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L3 Energy and Power To discuss energy, we first discuss the concept work done on an object. Work done is defined as the product of a force exerted on an object times the distance through which it is exerted. More specifically, we consider a force acting through a distance. Work = Force x distance or W = F.d Units - newtons x meters = joules (J), or pounds x feet (foot pounds, ft.lbs) BTU = 778 ft.lbs (energy of one wooden kitchen match) Pushing on a wall and wall doesn’t move (no work done on the wall) Conversion: 1J= 0.738 ft.lb But the concept of work done has one other characteristic. There is a directional aspect, i.e. the force involved is the part (component) that is the direction of the motion F Fy Fx x W Fx x A 10 lb weight is lifted 5 ft. A 20 lb weight is lifted 2.5 ft. Which lifting required the most work? (a) 10 lb weight (b) 20 lb weight (c) same work for each lifting (d) not enough information is given to work the problem Two cars, A and B, travel as fast as they can to the top of a hill. If their masses are equal and they start at the same time, which one does the most work if A gets to the top first? (a) A (b) B (c) they do the same amount of work 3. MECHANICAL ENERGY When work is done on an object, the object generally has acquired the ability to do work. This is called energy and it has the same units as work. Two Types of Mechanical Energy Potential Energy Kinetic Energy Potential Energy Energy of position or configuration Other examples - Springs, bow, sling shot, chemical energy, and gravitational potential energy The latter is GPE = mgh (the force required to lift at constant speed times the distance ) The potential energy of an object depends on a reference position. It represents the work done against gravity to put the mass m in its position h above some reference position. It is an energy of position. Kinetic Energy If the body being lifted experiences an increase in speed, it gains an energy of motion called kinetic energy. KE mv 1 2 2 It is a square law. A 20 pound weight is lifted 4 feet. The change in potential energy of the weight in ft.lb is (a) 20 (b) 24 (c) 16 (d) 80 (e) 5 Conservation of Energy Energy cannot be created or destroyed. It may be transformed from one form into another, but the total amount of energy never changes. (from relativity, we find that mass is a form of energy….) CT 2.4.4 You are going skydiving. While you are free falling what is happening to the energy in the system? a) b) c) d) e) Potential energy is being transferred (or “transformed”) to kinetic energy Kinetic energy is being transferred (or “transformed”) to Potential energy The total energy of the system is decreasing The total energy of the system is increasing ?? An object of mass 6 kg is traveling at a velocity of 30 m/s. How much total work was required to obtain this velocity starting from a position of rest? (a) 180 Joules (b) 2700 Joules (c) 36 Joules (d) 5 Joules (e) 180 N 2. POWER Power = Work/time or P = W/t Units - J/s = Watt W 550 ft.lb/s = 1 hp 1 hp = 746 J/s = 746 W 1 BTU/hr = 0.293 W 100 W bulb = 0.1341 hp 250 hp engine = 186,450 W 8. SOURCES OF ENERGY/POWER Except for nuclear and geothermal power, the source of practically all our energy is the sun. Nuclear power Geothermal power Solar power (this includes biomass, photovoltaics, solar thermal, etc.) Wind power We will discuss audio power in detail later, but keep in mind a few numbers: A good audio amplifier is rated at about 100-200 W (input) A trombone can produce about 6 W of audio power. MP3 players are in the tens of mW. Note that these numbers describe the sound source power. We will discuss separately the loudness of sound in terms of ” sound intensity” in a unit to be defined later, called the decibel (db).