Review 29:008 Exam 2. Ch. 6 Energy & Oscillations.

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Review 29:008 Exam 2 Slide 2 Ch. 6 Energy & Oscillations Slide 3 Kinetic Energy, and the Work-Energy Principle Apply a force to accelerate a bus: the work done here is We define the kinetic energy: Slide 4 6-3 Kinetic Energy, and the Work-Energy Principle This means that the work done is equal to the change in the kinetic energy: If the net work is positive, the kinetic energy increases. If the net work is negative, the kinetic energy decreases. (6-4) Slide 5 6-3 Kinetic Energy, and the Work-Energy Principle Because work and kinetic energy can be equated, they must have the same units: kinetic energy is measured in joules. Slide 6 6-4 Potential Energy An object can have potential energy by virtue of its surroundings. Familiar examples of potential energy: A wound-up spring A stretched elastic band An object at some height above the ground Slide 7 Potential Energy In raising a mass m to a height h, the work done by the external force is We therefore define the gravitational potential energy: (6-5a) (6-6) Slide 8 Potential Energy This potential energy can become kinetic energy if the object is dropped. If, where do we measure y from? It turns out not to matter, as long as we are consistent about where we choose y = 0. Only changes in potential energy can be measured. Slide 9 Potential Energy Potential energy can also be stored in a spring when it is compressed; the figure below shows potential energy yielding kinetic energy. Slide 10 6-4 Potential Energy The force required to compress or stretch a spring is: where k is called the spring constant, and needs to be measured for each spring. Slide 11 Potential Energy The force increases as the spring is stretched or compressed further. We find that the potential energy of the compressed or stretched spring, measured from its equilibrium position, can be written: Slide 12 Conservative and Nonconservative Forces If friction is present, the work done depends not only on the starting and ending points, but also on the path taken. Friction is called a nonconservative force. Slide 13 Conservative and Nonconservative Forces Potential energy can only be defined for conservative forces. Slide 14 Conservation of Energy. total energy: Total energy conserved for a system that has no non-conservative forces acting on it Slide 15 Problem Solving Using Conservation of Mechanical Energy Slide 16 If there is no friction, the speed of a roller coaster will depend only on its height compared to its starting height. Slide 17 Problem Solving Using Conservation of Mechanical Energy For an elastic force, conservation of energy tells us: Slide 18 Power Power is the rate at which work is done (6-17) In the SI system, the units of power are watts: Slide 19 Ch. 7 Momentum & Impulse Slide 20 Momentum and Its Relation to Force Momentum is a vector symbolized by the symbol p, and is defined as The rate of change of momentum is equal to the net force: Slide 21 Conservation of Momentum During a collision, total momentum does not change: Slide 22 Conservation of Momentum The law of conservation of momentum states: The total momentum of an isolated system of objects remains constant. Slide 23 Conservation of Momentum Momentum conservation works for a rocket as long as we consider the rocket and its fuel to be one system, and account for the mass loss of the rocket. Slide 24 Collisions and Impulse Impulse = change in momentum = average force X time Slide 25 Conservation of Energy and Momentum in Collisions Momentum is conserved in all collisions. Collisions in which kinetic energy is conserved as well are called elastic collisions, and those in which it is not are called inelastic. Slide 26 Center of Gravity The center of gravity can be found experimentally by suspending an object from different points. The CM need not be within the actual object a doughnuts CM is in the center of the hole. Slide 27 Ch. 8 Rotational Motion Slide 28 Angular Quantities Angular displacement: The average rotational velocity is defined as the total angular displacement divided by time: Slide 29 Angular Quantities The rotational acceleration is the rate at which the angular velocity changes with time: Slide 30 Angular Quantities Correspondence between linear and rotational quantities: Slide 31 Constant Angular Acceleration The equations of motion for constant angular acceleration are like those for linear motion: Slide 32 Torque The perpendicular distance from the axis of rotation to the line along which the force acts is called the lever arm. Torque = Perpendicular Force X Lever Arm Slide 33 Rotational Inertia The quantity is called the rotational inertia of an object. The distribution of mass matters here these two objects have the same mass, but the one on the left has a greater rotational inertia, as so much of its mass is far from the axis of rotation. Slide 34 Rotational Inertia The rotational inertia of an object depends : Mass Shape Location of axis Slide 35 Angular Momentum and Its Conservation In analogy with linear momentum, we can define angular momentum L: Conservation: If the net torque on an object is zero, the total angular momentum is constant. Slide 36 Angular Momentum and Its Conservation Therefore, systems that can change their rotational inertia through internal forces will also change their rate of rotation: Slide 37 Vector Nature of Angular Quantities Vectors for rotational velocity & Angular momentum: point along the axis of rotation direction is found using a right hand rule: Slide 38 Ch. 9 Fluids Slide 39 Density The density of an object is its mass per unit volume: Slide 40 Pressure in Fluids Pressure is defined as the force per unit area. the units are pascals: 1 Pa = 1 N/m 2 Pressure is the same in every direction in a fluid at a given depth; if it were not, the fluid would flow. Slide 41 Pressure in Fluids Also for a fluid at rest, there is no component of force parallel to any solid surface once again, if there were the fluid would flow. Slide 42 Pascals Principle If an external pressure is applied to a confined fluid, the pressure at every point within the fluid increases by that amount. This principle is used in hydraulic lifts Slide 43 Buoyancy and Archimedes Principle For a floating object, the portion of the object that is submerged displaces a mass of water equal to the mass of the entire object. Slide 44 Continuity of Flow Slide 45 Bernoullis Principle Lift on an airplane wing is due to the different air speeds and pressures on the two surfaces of the wing. Slide 46 Ch. 10 Temperature & Heat Slide 47 Heat As Energy Transfer Heat is a form of energy. 