Unformatted text preview: Basic Physics, Part II
Work, Energy, and Power UCSD: Physics 8; 2 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 UCSD: Physics 8; 2 Work: more than just unpleasant tasks In physics, the definition of work is the application of a force through a distance W = Fd 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 UCSD: Physics 8; 2 Units of Energy Force is a mass times an acceleration 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 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 UCSD: Physics 8; 2 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 = cDAv2 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 units: (kg/m3)(m2)(m/s)2 = (kgm2/m3) (m2/s2) = kgm4 = m3s2 = kgm/s2 = Newtons kgm2m2 m3s2 UCSD: Physics 8; 2 Kinetic Energy Kinetic Energy: the energy of motion Moving things carry energy in the amount: K.E. = mv2 Note the v2 dependence--this is why: a car at 60 mph is 4 times more dangerous than a car at 30 mph hurricane-force winds at 100 mph are much more destructive (4 times) than 50 mph gale-force winds a bullet shot from a gun is at least 100 times as destructive as a thrown bullet, even if you can throw it a tenth as fast as you could shoot it UCSD: Physics 8; 2 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 UCSD: Physics 8; 2 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 UCSD: Physics 8; 2 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 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. UCSD: Physics 8; 2 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 Energy is conserved, so mv2 = mgh Can even figure out v, since v2 = 2gh mv2 UCSD: Physics 8; 2 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 UCSD: Physics 8; 2 Ramps Make Life Easy To get the same amount of work done, you can either: apply a LARGE force over a small distance OR apply a small force over a large distance as long as W = 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 UCSD: Physics 8; 2 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) raises one gram of H2O 1C One Calorie (4184 J) raises one kilogram of H2O 1C One Btu (1055 J) raises one pound of H2O 1F UCSD: Physics 8; 2 Energy of Heat, continued Food Calories are with the "big" C, or kilocalories (kcal) Since water has a density of one gram per cubic centimeter, 1 cal heats 1 c.c. of water 1C, and likewise, 1 kcal (Calorie) heats one liter of water 1C these are useful numbers to hang onto Example: to heat a 2-liter bottle of Coke from the 5C refrigerator temperature to 20C room temperature requires 30 Calories, or 122.5 kJ UCSD: Physics 8; 2 Heat Capacity Different materials have different capacities for heat Add the same energy to different materials, and you'll get different temperature rises Quantified as heat capacity Water is exceptional, with 4,184 J/kg/C 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 350,000 J (= 83.6 Cal) UCSD: Physics 8; 2 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 100200 kJ per mole a mole is 6.022 1023 molecules/particles works out to typical numbers like several thousand Joules per gram, or a few Calories per gram (remember, 1 Cal = 1 kcal = 4184 J) UCSD: Physics 8; 2 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 of chemical energy, or roughly 5 Cal/g Burning gasoline yields about 39 kJ per gram, or just over 9 Cal/g UCSD: Physics 8; 2 Power Power is simply energy exchanged per unit time, or how fast you get work done (Watts = Joules/sec) One horsepower = 745 W Perform 100 J of work in 1 s, and call it 100 W Run upstairs, raising your 70 kg (700 N) mass 3 m (2,100 J) in 3 seconds 700 W output! Shuttle puts out a few GW (gigawatts, or 109 W) of power! UCSD: Physics 8; 2 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) = 200J 200 J in 2 seconds 100 Watts If you want to heat the 3 m cubic room by 10 C 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, so 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.) UCSD: Physics 8; 2 Announcements/Assignments Next up: flow of energy and human energy/exercise a simple model for molecules/lattices electrons, charge, current, electric fields Assignments: Transmitters start counting for participation credit Tuesday 4/11 HW1: Chapter 1 in Bloomfield: 1.E.4, 1.E.7, 1.E.8, 1.E.20, 1.E.25, 1.E.34, 1.P.1, 1.P.8, 1.P.9, 1.P.10, 1.P.14, 1.P.16, 1.P.18, 1.P.22; Chapter 2: 2.E.28, 2.P.10, 2.P.11 E Exercise; P Problem due Thursday 4/13 in class (or in box outside 336 SERF by 3:30PM Thursday) First Q/O due Friday, 4/14 by 6PM via WebCT read chapter 2: pp. 5459, 6162, 7172; chapter 7: pp. 206207 ...
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