Unformatted text preview: Basic Physics, Part II Work, Energy, and Power Prefixes: You need to know all these!
Prefix n (Greek mu) m c k M G T pronounc ed nano micro milli centi kilo mega giga tera 1/billion one-millionth one-thousandth one-hundredth one thousand one million one billion one trillion meaning power of 10 UCSD: Physics 8; 2007 10-9 10-6 10-3 10-2 103 106 109 1012 1/1,000,000,000 1/1,000,000 1/1000 1/100 1000 1,000,000 1,000,000,000 1,000,000,000,000 1km = kilometer = 1000 m, m=meter
2 UCSD: Physics 8; 2007 Energy: the capacity to do work This notion makes sense even in a colloquial context: hard to get work done when you're wiped out (low on energy) work makes you tired: you've used up energy But we can make this definition of energy much more precise by specifying exactly what we mean by work 3 UCSD: Physics 8; 2007 Work: more than just unpleasant tasks In physics, the definition of work is the application of a force through a distance Work = W = F x d W is the work done F is the force applied d is the distance through which the force acts Only the force that acts in the direction of motion counts towards work 4 UCSD: Physics 8; 2007 Units of Energy Force is a mass times an acceleration: F=ma mass has units of kilograms acceleration is m/s2 force is then kgm/s2, which we call Newtons (N) Work is a force times a distance: W=Fd=mad units are then (kgm/s2)m = kg m2/s2 = Nm = Joules (J) One joule is one Newton of force acting through one meter Imperial units of force and distance are pounds and feet, so unit of energy is foot-pound, which equals 1.36 J Energy has the same units as work: Joules 5 UCSD: Physics 8; 2007 A note on arithmetic of units You should carry units in your calculations and multiply and divide them as if they were numbers Example: the force of air drag is given by: Fdrag = cD Av2 cD is a dimensionless drag coefficient is the density of air, 1.3 kg/m3 A is the cross-sectional area of the body in m2 v is the velocity in m/s kgm2m2 units: (kg/m3)(m2)(m/s)2 = (kgm2/m3) (m2/s2) =s2 m3 kgm4 = m3s2 = kgm/s2 = Newtons 6 UCSD: Physics 8; 2007 Kinetic Energy Kinetic Energy: the energy of motion Moving things carry energy in the amount: 7 UCSD: Physics 8; 2007 Numerical examples of kinetic energy A baseball (mass is 0.145 kg = 145 g) moving at 30 m/s (67 mph) has kinetic energy: K.E. = (0.145 kg) (30 m/s)2 = 65.25 kgm2/s2 65 J A quarter (mass = 0.00567 kg = 5.67 g) flipped about four feet into the air has a speed on reaching your hand of about 5 m/s. The kinetic energy is: K.E. = (0.00567 kg) (5 m/s)2 = 0.07 kgm2/s2 = 0.07 J 8 UCSD: Physics 8; 2007 More numerical examples A 1500 kg car moves down the freeway at 30 m/s (67 mph) K.E. = (1500 kg) (30 m/s)2 = 675,000 kgm2/s2 = 675 kJ A 2 kg (~4.4 lb) fish jumps out of the water with a speed of 1 m/s (2.2 mph) K.E. = (2 kg) (1 m/s)2 = 1 kgm2/s2 = 1 J Which has more kinetic energy? 9 UCSD: Physics 8; 2007 Gravitational Potential Energy It takes work to lift a mass against the pull (force) of gravity The force of gravity is mg, where m is the mass, and g is the gravitational acceleration
F = mg (note similarity to F = ma) g = 9.8 m/s2 on the surface of the earth g 10 m/s2 works well enough for this class Lifting a height h against the gravitational force requires an energy input (work) of: E = W = F h = mgh = gravitational potential energy Rolling a boulder up a hill and perching it on the edge of a cliff gives it gravitational potential energy that can be later released when the roadrunner is down below. 10 UCSD: Physics 8; 2007 First Example of Energy Exchange When the boulder falls off the cliff, it picks up speed, and therefore gains kinetic energy Where does this energy come from?? from the gravitational potential energy The higher the cliff, the more kinetic energy the boulder will have when it reaches the ground
mgh becomes h mv2
