Pressure. Pressure is one of those words we frequently use, perhaps knowing intuitively what it means. In science, we define pressure as follows:

Transcription

1 Weather reports in the media provide information on variables such as temperature, precipitation and wind speed. In this chapter, we discuss three physical quantities that help determine weather: (1) Temperature, (2) Air pressure and (3) Humidity. Lesson 2 Air Pressure What Is Pressure? Pressure Pressure is one of those words we frequently use, perhaps knowing intuitively what it means. In science, we define pressure as follows: Pressure is a measure of how much force is exerted over a unit of surface area. Pressure could be expressed in newtons per square metre (N/m 2 ). The standard unit for pressure, however, is the pascal (Pa), named after a French scientist, Blaise Pascal ( ). Examples Pressure = Force Area 1 pascal = 1 newton metre 2, or 1 Pa = 1 N m You lift a 4 L can of paint by its wire handle, using one finger. After holding the can for a few moments, your finger starts to ache. You set the can down, and then lift it using four fingers. The can still weighs the same as before. Why is it more comfortable carrying the paint can using four fingers? Answer: When you first lifted the heavy can, all its weight was concentrated on the small area of one finger. Since pressure is force divided by area, and the area is small, the pressure on your finger will be high! Eventually you experience pain in your finger. When you lift the can with four fingers, the area is about four times as great, so the pressure will be one quarter of what it was before. 2. The force of gravity on a figure skater is 500 N. As she makes a turn on the ice, all this force is concentrated over the area of the bottom of one skate blade. Assume the area of the blade contacting the ice is 5.0 cm 2. What pressure is exerted on the ice by the skater, in N/cm 2? Answer: Pressure = Force Area = 500 N 2 = 100 N / cm2 5.0 cm

2 3. After the skate, the same figure skater stands on the floor in her shoes, and the area of the bottom of her shoes contacting the floor is about 100 cm 2. What pressure does she exert on the floor now? Answer: Pressure = Force Area = 500 N 2 = 5.0 N / cm2 100 cm In Examples 2 and 3, the force exerted by the figure skater on the surface was the same. She exerted a force equal to the force of gravity on her, which was 500 N. But pressure changes dramatically in the two situations, because the area over which the force is exerted changes so much. Review 1. Why do power golf carts and all-terrain vehicles have such large tires? 2. Why might high-heeled shoes be harmful to linoleum floors? 3. The figure skater in Example 2 exerted a pressure on the ice of 100 N/cm 2. Use the fact that 1 cm 2 = m 2 to convert the pressure she exerted into pascals. 4. A finishing nail has a cross-sectional area of 1 mm 2, which is m 2. (a) If a force of 10 N is applied to the nail by a hammer, what is the pressure exerted by the nail on the wood below it, in Pa? (b) What is the pressure in kilopascals (kpa), if Pa = 1 kpa? Figure 9 5. Why can someone recline on a bed of nails (Figure 9) without feeling any pain?

3 Air Pressure An ocean of air surrounds us. (See Figure 10.) Air has mass, and the earth exerts a force of gravity on it. Because of this, air exerts pressure. Air pressure in a particular location varies from hour to hour as atmospheric conditions change. Weather forecasts usually describe how the air pressure is changing. Higher air pressure is associated with good weather, while lower air pressure is associated with bad weather. Air pressure is important in other ways. Every time you breathe in, air pressure allows air to enter your lungs. Basketballs, soccer balls, footballs and bicycle tires require just the right amount of air pressure. Some truck brakes and shock absorbers use compressed air, which is air under unusually high pressure. What is air pressure at the earth s surface? Imagine a column of air with a base that measures 1 m x 1 m, or 1 m 2. This column reaches to the top of the atmosphere. The force of gravity on this column of air is N. Therefore the pressure due to this column of air would be N/m 2, or Pa, which is 101 kpa. To get a feeling for just how much air is pushing down on you, it might help to do this calculation: The mass of air in the imaginary column of air going to the top of the atmosphere is about kg. Estimate the average mass of a student in your group. Divide this average mass into kg, and see how many people in your group would have to arrange themselves in a column 1 m 2 in area, to produce the same pressure as the atmospheric air pressure. For example, if the average mass of people in your group is 50 kg, then the number of people required to produce the same pressure as atmospheric air pressure would be kg 50 kg = 206 people. In other words, for this group, air pressure is equivalent to 206 people/m 2! Figure 10

4 Demonstrating Air Pressure Figure 11 Figure 12 In Figure 11, a hand vacuum pump is connected to a plastic pop bottle by way of a 1-hole rubber stopper and some rubber tubing. Initially, the plastic pop bottle contains air at the same pressure as the air outside the bottle. When air is pumped out of the bottle using the vacuum pump, the bottle is flattened! Push a toilet plunger straight down onto a smooth surface, in such a way that the air inside the suction cup is expelled, and there is almost a vacuum between the cup and the smooth surface. Then, using the handle, try pulling the suction cup straight up and off the surface. It is very difficult! Air pressure above the cup is high enough that a large force is needed to overcome it. The youngster in Figure 12 has pushed two identical suction cups together, so that the air is expelled from the space between them. It is very difficult for him to pull the cups apart. Note! The area of one of these suction cups is about 50 cm 2. Air pressure is about N/m 2, which is the same as 10 N/cm 2. This means that the force on each 1 cm 2 of area is 10 N. The force on the 50 cm 2 surface of each cup is 500 N. The force needed to pull the cups apart is 500 N, which is equivalent to the force you need to lift about fifty 1-kg masses! Think About It! 1. Make a rough estimate of the surface area of the top of your head. Multiply this area (in cm 2 ) by 10 N/cm 2, to estimate the downward force due to air pressure on the surface of your head. 2. Why do you not feel crushed by the downward force due to air pressure?

