Unformatted text preview: UCSD Physics 8 Jan 2008 The Flow of Energy
Where it comes from; where it goes
1 UCSD Physics 8 Jan 2008 Energy as a tool in physics We use the conservation of energy to predict behavior by setting E = mgh + mv2 = constant we can elucidate the value of the velocity at any height: v2 = 2g (height fallen from when rest) We rely on the fact that energy is not created Where did the energy we see around us come from? most of what we use derives from the sun some derives from other, exploded stars (nuclear fission) ultimately, all of it was donated in the Big Bang A re-arrangement so that the net energy of the universe can remain zero! 2 UCSD Physics 8 Jan 2008 Energy is Conserved Conservation of Energy is different from Energy Conservation = using energy wisely Conservation of Energy means energy is neither created nor destroyed. The total amount of energy in the Universe is constant Don't we create energy at a power plant? No, we simply transform energy at our power plants The sun does not create energy it exchanges mass for energy as given by E=mc2 Which is an equation for.. Why is the equation .. 3 UCSD Physics 8 Jan 2008 Energy Exchange Though the total energy of a system is constant, the form of the energy can change A simple example is that of a pendulum, in which a continual exchange goes on between kinetic and potential energy Q: What happens in the loop track..?
pivot K.E. = 0; P. E. = mgh h K.E. = 0; P. E. = mgh
height reference h=0 P.E. = 0; K.E. = mgh
4 UCSD Physics 8 Jan 2008 Perpetual Motion Why won't the pendulum swing forever? The pendulum slows down by several mechanisms Friction at the contact point: requires force to oppose; force acts through distance work is done Air resistance: must push through air with a force (through a distance) work is done Gets some air swirling: puts kinetic energy into air (not really fair to separate these last two) Perpetual motion means no loss of energy Electrons in atoms do move for ever with no friction Solar system orbits also come close But tides on planets and sun are a form of friction There is no perpetual motion in macroscopic (large) systems There is always friction, air resistance, tides.. That lead to energy coming from the motion of the object (KE) and going into the motion of the atoms (heat) 5 UCSD Physics 8 Jan 2008 Perpetual Motion Leonardo da Vinci sketched to show the impossibility of the perpetual motion machine shown here. We agree: all large devices have friction and share energy with the outside 6 UCSD Physics 8 Jan 2008 Example of Energy Conversion A toilet bowl with some gravitational potential energy is dropped potential energy turns into kinetic energy kinetic energy of the toilet bowl goes into: ripping the toilet bowl apart (chemical: breaking bonds) sending the pieces flying (kinetic) into sound into heating the ground and pieces through friction as the pieces slide to a stop In the end, the local environment is slightly warmer 7 UCSD Physics 8 Jan 2008 How Much Warmer? A 20 kg toilet bowl held 1 meter off the ground has 200 J of gravitational potential energy mgh = (20 kg)(10 m/s2)(1 m) = 200 kgm2/s2 = 200 J A typical heat capacity is 1000 J/kg/C (a property of materials) So 200 J can heat 1 kg by 0.2C or 20 kg by 0.01C heat capacity follows intuitive logic: to get same T, need more energy or less mass given fixed energy input, get smaller T for larger mass for a given mass, get larger T for more energy input So how much mass is effectively involved? initially not much (just contact surfaces): so hot at first but heat diffuses atom to atom into surrounding bulk: cools down so answer is ill-defined: depends on when But on the whole, the temperature rise is hardly noticeable 8 UCSD Physics 8 Jan 2008 Gasoline Example Put gas in your car Combust gas, turning chemical energy into kinetic energy of the explosion (motion of gas particles) Transfer kinetic energy of gas to piston to crankshaft to drive shaft to wheel to car as a whole That which doesn't go into kinetic energy of the car goes into heating the engine block (and radiator water and surrounding air), and friction of transmission system (heat) Much of energy goes into stirring the air (ends up as heat) Apply the brakes and convert kinetic energy into heat It all ends up as waste heat, ultimately, since no change in height (no change in PE = mgh) 9 UCSD Physics 8 Jan 2008 Bouncing Ball Superball has gravitational potential energy Drop the ball and this becomes kinetic energy Ball hits ground and compresses (force times distance), storing energy in the spring Ball releases this mechanically stored energy and it goes back into kinetic form (bounces up) Inefficiencies in "spring" end up heating the ball and the floor, and stirring the air a bit In the end, all is heat
10 UCSD Physics 8 Jan 2008 Why don't we get hotter and hotter If all these processes end up as heat, why aren't we continually getting hotter? If earth retained all its heat, we would get hotter All of earth's heat is radiated away as infrared light hotter things radiate more heat If we dump more power, the temperature goes up, the radiated power increases dramatically comes to equilibrium: power dumped = power radiated stable against perturbation: T tracks power budget 11 UCSD Physics 8 Jan 2008 Another type of Energy: Light The power given off of a surface in the form of light is proportional to the fourth power of that surface's temperature! P = A T4 in Watts (1 Watt = 1 Joule/second) A = surface area of hot thing, in square meters the constant, = 5.67 10-8 W/K4/m2 temperature must be in Kelvin K = C + 273 C = (5/9) (F 32) Example: radiation from your body:
