Key poins Uni 7 Energy Sorage and Transfer Model Energy-a conserved, subsance-like quaniy wih he capabiliy o produce change in physical sysems I does no come in differen forms i s jus energy. I s sored in differen conainers. I can be ransferred from conainer o conainer and spli beween hem. Thinking his way divers your aenion from he changes in maer ha we CAN describe. Describing he Ineracion beween energy and maer Think money We have money and i s jus money, no maer how you pu i Bu we pu i, sore i, in differen spos-credi card, debi card, checking accoun, savings accoun, cash, coins, your walle I s sill all money, he only hing ha changes is how i is sored. Energy is he same way Describing he Ineracion beween energy and maer coninued We creae various "accouns" (or sorage modes) in which energy can be sored in a given sysem I can be ransferred from one accoun o anoher as some aspec of he sysem undergoes a change I can be ransferred beween sysem and surroundings via several mechanisms, alhough "working" (W) is he primary ransfer mechanism used in his uni Energy Sorage Energy is no disembodied; i is eiher sored In an objec Labeled kineic energy when he objec is moving Labeled elasic energywhen i undergoes a resorable deformaion By a field Graviaional, elecric, or magneic Labeled poenial energy Kineic Energy -E K orke Energy sored kineically Energy of moion Locaed wihin he moving objec 1
Chemical Energy -E Chem Energy sored chemically Sored in molecular and aomic bonds When you break he bond and form new bonds which require less energy o make, he difference is ransferred o oher conainers Graviaional Poenial Energy U g; U G Energy sored graviaionally Where is his energy sored? Wihin he ball? Wihin Earh? Sored wihin he field sored relaive o GF Wha does GF look like? GF lines vecors poining owards cener of Earh Why is NULG and all oher field forces modeled as an inverse square law? We live in a 3d universe, so he field will decrease in srengh as you move ouwards (in one dimension), bu ha srengh mus be disribued over he 2d space of a sphere he surface area of a spaial sphere Which is 4πr 2 GPE Newonian View GPE Relaivisic View Mass curves/bends spaceime We sill see he surface area of sphere (kind of), Newon s calculaions were prey good bu relaiviy gives us more accuracy (and an acual explanaion for graviy) Poenial Energy in general U subscrip Energy of an objec due o is posiion relaive o a force field or due o ha sysem s curren sae relaive o is res sae Ohers? Elecric Poenial Magneic Poenial Chemical Poenial his is E chem Thermal Energy E Therm; E Th; E In Energy sored hermally or inernally can be described hrough is emperaure, bu i is NOThe emperaure Sored in vibraions or kineic/poenial energy (movemen and posiion) of molecules/aoms Hard o quanify wihou hermodynamic equaions and saisics Why? 2
The Law of Conservaion of Energy Elasic Energy E Spring; E S; U S Energy sored elasically Poenial Energy sored in configuraion of maerial Usually deals wih he deformaion of he maerial away from is res sae hps://www.youube.com/wach?v=6ta1s1onpbk hps://www.youube.com/wach?v=akb81u5im3i hps://www.youube.com/wach?v=qfleiybc7ru Spring F vsx graph Hooke s Law Think abou he equaion of he bes fi line (y=mx+b) y is Force applied (N), m represens he spring consan (k), and x is how much he spring is sreched/compressed. We ll ignore he y-inercep in his course. F=kx. The value ofhe spring consan, k,ells us how much force (in Newons) mus be applied o he spring o srech/compress i a cerain disance (in meers). So he unis are N/m. Hooke s Law coninued Someimes Hooke s law is formulaed asf= kx. In his expressionf no longer means he applied force bu raher means he equal and opposiely direced resoring force ha causes elasic maerials o reurn o heir original dimensions. We won use i his way, i s jus good informaion o know. Bu wha else can we deermine using he graph? 3
