If we change the quantity causing the deformation from force to force per unit area, we get a relation that does not depend on area.

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1 2/24 Chapter 12 Solids Recall the rigid body model that we used when discussing rotation. A rigid body is composed of a particles constrained to maintain the same distances from and orientations relative to the particles around them. Rigid bodies reasonably well describe solids. The role of the particles is played by atoms. An amorphous solid is one where the atoms have no regular structure. In a crystalline solid, atoms are placed in an orderly structure. Most of the glass you see on a daily basis is amorphous. Crystalline glass usually makes goblets and punch bowls. The sodium (Na) and chlorine (Cl) atoms in salt form a cubic structure. Sugar is amorphous. Elasticity Consider a rod immobilize one end of the rod apply a force F to the other end. The force will cause the rod to change in length by L. As long as the force is not too large, the force and the change in length are proportional. How the force and change in length are related depends on the geometry of the rod. Suppose we apply the same force F to two rods of the same material and same length, one fat and one skinny. The skinny rod will stretch farther than the fat one. The amount that a rod stretches depends on the cross-sectional area of the rod A. If we change the quantity causing the deformation from force to force per unit area, we get a relation that does not depend on area.

2 We define the stress produced by the force F on the rod as the force divided by the cross-sectional area of the rod: If we apply the same stress to any rod made of the same material and the same length, we find the same change in length. Suppose I have two rods identical except that one rod is longer than the other. Applying the same stress to both rods produces a larger change in length for the longer rod. 9/15 Model a rod as a string of atoms separated by springs. Each atom is at rest, which means that the net force on each atom is the zero. This means that each spring has the same force F applied to it each spring stretches the same amount. The more springs in the rod, the more stretch for the rod. The fractional stretch change in length divided by the length will be the same for both the short rod and the long rod. We define strain to be the change in length divided by the length: Stress is the force-like quantity that causes deformation. Strain is related to the deformation. Stress causes strain. As long as the stress is not too large, the stress and strain are proportional.

3 The constant of proportionality is called the elastic modulus or Young s modulus. It depends on the material in question. Scaling Giant Ants Small ant of size about 2 mm Large ant of size 20 m Large ant is 10,000 times as large as the small ant. A small ant can lift 10 times its own weight Assume that the large ant is made of the same material as the small ant. Note that the lifting capability of an ant is proportional to the size of the ant. This means that the large ant can lift 10,000 times as much as the small ant. The strength of an ant leg is proportional to the leg s cross-sectional area, which is proportional to the square of the length of the ant. This means that the strength of the large ant leg is 10,000 2 = 100,000,000 times stronger than the small ant leg. The weight of an ant is proportional to its volume, which is proportional to the cube of the size of the ant. This means that the weight of the large ant is 10,000 3 = 1,000,000,000,000 times the weight of the small ant. Since the weight increases by a trillion times and the lifting ability by only 10,000 times, the large ant can lift one-100 millionth of its weight. It legs are 10,000 times weaker compared to its weight for the large ant vs. the small ant. The large ant can t stand up and if it tries, it will break its legs. Chapter 13 Liquids Liquids take the shape of their container. Consider a glass of water it s hard to think of the force of the water on the glass or the force of the glass on the water. We can think of the force applied to a small area on the side of the

4 glass. The size of the force depends on the size of the area we can remove the area from the equation by dividing the force by the area this gives pressure. Pressure is force per unit area in a fluid. SI unit N/m 2 = pascal = Pa Pressure in a liquid supports the liquid above. The pressure is larger at greater depths. The increase in pressure is proportional to the change in depth. Also depends on density of the liquid the greater the density, the higher the pressure. Buoyancy Because pressure increases with depth, the pressure on the bottom of a submerged body will be greater than the pressure on the top of the body, which produces an upward force on the body called the buoyant force. If we imagine replacing the body with a body made of the fluid, the fluid body will sit at rest in the remainder of the fluid. By at rest, we mean no flow (in air, no breeze or wind). The net force on the fluid body must be zero since it is at rest. This means that the buoyant force on the fluid body must be the same as the weight of the fluid body. The buoyant force on the fluid body will be the same as the buoyant force on the original body. This leads to Archimedes Principle: Archimedes Principle: The buoyant force on a body either completely or partly submerged in a fluid is equal in magnitude but opposite in direction to the weight of the fluid displaced by the body. We can use this principle to measure the densities of things: where is the density of the body, W is the density of water, W is the weight of the body measured in a vacuum (air), and W is the apparent weight of the body when submerged. A body will sink if it is denser than water and will float if it is less dense than water.

