Physics 102 Lawrence Weinstein Homework Set 3 Solutions Chapter 14 Exercises: 16: Air pressure pushes up on the water with a pressure of 10^5 pascals. If the pump is a perfect pump and can create a perfect vacuum, then there will be zero pressure pushing down on the water. In this case, the maximum column of water than can be lifted will be one where the pressure of the column is just barely smaller than atmospheric pressure. For water, this is a column height of 10 m. Thus, the deepest well that a pump can extract water from is 10 m. 32: As anyone who has ever tried to inflate a rubber balloon knows, it takes extra force to make the rubber expand. Therefore, the rubber of the balloon exerts an inward force on the air. This force produces a pressure (since pressure = force / area) that increases the gas pressure inside the balloon. Note that this extra pressure is there for air balloons, helium balloons, etc. (If instead of a rubber balloon, you used a plastic bag full of air, then the internal and external pressures would be the same [since it does not take extra force to expand the plastic bag].) 44: There are two ways to look at this problem: Bernoulli and Newton's 3rd Law. Let's do Bernoulli first: The lift on the plane comes from the pressure difference between the air on top of the wing and the air on the bottom of the wing. The air pressure on top is lower because the air is flowing faster than on the bottom. At higher altitude there is less air density and less air pressure. When there is less air pressure (on both top and bottom of the wing) you have to make the air flow faster over the wing to get the needed lift. You do this by increasing the 'angle of attack' of the wing. Now Newton: Planes generate lift by exerting a downward force on the air flowing over the wing. This force makes the air flow downward as it leaves the wing. By Newton's third law, the air exerts an upward force on the airplane. Since, at higher altitude, there is less mass of air per volume (less density), the plane needs to either a) make more air flow over the wing [fly faster] or b) make the air flowing over the wing move more sharply downward [increase the angle of attack]. A flat wing does not make much air move downward. As you tilt the wing more and more (increase the angle of attack), it makes the air flow more downward. Either answer is correct. They are just two different ways of looking at the same problem. 46: The wind blows rapidly over the wavetops, lowering the pressure there. This makes the wave tops increase in height. The wind does not blow rapidly in the troughs (since they are sheltered by the wave peaks), thus the pressure in the troughs does not decrease. The pressure difference between peak and trough increases the height of the waves. Problems: 10: The difference in the top and bottom pressures is 4% or 0.04 * 1.01*10^5 Pa = 4.04 * 10^3 Pa. The lift (which is a force) = pressure * area = 4040 Pa * 100 m^2 = 4 * 10^5 N or about 40 tons (since one ton weighs 10^4 N). ------------------- Chapter 15: Exercises: 10: The rock transfers heat to the water. This decreases the temperature of the rock and increases the temperature of the water. If the water is just a pail of water, then the temperature rise will be significant. If the water is the Atlantic ocean, then the temperature will still rise, but it will be too small to measure. 12: When you increase the temperature, you are increasing the internal energy of the gas. This means that the gas molecules have a higher speed. Therefore, when the gas molecules collide with and bounce off the walls of the container, they exert a greater force on the walls. When you average this force over all the molecules in the gas and divide by the area of the container, you get the pressure on the container. Thus, increasing the temperature, increases the pressure on the walls (if the volume stays the same). 20: The jug of water would be better. It has a higher heat capacity. This means that it can transfer more heat to you (keeping you warm) before its temperature drops too far and it gets cold. 26: The air pressure in the tires increases because they heat up (with no change in volume). They heat up because of friction between the tires and road. More precisely, they heat up because the tire flexes as it rotates and this flexing heats up the tire. Modern tires are designed to reduce this kind of friction (so as to improve gas mileage). 34: The iron ring expands when it is heated. After it is slipped over the cold brass cylinder, the iron cools and contracts, the brass heats and expands. This means that the iron grips the brass incredibly tightly (since it exerts a tremendous force on the brass). ------------------------------------- Estimation: Water freezes at 0 C and boils at 100 C, therefore we will be heating the water by 100 C. It takes 100 cal = 420 J to heat 1 g of water by 100 degrees C. Therefore it takes 4.2 * 10^5 J to heat 1 kg of water 100 degrees C. Now we want to see how fast that much energy can make the water go. Remember that kinetic energy = 1/2 mv^2 so that v = sqrt(2 KE/m) so that V = sqrt(2 * 4.2*10^5 J / 1 kg) = 920 m/s This is rather fast! I guess we're lucky that the molecules in hot water are moving around randomly rather than all moving in the same direction!