Physics 102 Homework set 2 Solutions L. Weinstein Exercises: ---------- 13.10: The blood pressure is greater in your legs than in your upper body because of the weight of the fluid above your legs. (In other words, your legs are further below your head than your torso is, therefore h is greater and therefore p = dgh is greater.) In orbit you are in freefall and feel weightless, therefore the weight of fluid has no effect on the pressure. We showed this in class when I dropped the cup of water with the hole in it. Therefore in orbit, your blood pressure will be the same in your legs and your torso. 13.12: Both teapots are the same width. The one on the left is taller. However, both teapots have spigots at the same height. Therefore, you can put the same amount of water in each teapot before it overflows. 13.16: Lead and aluminum both sink; therefore both displace their volume of water, not their mass. A 10-N block of lead has a greater density and hence a smaller volume than a 10-N block of aluminum (since d = m/V and thus V = m/d). Therefore, the lead displaces less water than the aluminum. The answers to this question are identical to those of question 15 since all 1-kg blocks (of anything) have a weight of 10 N. The answers to this question are different from question 14. In question 14, both blocks have the same volume and therefore displace the same amount of water. 13.23: The stones hurt your feet less when you are in deep water because the water supports more of your weight. Therefore the stones exert less force on your feet when you are standing in deep water. 13.30: The buoyant force on the volleyball is equal to the weight of the displaced water. When the volleyball is held below the surface, it displaces much more water than when it is floating on the surface, therefore the buoyant force is much greater when it is held underwater. 13.34: When the iron is suspended below the wood, the wood will float higher than if the iron is on top of the wood block. In either situation, the total weight of the displaced water equals the total weight of the iron plus wood. When the iron is on top, the wood must displace all of that water. When the iron is below, the iron displaces some water and the wood displaces the rest. Therefore, when the iron is below, the wood does not have to displace as much water and therefore floats higher in the water. 13.38: The water would go down. We did this in class twice, once with the iron weights in the boat being thrown overboard (the soda bottle boat in the aquarium) and once with the iron spike in the iceberg question. When the battleship floats, it displaces its weight of water; when it sinks it displaces it volume of water. Since the battleship is denser than water, its volume of water is less than its weight. 13.44: The buoyant force on the ship does not change. The total force on the ship is zero (since the ship is not accelerating up or down), therefore the buoyant force equals the weight of the ship in both cases. The ship needs to displace more fresh water to achieve the same buoyant force. 13.46: This means that the fluid displaced by the brain is 14.5 N. It gives us no information about the amount of fluid remaining. 13.50: If anything is placed in half-full bucket of water, its weight will increase. We tried this in class with a beaker of water on a scale when we put in something that sank (a paperclip), something that floated (some balled-up aluminum foil), and then a finger. If you place something that floats in a brim-full bucket of water, its weight will not change (since the object displaces its weight of water). 13.52: If you increase the gravitational field of the Earth, then the weight of the fish will increase and the weight of the diplaced water will also increase by the same amount. The fish will stay at the same depth. Problems: ------------- 13.8: a) the swimmer plus belt weighs 600 N (weight = mg), b) the swimmer's volume is V = m/d = 60 kg / (1000 kg/m^3) = 0.06 m^3 c) When she is under water, the buoyant force is also 600 N because she is neutrally buoyant. Therefore the net force is zero. Estimation: ---------------- There are 6 billion = 6*10^9 people in the world. You can crowd about 5 people into a square 1 m (about 3 feet) on a side. This means that 6*10*9 people will need about 10^9 m^2 of area. Now we need to convert this to km^2. A = 10^9 m^2 * (1 km / 10^3 m) * (1 km / 10^3 m) = 10^3 km^2 Thus, we can fit the entire population of the world into Virginia Beach if we cram everybody together. Wow!