls would end up on top of the ball bearings, not because the ping-pong balls were floating on top of the ball bearings, but because the ball bearings, being denser than the ping-pong balls, experienced a greater gravitational force, and thus sank lower than the ping-pong balls. This can t be the whole answer, though. Water must be exerting an upward buoyancy force, because it s easier to lift something while it s underwater than it is to lift it up out of the water. The reason it s easier to lift a submerged object is that water is helping to lift it, by pushing up on the submerged object with buoyancy force. A rock weighing 10 kilograms on land weighs less than that if you weigh it at the bottom of a lake. The difference in weight is due to the upward buoyancy force of water. Slide 17: Gravity and gravitational force Why do things weigh anything at all? They don t weigh anything in outer space. Weight is caused by gravity, but what is gravity? We know that gravity surrounds every object, and doesn t exist unless there is some object to generate the gravitational field around it. Einstein said that gravity is what happens to space as a result of some object. Objects, Einstein said, distort space just as a bowling ball sitting on a trampoline causes the fabric of the trampoline to sag.

17 Gravity is the sagging of space around an object. So when one object enters the sagging gravitational field around another object, the approaching object starts sliding downhill toward that other object. The approaching object picks up speed and accelerates toward the other object, which to us looks like the approaching object being attracted to the other object by the force of gravity. But gravity is not a force. It s a slanted field that causes objects to accelerate toward whatever is generating the gravitational field. Gravity around an object is not a force, until some other object happens to wander into the gravitational field. Only then does gravity acting on the approaching object produce a force. Gravity by itself is not a force. It does create a force, but only if some object encounters a gravitational field. We measure the force created by earth s gravitational field with a scale. Your bathroom scale measures the force created on you because you are now in the gravitational field around earth. So instead of saying the force of gravity, we should say the force created by gravity. Slide 18: Weight results when an object encounters gravity Why, though, do some things experience a greater force than other things? In other words, why do some things weigh more than others? Two reasons. First off, the strength of the gravitational field increases the closer you get to the object creating the gravitational field. Things in outer space don t weigh anything, but as they drift closer to the earth, they weigh more and more and eventually they weigh whatever the bathroom scale says they weigh. The reason the strength of a gravitational field is stronger right around an object is that the strength of a gravitational field decreases the further you get from the object. The reason for this is that gravity radiates from an object in all directions, and thus has to spread out over a bigger and bigger surface area. Light does the same thing, which is why a light bulb appears dimmer and dimmer the farther you are from the light.

18 So two identical objects can have different weights if one of them is closer to the object generating the gravitational field. But even if two things are the same distance from the earth, say, right on the surface of the earth like you and me, one object can weigh more than another. Happens all the time. Why? What does the heavier object have more of than the lighter object? Slide 19: Mass is not the same as weight Mass. The more mass something has, the more it weighs. Mass and weight are not the same thing. You may weigh 100 kg on earth, but in outer space, you weigh nothing. Does your mass change when you go into outer space? No. The mass of an object on earth is the same as its mass in outer space. And that mass in outer space will only move if a force pushes or pulls it. The bigger the mass, the more force needed to get it moving. Mass, then, is the resistance of an object to being moved when gravity is not around. Weight is a specific force the force created by earth s gravity acting on an object. When a force acts on a mass that s not moving, the mass accelerates from its resting position. The bigger the force, the faster the acceleration. If earth s gravity is causing the acceleration, the acceleration is gravity. So force and weight are the same thing and so are acceleration and gravity. We have two ways to express the relationship between force, mass, and acceleration. A force acting on a stationary mass causes the mass to accelerate. Or, a mass that suddenly finds itself accelerating in a gravitational field creates a force. If that gravitational field is the gravitational field around the earth, the resulting force is the object s weight. The mathematical formula relating mass, acceleration, and force was described by Sir Isaac Newton, who in the 1600 s said that force equals mass times acceleration.