11 UCSD: Physics 8; 2007 Energy Conservation Energy is conserved neither made or destroyed, but can be converted, Total Energy before = Total energy after KE1 + PE1 = KE2 + PE2 (if no friction) mv12 + mgh1 = mv22 + mgh2 Here, v1=0 and h2=0, so simplifies to mgh1=1/2mv22 This can solve for v2 = 2gh1
PE = mgh becomes Excellent text, examples on web: http://www.physicsclassroom.com/Class/en If I drop a penny.. h KE = mv2
12 UCSD: Physics 8; 2007 Examples of Gravitational Potential Energy How much gravitational potential energy does a 70 kg high-diver have on the 10 meter platform? mgh = (70 kg) (10 m/s2) (10 m) = 7,000 kgm2/s2 = 7 kJ How massive would a book have to be to have a potential energy of 40 J sitting on a shelf two meters off the floor? mgh = m (10 m/s2) (2 m) = 40 J so m must be 2 kg If it takes 500 J to...what is the mass?
13 UCSD: Physics 8; 2007 Ramps Make Life Easy To get the same amount of work done, you can either: Lift vertical: apply a large force over a small distance Ramp: apply a small force over a large distance For both, mgh = Fd is the same h mg Ramp with 10:1 ratio, for instance, requires one tenth the force to push a crate up it (disregarding friction) as compared to lifting it straight up total work done to raise crate is still the same: mgh but if the work is performed over a longer distance, F is smaller: mg/10 How much energy to go up ramp? Why do we use ramps? 14 UCSD: Physics 8; 2007 The Energy of Heat Hot things have more energy than their cold counterparts Heat is really just kinetic energy on microscopic scales: the vibration or otherwise fast motion of individual atoms/molecules Even though it's kinetic energy, it's hard to derive the same useful work out of it because the motions are random Heat is frequently quantified by calories (or Btu) One calorie = 4.184 J can raise one gram of H2O 1C One Calorie (Food calorie) = 4184 J Can raise one kilogram of H2O 1C One Btu =1055 J can raise one pound of H2O 1F 15 UCSD: Physics 8; 2007 Energy of Heat, continued Since water has a density of one gram per cubic centimeter, can connect mass of water to volume of water 1 cal heats 1 c.c. of water 1C 1 kcal (=1Calorie) heats one liter (1000 cubic centimeters) of water 1C Example: to heat a 2-liter bottle of Coke from the 5C refrigerator temperature to 20C room temperature requires: 15 degrees x 2000 cubic centimeters = 30000 calories = 122.5 kJ 16 UCSD: Physics 8; 2007 Specific Heat Different materials have different capacities for heat Add the same energy to different materials, and you'll get different temperature rises Specific heat = energy to heat 1 kg by 1oC Water is exceptional, with 4,184 J/kg/C - needs lot energy to heat Most materials are about 1,000 J/kg/C (including wood, air, metals) Example: to add 10C to a room 3 meters on a side (cubic), how much energy do we need? air density is 1.3 kg/m3, and we have 27 m3, so 35 kg of air; and we need 1000 J per kg per C, so we end up needing 35 kg x 10 C x 1000 J/kg/C = 350,000 J (= 83.6 Cal)
17 UCSD: Physics 8; 2007 Chemical Energy Electrostatic energy (associated with charged particles, like electrons) is stored in the chemical bonds of substances. Rearranging these bonds can release energy some reactions require energy to be put in Typical numbers are several thousand Joules per gram, or 100200 kJ per mole a mole is 6.022 1023 molecules Mass of one mole = atomic weight of molecule, depends on the molecule, eg 50 grams 18 UCSD: Physics 8; 2007 Chemical Energy Examples Burning a wooden match releases about one Btu, or 1055 Joules a match is about 0.3 grams, so this is >3,000 J/g, nearly 1 Cal/g Burning coal releases about 20 kJ per gram = 5 Cal/g of chemical energy Burning gasoline yields 132MJ per gallon Convert to J/gram I gallon is 3785 cm3 Density is 0.737 g/cm3 http://www.simetric.co.uk/si_liquids.htm 1 gallon weighs 2782 g Gasoline releases 132MJ/2782g = 47 kJ/g about 500 h of human effort at 75 W How much energy is used by SUV going... How much power does the SUV use?