1 cal is the amount of heat necessary to raise the temperature of 1 g of water by 1 Celsius degree. Slide 48 Definition of heat Heat is energy transferred from one object to another because of a difference in temperature. Slide 49 Internal Energy The total of all the energy of all the molecules in a substance is its internal energy. Temperature: measures average kinetic energy of molecules Internal energy: total energy of all molecules Slide 50 Specific Heat The amount of heat required to change the temperature of a material is proportional to: mass temperature change specific heat, c (a material propert) Slide 51 1Latent Heat Energy is required for a material to change phase, even though its temperature is not changing. Slide 52 Latent Heat Heat of fusion, L F : heat required to change 1.0 kg of material from solid to liquid Heat of vaporization, L V : heat required to change 1.0 kg of material from liquid to vapor Slide 53 Latent Heat The total heat required for a phase change depends on the total mass and the latent heat: Slide 54 Heat Transfer: Convection Convection occurs when heat flows by the mass movement of molecules from one place to another. It may be natural or forced; both these examples are natural convection. Slide 55 Heat Transfer: Radiation The most familiar example of radiation is our own Sun, which radiates at a temperature of almost 6000 K. Slide 56 Summary p. 1 In an isolated system, heat gained by one part of the system must be lost by another. Calorimetry measures heat exchange quantitatively. Phase changes require energy even though the temperature does not change. Heat of fusion: amount of energy required to melt 1 kg of material. Heat of vaporization: amount of energy required to change 1 kg of material from liquid to vapor. Slide 57 Summary p. 2 Heat transfer takes place by conduction, convection, and radiation. In conduction, energy is transferred through the collisions of molecules in the substance. In convection, bulk quantities of the substance flow to areas of different temperature. Radiation is the transfer of energy by electromagnetic waves. Slide 58 Ch. 11 Thermodynamics Slide 59 The First Law of Thermodynamics The change in internal energy of a closed system will be equal to the energy added to the system minus the work done by the system on its surroundings. This is the law of conservation of energy, written in a form useful to systems involving heat transfer. Slide 60 Isothermal process In order for an isothermal process to take place, heat flows from a hot body (heat reservoir) to a cold body. An isothermal process is one where the temperature does not change. Slide 61 Adiabatic Processes An adiabatic process is one where there is no heat flow into or out of the system. Slide 62 The Second Law of Thermodynamics Introduction The process above doesnt happen. This tells us that conservation of energy (First Law) is not the whole story. If it were, movies run backwards would look perfectly normal to us! Slide 63 The Second Law of Thermodynamics Introduction The second law of thermodynamics is a statement about which processes occur and which do not. There are many ways to state the second law; here is one: Heat can flow spontaneously from a hot object to a cold object; it will not flow spontaneously from a cold object to a hot object. Slide 64 15-5 Heat Engines It is easy to produce thermal energy using work, but how does one produce work using thermal energy? This is a heat engine; mechanical energy can be obtained from thermal energy only when heat can flow from a higher temperature to a lower temperature. Slide 65 Heat Engines We will discuss only engines that run in a repeating cycle; the change in internal energy over a cycle is zero, as the system returns to its initial state. The high temperature reservoir transfers an amount of heat Q H to the engine: part of it is transformed into work W the rest, Q L, is exhausted to the lower temperature reservoir. Note that all three of these quantities are positive. Slide 66 Heat Engines A steam engine is one type of heat engine. Slide 67 Heat Engines The efficiency of the heat engine is the ratio of the work done to the heat input: Slide 68 Heat Engines The Carnot engine is idealized, as it has no friction. Each leg of its cycle is reversible. The Carnot cycle consists of: Isothermal expansion Adiabatic expansion Isothermal compression Adiabatic compression Slide 69 Heat Engines Slide 70 Carnot engine efficiency is: (15-5) From this we see that 100% efficiency can be achieved only if the cold reservoir is at absolute zero, which is impossible. Real engines have some frictional losses; the best achieve 60-80% of the Carnot value of efficiency. Slide 71 Refrigerators, Air Conditioners, and Heat Pumps These appliances can be thought of as heat engines operating in reverse. By doing work, heat is extracted from the cold reservoir and exhausted to the hot reservoir. Slide 72 Refrigerators, Air Conditioners, and Heat Pumps Slide 73 A heat pump is like an air conditioner turned around, so that the coils dump heat inside the house: Slide 74 Entropy and the Second Law of Thermodynamics Another statement of the second law of thermodynamics: The total entropy of an isolated system never decreases. Slide 75 Order to Disorder Entropy is a measure of the disorder of a system. This gives us yet another statement of the second law: Natural processes tend to move toward a state of greater disorder. Example: If you put milk and sugar in your coffee and stir it, you wind up with coffee that is uniformly milky and sweet. No amount of stirring will get the milk and sugar to come back out of solution.