The area under he line seems o have meaning The area under he line seems o have meaning Tha s a riangle: ½ b * h So.. ½ F * x bu we know F = k*x Subsiue in k*x for F ½ k*x*x or U s = ½ kx 2 Hooke s Law The area under he line seems o have meaning The area shaded represens he spring poenial energy Eel= ½ kx 2 We can use his value, measured in Joules, o deermine how energy is ransferred o oher sorage accouns. Energy Bar Chars Energy can be sored and i can be ransferred from one sorage mechanism o anoher. The objecs involved in energy sorage for a paricular siuaion are lised inside he Sysem box. Objecs ransferring energy ino he sysem, or receiving energy from he sysem, are lised ouside he circle. Energy bar chars Iniial quaniies of sore energy are represened wih bars on lef. Bars of energy enering or leaving he sysem are shown a he circle Final quaniies of sored energy, using bars, go on he righ. Energy bar chars The oal iniial energy, plus or minus any energy ransferred ino or ou of he sysem, mus equal he oal final energy. This is he firs law of hermodynamics and represens he law of conservaion of energy. 4
Energy Transfer labs Spring poenial energy ransferred o kineic energy No relaionship beween Energy and Velociy bu if we linearize our daa by squaring velociy we ge he graph on he righ. Energy Transfer labs Analyze he slope: Now we have a linear relaionship Slope unis reduce o kilograms and he value is ½ he mass of he car Energy Transfer labs General equaion of he line: E k = ½ m * v 2 Energy Transfer Labs Spring poenial energy ransferred o graviaional poenial energy Analyze he slope We see he unis are Joules (a N*m) divided by meers; so Newons (N) Slope represens Force, in his case weigh (m*g) Energy Transfer Labs Equaion of he line ells us ha energy, in his case graviaional poenial energy (U g ) depends on he srengh of he field and he arrangemen of objecs (a leas wo) in he field U g = mgy where gis he srengh of he graviaional field (in N/kg), and y is he heigh above some zero reference posiion. We now have 3 ways o quaniae energy sorage Spring poenial energy (U s ) U s = ½ kx 2 Graviaional poenial energy (U g ) U g = mgy Kineic energy (E k ) E k = ½ mv 2 Remember, g= 9.8 N/kg 5
Bu Wha else can an F vsδx graph ell you? How does he spring in our experimen acually sore more energy? Le s say he force we used was consan, no changing.. Work is also area under F vs. Δx curve This area represens energy ransferred ino he sysem by work Work = ΔE = FΔx A force does workif, when acing on a body, here is a displacemen of he poin of applicaion in he direcion of he force. Energy is ransferred by forces ha cause displacemens. Force and moion mus be in he same direcion. On a force vsposiion graph, his is he area under he graph. Unis Force is measured in Newons. Disance is measured in meers. N x m = Nm= Joules Joulesand Nmare he same hings. Force and Disance mus be in he same direcion!! If you pick an objec up, he force mus be he upward force. Force bu no displacemen Work = Zero If you slide an objec sidewayson a able, he force mus be he sideways force. If you measure he disance up an incline, he force mus be he one exered in a direcion up he incline. 6
Displacemen bu no force Work = Zero Force bu no displacemen Work = Zero No Work Done! The force (weigh) is downward. There is virually no sideways force. The displacemen is sideways. There is no downward moion. W = 14 N x 0 m = 0J W = 0 N x 10 m = 0J How much work is done o lif a 15 N objec upward 4 meers? When you pick an objec up, you have o apply a force equal o is weigh (15 N). W = F x d W = 15 N x 4 m = 60 J How much work is done o lif a 5.00-kg objec upward 4.00 meers? When you pick an objec up, you have o apply a force equal o is weigh (5kgx9.8m/s 2 =49 N). W = F x d W = 49 N x 4 m = 196 J How much work is done o slide a 15 N objec 4.0 meers sideways if he force of fricion is3.0 N? When you slide an objec sideways, you have o apply a force equal o fricion (3 N). W = F x d W = 3.0N x 4.0m = 12 J 7
