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Energy Makes it Go!! Energy? What energy? • • • • nervous energy? negative energy? positive energy? Nuclear ( not nucular!) energy? energy crisis? What is Energy? ENERGY Motivation: Assume you want to study the kinematics v(t) or x(t) of the sliding object in the picture. It is too complicated w/out the exact knowledge of the path. This, and other, kind of studies are greatly simplified if one uses the concept of energy. ENERGY Motivation: Assume you want to study the kinematics v(t) or x(t) of the sliding object in the picture. It is too complicated w/out the exact knowledge of the path. This, and other, kind of studies are greatly simplified if one uses the concept of energy. • It is hard to define Energy but we can say that it relates to the state, the condition of the object or the configuration of a system of objects. e.g. the kinetic condition/state of the object (kinetic energy). Other examples include a spring in compressed state (potential energy), a piece of metal in hot condition (thermal energy) etc. • Kinetic or Potential energy are referred to as form of Mechanical energy. Thermal energy is considered to be a different category. • Energy is a scalar quantity. Energy is like $$$ • • • • • • • you can change it it can do useful things for you you can save it or spend it its better to have it than not have it you can waste it (Chapter Five) useless by itself: merely a concept this is one way to think about it (analogy only!!!) two kinds of crashes • bounce back elastic • stick together inelastic • What’s the difference? Vis Viva • (living force) • for elastic (bounce back) collisions, vis viva is the same before and after • for inelastic (sticky) collisions, vis viva is smaller after collisions • we call this KINETIC ENERGY energy of motion! Kinetic Energy • Kinetic Energy characterizes the state of motion of an object • If an object moves, then it has kinetic energy. It is clear that this statement is reference frame dependent. For an object of mass m and moving with velocity v its kinetic energy (K) is defined as: 1 2 K = mv 2 • Kinetic Energy can’t be negative, it is always positive or zero. Is rock climbing dangerous? • potential to gain large kinetic energy (by falling down!) • Energy due to something’s position is POTENTIAL ENERGY Potential Energy characterizes the configuration of a system of particles. Potential Energy • Two common subcategories of potential energy are: • Gravitational potential energy: state of separation between objects which attract each other with gravitational force. It increases with distance. • Elastic potential energy: state of compression of elastic objects (e.g. spring) Determining potential energy values • The graviational potential energy of an object (in a system) is equal to the product of its weight times the distance (height) of separation P.E.=(Weight)x(height) How is energy exchanged? • The Pit and the Pendulum (example) • What happens to that energy if we stop at top??? • stored as potential energy So what? • pendulum: kinetic energy and potential energy are both always changing • Is anything that is not changing? – clue: always comes back to same height when changes direction • kinetic plus potential energy does not change • It is called MECHANICAL ENERGY CONSERVED (stays the same) Mechanical Energy • As we mentioned before we call mechanical energy of a system the sum of its kinetic and potential energy. E = K.E + P.E. • If there are no frictional forces, i.e. losses of energy into heat mechanical energy is conserved • MECHANICAL ENERGY CONSERVED (stays the same) Work • Objects can exchange energy – • via either forces or heat • It is called work, which is the process of transferring energy between two objects via a force. • Who is doing work? the force E.g. If you apply a force to an object it will accelerate, i.e. its velocity will increase and so does its kinetic energy; the applied force is transferring energy from one object to another, it is doing work. Work • Work is energy transferred from (to) an object by means of a force acting on it • If it is “To” an object; then we say that the force is doing positive work • From an object; then we say that the force is doing negative work. • Note: Transfer of energy doesn’t mean flow of any material or exchange of mass between the objects Work done by a Force We can distinguish the following cases (φ is the angle between the force and the direction of motion): • φ=0 (force along direction of motion) à Work is positive • φ<900 W>0 (force is doing positive work, speed is increasing) • φ=900 • φ>900 (force normal to velocity - is not doing work) W=0 W<0 (force is doing negative work, slowing down) • φ=180 (force along opposite direction of motion) à Work is negative Work done by a Force W=0 W<0 W>0 d Multiple Forces In the case of multiple forces we can apply the superposition principle: So you can either replace all forces by just their sum, or sum all individual works done. Example Work done by Weight • For horizontal displacements, Wg = 0 • For vertical motion if f=1800 (going up) then work is negative (object slows down) • If f=00 (falling down) then work is positive (accelerates). Power • Power is the rate at which work is done, i.e. if work W is done by a force in time Δt, the average power due to the force is defined to be: W P= Δt The SI Unit of power is Watt, but we also use ft.lb/s and horsepower (hp). 1 Watt = 1 W = 1 J/s = 0.738 ft lb/s, 1hp = 550 ft lb/s = 746 W But, eventually…. • pendulum slows down • what happens to energy? • • Where does it go???? • What is it? • How can we make it? • Is it the same as temperature? The heat is on!! • burning match vs. tub-full of hot water – which is hotter?? – which contains more heat?? • first question, more precisely: which has higher temperature? Temperature vs. Heat • Temperature (roughly) describes the “intensity” of heat • Heat content (roughly) describes the total amount of heat. • Match has higher temperature, but bath tub has greater heat content • higher temperature : more molecular kinetic energy (sort of) Low fat: only 3,452 Calories! • that’s right folks, heat is measured in calories • It takes one calorie of heat to raise the temperature of one gram of water one degree Celsius • careful: nutritional Calorie = 1000 calories James Joule (1818-1889) • Industrial Revolution • Demonstrated that mechanical energy could be directly converted into heat Joule’s churn • weight falls; gives up potential energy • water temperature rises! • the further the weight falls, the more the temperature goes up • mechanical equivalent of heat what can this mean? • potential energy can be converted directly into heat! • heat must be just another form of energy!!! • (we need to be able to convert heat into other energy: we will come back later) Recall... • mechanical energy is in some cases conserved (elastic collisions, ideal pendula, etc.) • in some cases it’s not (inelastic collisions, imperfect pendula, etc) • When we consider heat as a form of energy, TOTAL ENERGY is conserved!! • Conservation of Energy Principle!!!! one more detail.. • how do we most often produce heat? • burn gasoline, wood, coal, whatever. • These contain “chemical” energy So… • When we account for all the energy: – kinetic, potential, heat, chemical • The total energy of the universe stays the same!!!! • Energy can be neither created nor destroyed! • A Universe Shaking Idea!!!! (but Universe itself seems to have escaped this law!) Tie it up • all different types of things • can become one another • must all be essentially the same thing: energy • just changes from one form to another; never destroyed --- never created