Physics 102 Homework set 3 Solutions L. Weinstein Exercises: ---------- 14.4: The force exerted will quadruple. Force = Area times pressure. If you increase the diameter of the valve stem then you will not change the pressure but you will change the area. A = pi*r^2 = (pi/4)*d^2. If you double the diameter d, then you will quadruple d^2 and you will quadruple the force needed. 14.6: When you go to high elevation, the air pressure decreases. Since pressure times volume is a constant (PV = constant), if you decrease P, then the volume of the football will increase. 14.7: In order to get liquid into the container through the funnel, the air in the container must be able to escape (to make room for the liquid). The ridges make sure that there is room in between the funnel and the bottle mouth for the air to escape. 14.14: Bricks are incompressible; they do not get smaller when pressure is applied. Air is compressible. A cubic meter of air at sea level has a much larger density and hence a larger mass than a cubic meter of air ten kilometers up. If the bricks were made of foam rubber, then the bricks at the bottom would be denser than the bricks at the top, just like the air in the atmosphere. 14.16: 10 m. Vacuum does not suck, air pushes. Air pressure at sea level can only push a column of water up 10 m. (In other words, the pressure of a 10 m column of water is the same as the pressure of the atmosphere). 14.22: The atmospheric pressure does not crush you because you have the same pressure on the inside pushing out as you do on the outside pushing in. The pressure applied by the elephant is not balanced. 14.28: An object in air has a buoyant force corresponding to the weight of the displaced air. This reduces the support force needed to support the object. This would be significant for very low density objects, such as balloons. 14.29: Inertia. The car moves forward. Her head does not move forward until a force makes it do so. Therefore her head moves backward with respect to the car. Similarly, the air in the car does not move forward until a force makes it do so. The air moving backward (with respect to the car) makes the balloon move forwards. 14.34: When the gas is heated, its volume increases. (The atmospheric research-type balloon has lots of extra space to let it expand.) 14.40: The non-rigid balloon will rise higher. Both balloons will rise until the air density outside is equal to the density of the balloon. The non-rigid balloon will expand as the pressure outside decreases, causing its density to decrease and allowing it to rise higher. 14.48: When a steadily flowing gas flows from a larger diameter pipe to a smaller diameter pipe, a) its speed increases b) its pressure decreases c) the spacing between the streamlines decreases Problems: --------------------- 14.2: PV = constant. If the volume decreases by a factor of 10, then the pressure will increase by a factor of 10. 14.4: I have a mass of 80 kg. This means that my volume is V = m/density = 80 kg / (1000 kg/m^3) = 0.08 m^3. I assumed that I have the same density as water (which is certainly accurate to within 10%). The buoyant force is equal to the weight of the displaced air which is F_b = m*g = V * density * g = 0.08 m^3 * (1.2 kg/m^3) * 10 m/s^2 = 1 N (or about 0.2 lb) Not much! Estimation: ------------------------ The big insight here is that the fraction of people picking their nose right now is the same as the fraction of TIME that the average person spends picking his or her nose. This means that we just need to estimate how much time the average person spends picking their nose in one day. It is certainly more than 1 sec and less than 10 minutes (600 sec). Therefore, I'll use 0.5 minute or 30 sec (since it is 30 times more than 1 sec and 20 times less than 10 minutes). Now we need the length of the day in minutes. 1 day = 24 hours * (60 min/1 hour) = 1400 minutes Therefore: # people picking now 1/2 minute -------------------- = ------------ = 1/3000 world population 1400 minutes and: # people picking now = world population / 3000 = 6*10^9 / 3*10^3 = 2*10^6 = 2 million people. Ick! Answers must be in scientific notation with 1 significant figure. Answers should be within a factor of ten of my answer.