19 Because mass and weight are different, we should be using different terms when we measure them, and we do, at least we do in the metric system. In the metric system, the units of mass are grams, kilograms, and milligrams. The units of force and weight are newtons, honoring Sir Isaac Newton. The units for acceleration describe what acceleration is: the increase in speed over time. Speed is distance divided by time, so acceleration is how many, say kilometers per hour you increase every, say, minute. So if you accelerate from a stop sign by 10 kilometers per hour every minute, your acceleration is 10 kilometers per hour, per minute. In the American system, the units for mass are slugs, but we end up using pounds to refer to both mass and weight. Instead of describing mass in units of slugs, everyone today uses the metric system where mass is in grams, kilograms, and milligrams, and weight is measured in newtons. If force and weight are the same, why do we say something weighs 100 kilograms? Shouldn t we say it weighs 100 newtons? Yes, but because gravity on the surface of the earth is constant, we don t even think about gravity and simply use kilograms to measure something s weight, when we should be using newtons. Slide 20: Force, mass, and acceleration Now that you understand that force and weight are the same thing, you understand why the downward weight of an object floating on water is being opposed by an equal upward buoyancy force whose magnitude is the weight of the water displaced by the floating object. If the upward buoyancy force on a floating object equals both the weight of the object and the weight of the displaced water, we can calculate the weight of a large ship without weighing it on dry land. We can just measure how much water it displaces, and multiply that volume by the density of water: 1 kilogram per liter. So far all we ve talked about are ways to oppose the force created by gravity. Can you think of a way to increase gravitational force and make yourself feel like you weigh more than you do?

20 Since force is mass times acceleration, all we have to do is increase our acceleration. Going up in an elevator will do it, and so will roller coasters. Roller coasters accelerate us around three times the acceleration of gravity, or 3-g s. Airplane fighter pilots may experience 9-g s of acceleration. Spinning centrifuges can accelerate test tubes thousands of times the acceleration of gravity. On earth, gravity is always creating a force on a mass, so how do we create a situation where a force is the only force acting on the mass? We can t. The only thing we can do is neutralize the gravitational force and then try to move the object with another force. We can do that with a ball by placing it on a table top and pushing it. The more mass, the more force we have to use to get it rolling. To measure the mass of anything other than a ball, we would have to place it on a frictionless surface, like wet ice, and push it. Slide 21: How fish adjust buoyancy Now if things float because their density equals the density of the surrounding water, why is this ship sinking? Yes, it sprang a leak but how did that increase its density above that of the surrounding water? What is the mathematical definition of density? Weight per volume. What increased? The weight of the ship because now it s loaded with water. Then why is this ship sinking? It didn t spring a leak.

21 What you re looking at is an exploding volcano at the bottom of the ocean heating up the water underneath the ship. Hot water is less dense than cold water because when water molecules heat up they bounce further away from each other and the water becomes less dense. The ship is now denser than the water beneath it, and the ship sinks. How, then, are fish able to stop swimming and stay suspended in water? Fish have a balloon inside them called a swim bladder. They can fill their swim bladder with oxygen which they absorb through their gills. Let s see how this works. When the swim bladder fills up with oxygen, the fish ascend and when the swim bladder is emptied, the fish descend. Does filling the swim bladder with oxygen make the fish lighter? How could adding molecules of a gas make something lighter? Gas weighs something, so if you re adding oxygen, you re adding weight. Filling up a swim bladder can t be making the fish lighter. What filling a swim bladder with oxygen does do is make the fish less dense. How does that happen? How does filling up a fish s swim bladder make the fish less dense? Filling up the swim bladder alone doesn t make the fish less dense. What makes the fish less dense is that as the swim bladder fills with oxygen, the entire fish expands in size. So the volume of the fish expands a lot but its weight, not so much. Weight divided by volume is density. So if the fish s volume expands more than its weight, the fish becomes less dense.