5 Pascal s Principle Pascal s Principle: Any change in pressure at any point in a fluid is transmitted throughout the fluid undiminished. Used in hydraulics systems: Automobile brakes press you brake pedal, you increase the pressure in the brake fluid. This increases the pressure in the fluid at the brakes at the wheels and pushes the brake pads against the wheels to provide friction to slow the car. Consider the hydraulic lift shown in the picture at right. There is fluid throughout the system from small piston to the large piston. Pressure depends only on depth, which means that the pressure just below the small piston must be the same at that just below the large piston. This means that the force on the smaller piston is smaller than the force on the large piston. Thus, a small force can support the weight of the car. Note, though, to lift the car a certain height, the small piston must move a much greater distance. A real hydraulic lift system works by pumping fluid into the system which increases the pressure from a reservoir of fluid. Chapter 14 Gases and Plasmas Atmosphere roughly 80% nitrogen and 20% oxygen with traces of other gases. The air is a fluid and has a pressure atmospheric pressure plays a role in the weather. Measuring Pressure Mercury Barometer Made as follows: Capillary tube about a meter long closed at one end open at the other. Fill the tube to the brim with mercury. Close the open end and invert in a pool of mercury. Open the end of the tube and some but not all of the mercury will flow out of the tube. When stabilized, the air pressure down on the pool of mercury causes the mercury to be supported in the tube.

6 The height of the mercury in the tube is a measure of the air pressure. A unit for pressure mmhg millimeter of mercury or cmhg. Note one standard atmosphere is 760 mmhg = 101,300 Pa Note: when you measure the pressure in your tire, you are measuring gauge pressure the difference between the pressure in the tire and atmospheric pressure. Buoyancy in Air first flight, lighter than air should be less dense than air flight. Balloon, dirigible Bernoulli s Principle involves fluid flow Bernoulli s Principle: Regions of low fluid pressure are regions of high fluid speed and regions of high fluid pressure are regions of low fluid speed. Can be understood from the work-energy principle. Consider a high-pressure region and a low-pressure region the pressure difference will cause fluid to flow from high to low pressure. We can translate the pressure difference into a net force in the direction of high to low pressure. The displacement of the air is in the direction of the flow from high to low pressure. The net force does positive work on the air as it flows, which increases its kinetic energy, which means higher speed. This leads to Bernoulli s principle as stated above. In weather high pressure is a balmy day with at most gentle breezes low pressure is a storm with blustery winds. Examples: Air Plane Wing

7 Bernoulli air above the wing has greater speed, lower pressure, than air under the wing produces a net upward force on the wing called lift. Newton wing applies a downward force on the air deflecting it downward, which, by Newton s third law means that the air applies an upward force on the wing called lift. Actually: Just two ways of describing the same thing. Bernoulli is derived from Newton. Hurricane Consider a house with a flat roof. High speed and low pressure above the roof, zero speed and high pressure below the roof. Upward force produced can tear the roof off the house. Floating Beach Ball In department store air blast by vacuum cleaner (in reverse) high speed low pressure in the stream is enough to support a beach ball because the speed outside the stream is zero. Chapter 15 Temperature, Heat, and Expansion Terminology: 1. Temperature You will feel hot if the air molecules are moving rapidly and cold if they are moving slowly. The faster the molecules move, the more kinetic energy they have. Temperature is a measure the average translational kinetic energy of the molecules in a system. 2. Thermal Energy total kinetic energy of the molecules in a system including rotational and vibrational. 3. Internal Energy the thermal energy of a system plus the total interaction potential energy between molecules. 4. Heat a manifestation of energy transfer between two systems. Systems do NOT contain heat! When two systems exchange internal energy, we talk of heat as the energy transferred or energy in transit. For an ideal gas whose molecules have no interaction potential energy, thermal energy and internal energy are the same. Measuring Temperature:

8 Celsius scale: freezing point of water is 0 C and the boiling point of water is 100 C. Fahrenheit: freezing point of water is 32 F and the boiling point of water is 212 F. Put a thermometer into ice-water mix and make a mark and call it either 0 C or 32 F and then into boiling water and mark either 100 C or 212 F and then divide the middle into either 100 divisions or 180 divisions. Absolute Temperature Scales There is a minimum temperature, that is, there is a limit to how cold a system can get. Remove heat from a system and its temperature and average kinetic energy per molecule drops. Eventually, the average KE drops to zero temperature can t get lower than this. This is absolute zero C We can use absolute zero as one of our reference temperatures. As a second reference temperature, we will use the temperature of the triple point of water. The triple point of water is the precise temperature and pressure (roughly 5% of an atmosphere) at which ice, water, and water vapor can coexist.: 0.01 C. We define the kelvin temperature unit such that the temperature of the triple point is K. Note that the freezing point of water is K and that the kelvin is the same size as the Celsius degree.