Capillaries are the narrowest elements in the blood transport system of animals. They connect the arteries (the vessels that carry blood away from the heart) to the veins (the vessels that carry blood back to the heart). They are the place where the chemicals that the blood is carrying are taken from source regions (lungs for air, intestines for food, glands for hormones) and delivered to the cells that need them. They are pretty small-about 5 um in diameter. One of the interesting questions about this process is: how do oxygen molecules know where to go? For example, Wikipedia says that red blood cells "take up oxygen in the lungs or gills and release it while squeezing through the body's capillaries." In order to consider this let's make an oversimplified model in which oxygen diffuses into the blood stream in the lungs, is carried by fluid flow out to the cells where it diffuses out. (In reality, the oxygen is bound to hemoglobin, carried, and released, but the beginning and end processes are as described here.) A. Consider a capillary in an alveolus in the lung. The density of oxygen inside the capillary is 0.3 million molecules/(um) and in the air outside is about 5 million molecules/(um) 3 Capillaries Arteriole Venule Artery capillaries Tissue cells Source: Wikimedia commons Which way will be the net flow of oxygen across the membrane? O equal flows into and out of the capillary O out of the capillary O into the capillary B. Consider an individual molecule in the air outside the alveolus. Capillary beds Connective tissue Alveolar sacs Alveolar duct Mucous gland Mucosal lining Pulmonary vein Alveoli Pulmonary artery Atrium Source: Wikimedia commons How is it moving? O moving within the capillary O moving out of the capillary into the muscle cell moving in random directions C. Now consider a capillary inside a muscle. The muscle has done work and used up its oxygen. The density of oxygen inside the capillary is 1 million molecules/(um)3 and in the fluid surrounding the muscle is 0.3 million molecules/(um) 3. Which way will the net oxygen flow be across the membrane? O out of the muscle cell into the capillary O into the muscle cell out of the capillary O equally in both directions D. Consider an individual molecule in the capillary in part C (after is has been released by the hemoglobin). How is it moving? O into the muscle cell in random directions O remaining within the capillary E. Fick's Law tells us how a concentration difference drives flow: J = -DAn/Ax. If the membrane in the alveolus (parts A and B) is 7 nm thick, and the diffusion constant, D, for oxygen through the membrane is 6 x 10-5 (um)2/s, calculate the rate of flow through the alveolar membrane. molecules/um-/s.If you are lying down and stand up quickly, you can get dizzy or feel faint. This is because the blood vessels don't have time to expand to compensate for the blood pressure drop. If your brain is 0.4 m higher than your heart when you are standing, how much lower is density of blood plasma is about 1025 kg/m and suppose your maximum (systolic) pressure of the blood at the heart is 121.2 mm of Hg (Note that 120 mm of Hg = 16 kp = 1.6 x 104 N/m2). Since most doctors still use mm of Hg, give your result in those units. Pressure at brain = mm of Hg.In this problem, take atmospheric pressure to be 1.0 x 105 Pa, and the density of water to be 1000 kg/m3. Use g = 10 N/kg. In 1690, Sir Edmund Halley (of comet fame) invented the diving bell. A drawing is shown below. Halley's bell was made of wood and roughly cylindrical in shape. We will treat the bell as if it were a cylinder 3 m high and 1 m in diameter. Air supply Lowered in weighted barrel Escaping air Used air was expelled here The bell is fully submerged underwater so that the bottom face of the bell is at a depth of 28 m. (a) What is the water pressure at the bottom of the bell? Pa What is the water pressure at the top of the bell? Pa (b) What is the force of the water on the bottom face of the bell? What is the force of the water on the top face of the bell? c) What is the net force of the water pushing on the top and bottom of the bell, and what direction is it? N, ---Select--- (Verify that this is the same as the buoyant force calculated using the equation B = Pfluid submerged9.) (d) If the bell and its contents have a mass of 840 kg, what is the net force on the bell, and what direction is it? Fnet= N, ---Select--The curator of a science museum is transporting a chunk of meteorite iron (i.e., a piece of iron that fell from the sky -- see picture at left) from one part of the museum to another. Since the chunk of iron weighs 1260 N and is too big for her to lift by herself, she is using a hand cart (see figure at right). While passing through the marine mammals section of the museum, she accidentally hits a bump and the meteorite tips off the handtruck and into the dolphin pool. Fortunately, the iron didn't hit a dolphin, but it quickly sinks to the bottom. Unfortunately, the meteorite has many sharp edges and she is worried the dolphins, curious creatures that they are, will come to inspect it and be cut when they rub against it. She wants to get it up out of the pool as quickly as possible. Fortunately, the meteorite has lots of holes in it and there are ropes with hooks on one end lying around. If she could get a hook into one of the holes, she might be able to pull it up to the top. Unfortunately, she remembers that the meteorite is too heavy for her to lift. (a) Will the fact that the meteorite is in the pool under water make it feel heavier or lighter to lift (slowly) with the rope? O Heavier Lighter O The same (b) The meteorite is sitting on the concrete bottom of the pool. Is the force the meteorite exerts on the bottom bigger or smaller than the force it would exert if the pool had no water in it? Bigger O Smaller The same (c) The pool is 3.7 m deep, the density of the meteorite is about 7800 kg/ms, and the density of water is 1000 kg/m . What is the buoyant force on the meteorite while it's fully submerged in the pool? B = N (d) Before the curator attaches the rope to the meteorite, what is the normal force of the bottom of the pool on the meteorite? n = (e) After managing to get the hook into one of the meteorite's holes, what is the minimum force the curator would need to apply with the rope to lift the meteorite? minimum force = (f) Assuming the curator can apply a maximum force of 450 N, will she be able to lift the meteorite? Yes ON O Cannot be determined (g) The curator applies her maximum force to the meteorite with the rope. What is the normal force of the bottom of the pool on the meteorite as she's pulling the rope? n = (h) Instead of pulling on the rope by hand, the curator attaches the rope to a crane for transferring dolphins in and out of the pool. The crane is able to apply the force necessary to lift the meteorite at constant speed. What is the tension in the rope? (Ignore the drag force from the water.) T = (i) When the meteorite is halfway to the surface, however, the rope breaks. What is the acceleration of the meteorite as it sinks back to the bottom of the pool? (Ignore the drag force from the water.) a = m/s/ (j) With a new rope, the curator again uses the crane to lift the meteorite, but now the crane gets stuck when the meteorite is half submerged at the surface of the pool. What is the tension in the rope at this point? T =A particle with a mass of 2.95 kg is acted on by a force F acting in the x-direction. If the magnitude of the force varies in time as shown in the figure below, determine the following. Fx (N) 8 6 4 2 t (s) 2 3 4 5 (a) impulse of the force (in kg . m/s ) kg . m/s (b) final velocity of the particle (in m/s) if it is initially at rest m/s (c) Find the final velocity of the particle (in m/s) if it is initially moving along the x-axis with a velocity of -1.70 m/s. m/sA baseball with a mass of 137 g is thrown horizontally with a speed of 39.3 m/s (88 mi/h) at a bat. The ball is in contact with the bat for 1.00 ms and then travels straight back at a speed of 46.0 m/s (103 mi/h). Determine the average force (in N) exerted on the ball by the bat. Neglect the weight of the ball (it is much smaller than the force of the bat) and choose the direction of the incoming ball to be positive. (Indicate the direction with the sign of your answer.) N