5 Measuring Air Pressure Figure 13 Figure 14 If a tall vessel is filled with water, then inverted over a dish of water, as in Figure 13, one might expect all the water to drain down into the dish. In fact, if you try this, you will see that the water stays up in the inverted vessel. What keeps the water up there? Air pressure will balance a column of water approximately 10.3 m high! (This is about the same height as five senior basketball players standing one above the other!) A tall tube of water closed at the top end could be used as a barometer to measure air pressure. However, a water barometer would be too tall. A barometer filled with mercury is more practical, because mercury is 13.6 times as dense as water. A mercury barometer only has to be 10.3 m 13.6 = 0.76 m, or 76 cm high. To allow for daily variations in air pressure, a mercury barometer is slightly taller than 76 cm. Mercury barometers are not practical for home use. Home barometers are most often aneroid barometers like the one in Figure 14. Aneroid barometers consist of an accordion-like metal container, which is partially crushed by air pressure. A needle arrangement attached to the accordion-like metal box moves in response to changes in pressure acting on the container. Aneroid barometers are far more compact than mercury barometers. They are also safer. Mercury is toxic, and the glass tube on a mercury barometer can be broken open quite easily.

6 Using Air Pressure: Your Lungs Figure 15 illustrates a model of how air is pumped into your lungs. The two balloons represent your lungs, and the rubber sheet at the bottom of the bell jar represents your diaphragm. When you breathe in, muscles contract and cause the diaphragm to be pulled down. This creates a low pressure around your lungs, and so atmospheric air pressure outside your body forces fresh air, containing 20% oxygen, into your lungs. When your diaphragm relaxes (moves upward), it raises pressure in your lungs, and used air containing carbon dioxide is forced out. Figure 15 Review 1. What evidence have you seen that suggests air pressure acts upward as well as downward and sideward? 2. When you open a can of juice, why is it a good idea to punch two holes in the can, rather than just one? 3. Why should a gas cap for a car not be perfectly airtight? 4. Why is your body not crushed by air pressure? 5. One side of a rectangular can has an area of 300 cm 2. On a day when the air pressure is 100 kpa, what is the force, in newtons, exerted on the side of the can? Why does the can not become crushed? Under what condition will the can be crushed? 6. What would happen to an astronaut doing a space walk if he or she did not wear a space suit? Why would this happen? 7. Why is it more difficult to cook an egg in boiling water if you live in a high altitude community? 8. Normal air pressure at sea level is 101 kpa. This pressure will support a column of mercury 76 cm high. On a certain day, the mercury level in a barometer reads just 72 cm. What is the pressure in kpa?

7 Figure In Figure 16, someone is drinking water through a glass straw from a plastic bottle. Can you explain why the bottle has become crushed? Air Pressure and Today s Weather Air pressure in your locality depends on a number of variables. One of these variables is altitude. Air pressure is due to the force of gravity on all the air molecules above your location. If you live at high altitude, there are fewer air molecules above you on average, so the air pressure will be less at that altitude. Also, air, a mixture of gases, is a compressible fluid. At sea level, pressure is greatest. Molecules of air are closest together at lower altitudes. At an altitude of just 5.6 km, half the molecules in the atmosphere are below you, and air pressure due to the other half of the molecules in the atmosphere still above you is therefore about half what it is at sea level. (The atmosphere extends to an altitude of more than 30 km.) Air pressure is also affected by air temperature. If air is cold, its molecules have less kinetic energy, so they move more slowly. As a result, cold air tends to be denser, and therefore it exerts more pressure than warm air. (Density is a measure of how much mass is contained in a unit volume of a material.) If air is warmed up, its molecules gain kinetic energy, move faster, and occupy a greater volume. The density of the air decreases, so the pressure exerted by the warmed air also decreases.

8 Weather Demonstrations (B) Air Pressure What is Pressure? Atmospheric pressure tells us how much force is exerted by the air in our atmosphere on a certain area of a surface. (Air pressure is about 15 pounds per square inch). We have an atmosphere because the gravitational force of planet Earth attracts air and keeps it here! The moon has no atmosphere because its gravitational force is too weak to hold on to an atmosphere. Do some of demonstrations from the Air Pressure show. Have students try to pull the rubber cups apart after you push them together and expel the air between them. These cups have an area of about 6 square inches, and there is 15 pounds of force on each square inch. It takes about 90 pounds of force to pull them apart. Ask kids how much they weigh, in pounds. Have a student pump the air out of a plastic pop bottle. Watch what air pressure does to the pop bottle! Show the aneroid barometer. Low pressure is usually associated with bad weather, high pressure with good weather. Show the water barometer.