P = A T4 = (1 m2)(5.67 10-8) (310 K)4 = 523 Watts (if naked in the cold of space: don't let this happen to you!) radiated power output is partially balanced by radiated power in from surroundings that are not at zero degrees Not 523 W/m2 in 70F room, more like 100 W/m2 We find the heat loss = heat emitted by hotter object minus head absorbed from cooled surroundings = ATh4 ATc4
12 UCSD Physics 8 Jan 2008 Radiant Energy, continued Example: The sun is 5800K on its surface, so: P/A = T4 = (5.67 10-8) (5800)4 = 6.4 107 W/m2 Multiply by the surface area of sun gives 3.9 1026 W Compare to total power of USA 3.3 1012 W One power plant is 0.51.0 GW (109 W) 13 UCSD Physics 8 Jan 2008 Rough numbers How much power does the earth radiate? P/A = T4 for T = 288K = 15C is 390 W/m2 Summed over entire surface area (4 R2, where R = 6,378,000 meters) is 2.0 1017 W For reference, global "production" is 3 1012 W Solar radiation incident on earth = 2 1017 W just solar luminosity of 3.9 1026 W divided by geometrical fraction that points at earth Same as the energy going out from the Earth 14 UCSD Physics 8 Jan 2008 Power Examples: Nature
Example Hurricane Sunlight on Earth Sun all directions 1 year 1 year Time Energy 1013 J 2x1017 J 1.2x1034 J 1.3 kW/m2 3.9 x 1026 W Power 15 UCSD Physics 8 Jan 2008 Human Energy Requirements Low energy use: 1,500 Calories per day 6,280,000 J = 6.28 MJ / 86,400 seconds 75 W We're like light bulbs, constantly putting out heat Large concert hall with few people is overcooled by its Air conditioning designed for when full. Need more like 2,400 Cal for active lifestyle when young much less each year as pass 30 100 W of power 16 UCSD Physics 8 Jan 2008 Power Examples: Life
Example Human brain Person Person continuously peddling 1 day Time Energy Power 20 W 2400 food calories = 100 W 2.4Mcal = 10MJ 125 W = 1/6 horse power 17 UCSD Physics 8 Jan 2008 Energy from Food Energy from fat, carbohydrates, protein 9 Calories per gram for fat 4 Calories per gram for carbohydrate Do not include Fiber 7 Calories per gram for alcohol 4 Calories per gram for protein Calculate Cals for the label: 63 fat + 84 CH + 40 protein = 187 Calories 180 Cal = 753 kJ set equal to mgh climb 1100 m vertically, assuming perfect efficiency 18 UCSD Physics 8 Jan 2008 Body is 25% Efficient Human body isn't 100% efficient: more like 25% To put out 100 J of mechanical work, must eat 400 J 180 Calorie candy bar only gets us 275 m, not 1100 m Maximum short term power output (rowing, cycling) is about 150-200 W (for 70 kg person) Consuming 600-800 W total, mostly as wasted heat For 30 minutes 800 J/s 1800 s = 1.44 MJ = 343 Cal Can burst 700 W to 1000 W for < 30 sec put out a full horsepower momentarily! 19 UCSD Physics 8 Jan 2008 impressive display of human power The Gossamer Albatross crossed the English Channel (25 miles) in 1979, powered by Bryan Allen Flight took 49 minutes, wiped Bryan out! Sustained power out ~250 W 20 UCSD Physics 8 Jan 2008 Air Resistance We're always "neglecting air resistance" in physics Can be difficult to calculate Affects projectile motion Friction force opposes velocity through medium Imposes horizontal force, additional vertical forces Terminal velocity for falling objects Dominant energy drain on cars, bicyclists, planes 21 UCSD Physics 8 Jan 2008 Drag Force Quantified With a cross sectional area, A (in m2), coefficient of drag, sealevel density of air, and velocity, v (m/s), the drag force is: Fdrag = cD Av2 Newtons cD is drag coefficient: ~1.0 for most things, 0.35 for car is density of medium: 1.3 kg/m3 for air, 1000 kg/m3 water typical object in air is then Fdrag 0.65Av2 Example: Bicycling at 10 m/s (22 m.p.h.), with projected area of 0.5 m2 exerts 32.5 Newtons requires Power = Energy/time = Fdistance/time =Fv = 325 Watts to maintain speed Demonstration: falling balloons
22 UCSD Physics 8 Jan 2008 Power Examples: Transport
BTU per 1960 passenger mile Domestic air Car SUV motorcycle Transit bus Intercity coach Rail (Amtrak) 2148 8633 4495 1980 5742 4341 6810 2125 2742 2003 3476 3553 4068 1969 4415 950 2100 Few passengers for size? Comments Improved engines Improved engine and aerodynamics, but larger Bureau Transport Statistics http://www.bts.gov/publications/national_transportation_statistics//2005/html/table_04_
23 UCSD Physics 8 Jan 2008 "Free" Fall Terminal velocity reached when Fdrag = Fgrav (= mg) For 75 kg person subtending area of 0.5 m2, vterm 50 m/s, or 110 m.p.h. which is reached in about 5 seconds, over 125 m of fall actually takes slightly longer, because acceleration is reduced from the nominal 10 m/s2 as you begin to encounter drag Free fall only lasts a few seconds, even for skydivers 24 UCSD Physics 8 Jan 2008 Announcements/Assignments Next up: a simple model for molecules/lattices electrons, charge, current, electric fields Assignments: Homework Friday night 25 ...
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