2/17/16 Chapter 9 Solids and Fluids Units of Chapter 9 Solids and Elastic Moduli Fluids: Pressure and Pascal s Buoyancy and Archimedes Fluid Dynamics and Bernoulli s Surface Tension, Viscosity, and Poiseuille s Law All solids are elastic to some degree, due to the spring-like structure of the intermolecular bonds holding them together. The stress results in a change in the shape of the solid, called the strain: Stress is defined as the force per unit area: Changes in length, shape, and volume are described by Young s modulus, the shear modulus, and the bulk modulus, respectively. Young s modulus: The strain is related to the stress; how much strain a particular stress causes depends on the material. 1
Stress is proportional to strain until the strain gets too large. Then a material becomes permanently deformed, and finally breaks. Shear modulus: is defined as the ratio of shear stress to the shear strain Bulk modulus (the only one relevant for fluids why?) Question 9.1 Density Question 9.2 Too Much Pressure If one material has a higher density than another, does this mean that the molecules of the first material must be more massive than those of the second? a) yes b) no Consider what happens when you push both a pin and the blunt end of a pen against your skin with the same force. What will determine whether your skin will be punctured? a) the pressure on your skin b) the net applied force on your skin c) both pressure and net applied force are equivalent d) neither pressure nor net applied force are relevant here 2
Pressure is defined as the force per unit area: Unit of pressure: the Pascal (Pa) If the force is at an angle to the surface, the more general form (blue box) is used. Density is defined as mass per unit volume: Question 9.3 You are walking out on a frozen lake and you begin to hear the ice cracking beneath you. What is your best strategy for getting off the ice safely? On a Frozen Lake a) stand absolutely still and don t move a muscle b) jump up and down to lessen your contact time with the ice c) try to leap in one bound to the bank of the lake d) shuffle your feet (without lifting them) to move toward shore e) lie down flat on the ice and crawl toward shore 9.2 Fluids: Pressure and Pascal s The pressure in a fluid increases with depth, due to the weight of fluid above it. Pascal s principle: Pressure applied to an enclosed fluid is transmitted undiminished to every point in the fluid and to the walls of the container. 3
Question 9.7b The Straw II You put a straw into a glass of water, place your finger over the top so no air can get in or out, and then lift the straw from the liquid. You find that the straw retains some liquid. How does the air pressure P in the upper part compare to atmospheric pressure P A? a) greater than P A b) equal to P A c) less than P A Question 9.4 Bubbling Up While swimming near the bottom of a pool, you let out a small bubble of air. As the bubble rises toward the surface, what happens to its diameter? a) bubble diameter decreases b) bubble diameter stays the same c) bubble diameter increases Question 9.5 Three Containers Three containers are filled with water to the same a) container 1 height and have the same surface area at the b) container 2 base, but the total weight of water is different for c) container 3 each. Which container has the greatest total force acting on its base? d) all three are equal Hydraulic lifts and shock absorbers take advantage of Pascal s principle. Since the pressure is constant, a small force acting over a small area can become a large force acting over a large area. There are a number of methods used to measure pressure. 4
Question 9.6 The Falling Bucket When a hole is made in the side of a cola can holding water, water flows out and follows a parabolic trajectory. If the container is dropped in free fall, the water flow will: a) diminish b) stop altogether c) go out in a straight line d) curve upward Absolute pressure is the total force per unit area. We often measure the gauge pressure, which is the excess over atmospheric pressure. Atmospheric pressure historically was measured using a mercury barometer. Cola The pressure corresponding to 1 mm of mercury is called the torr (in honor of Torricelli). 9.3 Buoyancy and Archimedes A body immersed wholly or partially in a fluid experiences a buoyant force equal in magnitude to the weight of the volume of fluid that is displaced: An object s density will tell you whether it will sink or float in a particular fluid. Question 9.9 Imagine holding two identical bricks in place underwater. Brick 1 is just beneath the surface of the water, and brick 2 is held about 2 feet down. The force needed to hold brick 2 in place is: Two Bricks a) greater b) the same c) smaller 9.3 Buoyancy and Archimedes The buoyant force on an object that is completely submerged: 1 2 5
9.3 Buoyancy and Archimedes Question 9.10a Cylinder and Pail I It is the average density that matters; a boat made of steel can float because its interior is mostly air. An object s density may be changed; submarines fill tanks with water to submerge, and with air to rise. An aluminum cylinder and a pail together weigh 29 N, as read on a scale. With the cylinder submerged, the scale reads 20 N. If the displaced water is poured into the pail, what will the scale read? a) less than 20 N b) 20 N c) between 20 N and 29 N d) 29 N e) greater than 29 N Question 9.11 On Golden Pond Question 9.12a Archimedes I A boat carrying a large chunk of steel is floating on a lake. The chunk is then thrown overboard and sinks. What happens to the water level in the lake (with respect to the shore)? a) rises b) drops c) remains the same d) depends on the size of the steel An object floats in water with ¾ of its volume submerged. What is the ratio of the density of the object to that of water? a) ¼ b) 1 / 3 c) 4 / 3 d) ¾ e) 2 / 1 Question 9.12b Archimedes II Question 9.12c Archimedes III The object is now placed in oil with a density half that of water. What happens? a) it floats just as before b) it floats higher in the water c) it floats lower in the water d) it sinks to the bottom An object floats in water with ¾ of its volume submerged. When more water is poured on top of the water, the object will: a) move up slightly b) stay at the same place c) move down slightly d) sink to the bottom e) float to the top 6
9.3 Buoyancy and Archimedes Specific gravity is the ratio of an object s density to that of water at 4 C. In an ideal fluid, flow is steady, irrotational, nonviscous, and incompressible. Steady flow means that all the particles of a fluid have the same velocity as they pass a given point. Steady flow can be described by streamlines. Irrotational flow means that a fluid element (a small volume of the fluid) has no net angular velocity. This condition eliminates the possibility of whirlpools and eddy currents. (The flow is nonturbulent.) In the previous figure, the paddle wheel does not turn, showing that the flow at that point is irrotational. Nonviscous flow means that viscosity is negligible. Viscosity produces drag, and retards fluid flow. Incompressible flow means that the fluid s density is constant. This is generally true for liquids, but not for gases. If the density is constant, of continuity: 7
Bernoulli s equation is a consequence of the conservation of energy. Question 9.15a Fluid Flow Water flows through a 1-cm diameter pipe a) one-quarter connected to a ½-cm diameter pipe. b) one-half Compared to the speed of the water in the c) the same 1-cm pipe, the speed in the ½ -cm pipe is: d) double e) four times 8