22 Do you recall going swimming and trying to float on your back? Taking a deep breath and holding your breath makes it easier to float because your chest expands with only a little additional weight from the inhaled air. You now displace more water so your weight to volume ratio is less low enough that your weight equals the water you re displacing, so you float. Slide 22: How diving mammals maintain buoyancy Whales, dolphins, and walruses don t have swim bladders, but because they re mammals, they do have lungs. Whales, dolphins, and walruses descend by exhaling air from their lungs, which increases their density and helps them descend into the ocean. When they want to ascend from deep down in the ocean, they obviously can t re-expand their lungs, because there s no air there to breathe. So, they have to use their strong muscles to swim back to the surface. Their muscles have enough oxygen to do this because the muscles have special proteins that store oxygen and provide the muscles with the oxygen they need to generate enough energy to swim back to the surface. Slide 23: How submarines maintain buoyancy How do submarines submerge and then resurface? Submarines have a steel hull that can t contract and expand like a fish, so how does a submarine change its density in order to descend and ascend in the ocean? Submarines have a hollow tank, called a ballast tank, inside their hull. In some submarines the ballast tank forms the inside wall of the submarine. When a submarine wants to ascend, tanks of compressed air fill the ballast tank with air. The weight of the submarine is now less than the weight of the water it displaces, and the submarine ascends.

23 When the submarine wants to descend, ocean water is allowed to enter the ballast tank, forcing the air out, and the weight of the submarine is now greater than the weight of the water it displaces, allowing the submarine to descend. Fish, diving mammals, and submarines demonstrate why it is so important to understand the mathematical definition of density. Density, you recall, is weight per volume. Fish and diving mammals change their density by increasing or decreasing the denominator the volume of their body. Submarines change their density by increasing or decreasing the numerator the weight of the submarine. Slide 24: How hot air balloons maintain buoyancy How do hot air balloons change their density? By changing both the numerator and the denominator both their weight and their volume. When the balloon is deflated, hot air is blown into the balloon, which greatly increases the denominator its volume but only slightly increases the numerator its weight with hot air. Once the balloon reaches its maximal volume, the continued heating of the air inside the balloon drives more and more air molecules out of the balloon and the air inside the balloon become less and less dense. This lowers the numerator the balloon s weight and reduces the density. Hot air balloons force us to return to the weight versus mass issue, because as the balloons ascend, they weigh less because they are moving further from the center of the earth s gravity. Does that reduce their density? Yes, if density if weight per volume, no if density is mass per volume, so which is it? Density is mass per volume but because we are so used to thinking of mass as weight and ignoring the effect of gravity, that we think of density as weight per volume. But can we continue to do so when hot air balloons are moving away from earth s gravity and weighing less and less?

24 Yes, because weight changes very little as you ascend in a balloon. We know that the force created by gravity decreases to one fourth each time we double our distance from the center of gravity. The radius of the earth is 6400 kilometers, so we are 6400 kilometers from the center of gravity. If we ascend another 6400 kilometers into the atmosphere, gravity will be only one-fourth as strong and we will weigh only onfourth of what we weigh on earth. If a hot air balloon floats up to 3300 feet, which is 1 kilometer, gravity is reduced only a tiny amount. Even on the space shuttle, earth s gravity is still pretty strong. The space shuttle orbits the earth at an altitude of around 500 kilometers. In order to reduce the earth s gravity to one-half of what it is on the surface of the earth, the space shuttle would have to orbit more than 2600 kilometers above the earth. So why do astronauts appear weightless as they repair the space shuttle? Because they re in free fall. Way back in the 1600 s, Newton realized that if you could get high enough in the atmosphere and throw an object with enough force, it wouldn t fall back to earth, but instead would continue to fall off the edge of the earth, and continue falling forever in a circular path around the earth. That s what the space shuttle and the space station do. That does it, folks, for why things float. In our next lesson, we ll continue with buoyancy, but the buoyancy of air and learn how clouds which are heavier than air are still able to remain suspended in air. We ll learn about air pressure and air currents so that the weather charts in a newspaper make sense. In future lessons, we ll return to water to find out why we spread salt on ice to make it melt, why there are ocean currents, why water pipes in our house can burst in wintertime, why water boils, why the temperature of boiling water never rises above 100 degrees Celsius, and why water can be made to boil at temperatures well below 100 degrees Celsius.