19 UCSD: Physics 8; 2007 Power Power = energy exchanged per unit time, how fast you get work done 1 Watts = 1 Joules/sec If do 300 J of work in 2 s, are using energy at the rate of 150 W Run upstairs, raising your 70 kg (700 N) mass 3 m (2,100 J) in 3 seconds 700 W output! One horsepower = 745 W Shuttle puts out a few GW (Gigawatts, or 109 W) of power! 20 UCSD: Physics 8; 2007 Power Examples How much power does it take to lift 10 kg up 2 meters in 2 seconds? mgh = (10 kg) (10 m/s2) (2 m) = 200 J 200 J/ 2 seconds = 100 Watts If you want to heat the 3 m cubic room by 10C with a 1000 W space heater, how long will it take? We know from before that the room needs to have 360,000 J added to it, at 1000 W = 1000 J/s this will take 360 seconds, or six minutes. But: the walls need to be warmed up too, so it will actually take longer (and depends on quality of insulation, etc.)
Many examples: http://hypertextbook.com/facts/index-topics.shtml
21 UCSD: Physics 8; 2007 Power Examples: Domestic
Example Empty a AA battery 1.2V 2500mAh Laser pointer (hazardous if viewed) Cell phone transmitting Hair Dryer Heater Typical US house 5 hour 600 sec 8 hours 1 year 18,000 J 600000 J 43 MJ 32 GJ Time 10 hours 1 hour Energy 3.0 J Power 0.08 mW 0.8 mW 2 mW 1W 1000 W 1500 W 1000 W A special ecologically friendly house..
22 UCSD: Physics 8; 2007 Power Examples: Industrial
Example Use one gallon of gasoline, 20 Miles/gallon 747 Jet engine San Onofre Power Plant USA (1999) All countries (1999) Time 20 min 20 min 1 year 1 year 1 year Energy 109 MJ 66 GJ 7x 1016 J 1020 J 4x1020 J Power 91 kW =122 Hp 55 MW 2150 MW 3 TW 12.5 TW http://video.google.com/videoplay?docid =9211793766758129558&q=jet+engine+power&hl=en
23 UCSD: Physics 8; 2007 Projected Energy Used 24 UCSD: Physics 8; 2007 How We use Energy
Individual Energy Use in USA Consumer goods (packaging, clothing, furniture, recreation) Services (government, education, health..) Transport Food Housing (12% construction) % energy (av British Columbia) 23 % energy 39 12 32 15 18 30 16 13 http://www.myfootprint.org/ http://www.bchydro.com/rx_files/community/community2236.pdf 25 UCSD: Physics 8; 2007 How Energy is Generated Quadrillion =1015 (USA) or 1024 UK
26 UCSD: Physics 8; 2007 Energy Growth by Region 27 UCSD: Physics 8; 2007 Energy and Power Conversions
1 calorie = 4.1868 J (exact since this is a definition) 1 food Calorie =1 Cal = 1k calorie =4187 J 1 BTU = 1055.056 J 1 kWh = 1 kJ/s x 3600s = 3.6 MJ 1 Watt = 1 Joule/second = 1J/s 1 horse power = 745.7 W approx. Heat capacity of water: 4,184 J/kg/C Energy needed to heat water (J) = 4184 x Mass (kg)x (change in temp)
28 UCSD: Physics 8; 2007 Announcements/Assignments Next up: flow of energy and human energy/exercise a simple model for molecules/lattices electrons, charge, current, electric fields Assignments: See syllabus 29 ...
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