Physics 102 Homework set 1 Solutions L. Weinstein Projects: ---------- 13.1: An egg placed in tapwater (ie: fresh water) sinks. Therefore it has a higher density than tapwater. When you add enough salt (and it takes a lot), the egg will float. Thus the egg has a lower density than salt water. (Note that it is much easier to add the salt if you take the egg out first.) One Steps: ------------ 13.2: p = dgh = (1000 kg/m^3) * (10 m/s^2) * 220 m = 2.2*10^6 kg/m s^2 = 2.2*10^6 N/m^2 = 2.2*10^6 Pa Exercises: ------------ 11.4: It takes a few seconds between when a woman wearing too much perfume enters a room and when you smell her. Since the distance between you may be 5-10 m (15-30 ft), this means that the perfume molecule covers the distance at an average velocity of only a few meters per second, much less than the molecule's average speed of 300 m/s. However, the molecule can only travel a few millionths of a meter before it collides with another molecule and bounces off in a different direction. Thus, the path of a gas molecule in the room is a lot like the path of an electron in a wire (see figure 23.14) or the path of a small child in a crowded room. 11.6: If no molecules could escape from your body, then no one could smell you. In order to smell something (or someone), molecules from that object must travel from it to you and enter your nose. 11.18: Cobalt has atomic number 27 (see the table of elements on p219), therefore all Cobalt atoms have 27 protons. a) Cobalt 59 has 27 protons and 59-27=32 neutrons. Cobalt 60 has 27 protons and 33 neutrons. b) If the atom is neutral, then the number of electrons equals the number of protons. Therefore, both Cobalt 59 and 60 each have 27 electrons. 11.36: Nitrogen has 7 protons and some number, N, of neutrons. (We do not know the number of neutrons because the question does not specify which isotope of nitrogen decays.) After one of the neutrons decays to a proton, the nucleus will have 8 protons and N-1 neutrons. Thus, it will now be oxygen. 13.2: Being stepped on by the woman will hurt more. Pressure hurts, not force. Remember the seat of nails. The force is the same whether there is one nail or several hundred, but the pressure is much greater if you sit on a single nail than on several hundred. We discussed this problem in class. If the woman is wearing spike heels, then the area she exerts her weight on is only about 1 in^2. Therefore the pressure is about 100 lb/in^2. (Since the weights are given in customary units, I use customary units to solve the problem. Metric solutions are fine too.) The man has a weight of 200 lbs. The total area of his shoes is about 2 shoes x 12" x 4" = 100 in^2. Therefore he exerts a pressure of about 2 lb/in^2 or about 100 times less then the woman. 13.3: We need to know a) how much an elephant weighs and b) how big its feet are. I googled elephants and found that they weigh between 4 and 7 tons. I'll use 5 tons (10,000 lbs or 5000 kg). An elephant's foot is a bit bigger than 1 foot (30 cm) in diameter, so I'll assume it is 16". Then the area is about 16" by 16" = 256 in^2. (Yes, I know the area of a circle is pi*r^2, but since I am estimating the diameter and estimating the mass, it seems very silly to precisely calculate the area corresponding to an estimated diameter.) Therefore the area of all 4 feet is 1000 in^2. This means that the pressure exerted by the elephant is 10,000 lb/ 100 in^2 = 100 lb/in^2. Thus the elephant and the lady in spike heels exert about equal pressure on the ground. Yikes! 13.6: A sharp knife cuts better than a dull one because you can exert much more pressure. You can exert the same force whether the knife is sharp or dull. However, a the edge of the blade of a sharp knife has a much small area than the blade edge of a dull knife. Therefore, the pressure is much greater. Problems: (number 4 corrected on 2/3/06) ----------------- 13.2: d = m/V = 6 kg/ 1 liter = 6 kg/liter. Alternatively, you can convert the answer to kg/m^3. d = 6 kg/l * (1000 l / 1 m^3) = 6000 kg/m^3 13.4: The pressure at that depth is p = dgh = (1000 kg/m^3) * (10 m/s^2) * 2 m = 2*10^4 N/m^2 = 2*10^4 Pa That pressure is exerted on an area A = 1 cm^2 * (1 m / 100 cm) * (1 m / 100 cm) = 1*10^(-4) m^2 Therefore the force is F = PA = 2*10^4 N/m^2 * 1*10^(-4) m^2 = 2 N. That is about 1/2 lb or the weight of an 8 oz cup of water. Not much. Estimation (extra credit): ------------------------------- 3 m under water, the water pressure on your body is p = dgh = (1000 kg/m^3) * (10 m/s^2) * 3 m = 3*10^4 N/m^2 = 3*10^4 Pa My body is about 2 m tall and 1/2 m wide so the area of the front of my body (and the back too) is A = 2 m * 0.5 m = 1 m^2 Therefore the force on the front of my body is F = 3*10^4 Pa * 1 m^2 = 3*10^4 N = 3 tons! The same force is exerted on the back of my body. That is a LOT of force.