How much work is done o slide a 15 N objec up an incline 4.0 meers long if he force he person mus push wih is 7.0 N? When you slide an objec up an incline, you have o use he force up he incline (7N). W = F x d W = 7.0N x 4.0m = 28 J How much work is done o slide a 5.0-kg objec sideways 4.0 m if he acceleraion is 6.0 m/s 2? F=ma F = 5-kg x 6 m/s 2 F = 30-N W = F x d W = 30 N x 4 m = 120 J Energy Bar Char Analysis The oal iniial energy, plus or minus any energy ransferred ino or ou of he sysem, mus equal he oal final energy. This is he firs law of hermodynamics. Remember The SI uni for energy is he joule (J). A joule is a or. Useful Energy Energy is defined as he abiliy o cause change, and, like he money analogy, some forms of energy are more useful or effecive in causing change han ohers. Kineic and poenial energies are useful energies. Thermal is no why? Rub your hands ogeher where did your chemical energy go? Now, use ha hermal energy o cause more change. Very hard o in fac, i is impossible. This will ulimaely lead o he Enropic Hea Deah of he Universe. Conservaive vs. Non-conservaive A conservaive force is a force for which is oal ne work does no depend on he pah aken. Graviy is conservaive; oal work will only depend on iniial and final posiions Fricion is non-conservaive; he longer he pah, he more work fricion does and he more energy goes ino he non-useable conainer Conservaive Forces Graviy Elasic Elecric Magneic Non-conservaive Forces Fricion Air resisance Tension Propulsion by rocke or moor Push/pull by a person 8
The difference beween conservaive and nonconservaive forces: Non-conservaive forces ransfer energy o non-useful conainers I can really use hermal energy o do much in erms of moion Consider a possible definiion of useful energy : he abiliy o do work Graviaional poenial energy can be used o do work Thermal energy canno be used o do work Thus graviy is a conservaive force, because his force mainains he usefulness of he energy as i sores i poenially Fricion is a non-conservaive force, because his force does no mainain he usefulness of energy as i sores i hermally You push down wih a force of 10 N on your friend s car which is suck in he snow. By pushing down you increase he normal force and, herefore, he fricion force. The car is now able o ge ou and moves a disance 5m. How much work did you do? None! There was a force bu no Δx! If you change he F N (push down) you change he fricional force A B C D Δ Δ Δ Δ When he rubber bands are sreched, which rubber band has more elasic energy or are hey he same? Rank he amoun of work done from posiive o negaive. Imagine a ball on a rack where no energy is ransferred beween he ball and he rack or beween he ball and he air around i (fricionless/air resisanceless). The ball sars from res a he posiion labeled Sar and moves along he rack oward Posiions 1, 2, and 3. Wha is he highes posiion he ball achieves? Same quesion air resisancelessand fricionless environmen. Does he ball make i o posiion 2? 9
Which book has less graviaional poenial energy or are hey he same? (Consider he reference poin o be he floor.) Which is faser if dropped? Law of Conservaion of Energy and he Work Energy Principle Toal Work (due o only conservaive forces; fricionless/air resisancelessenvironmens) always equals zero Essenially Iniial Energy = Final Energy Complee his in your noes A 70 kg skier sars from res from he op of a fricionless 35 incline wih a verical heigh of 20 m. Wha is he skier s speed jus before she eners he plane? Draw a energy bar char o help you organize your energy sorage accouns. Se E iniial = E final By how much will he spring compress? Draw a energy bar char o help you organize your energy sorage accouns. Se E iniial = E final Power The rae a which work is done or energy is consumed. Which does he mos work? Which is he mos powerful? 10
P = Power = Work / ime W Unis Work is measured in Joules. Time is measure in seconds. Joules = Was sec Common Meric Prefixes Was( W ) = kilowas( kw ) 1,000 Was( W ) = MegaWas( MW ) 1,000,000 No maer wha he problem says, you mus use sandard unis in he equaion. Disance meers (m) Time seconds (s) Force Newons (N) Mass kilograms (kg) Velociy meers per second (m/s) Power Was (W) Work Joules (J) James Wa Was The uni was names for James Wa, he invenor of he seam engine. Was engine was beer han he curren mehod geing work done (horses). To help sell engines, Wa developed a way o rae heir abiliies. 11
Rearranging he Power Formula The power formula can be rearranged ino hree common forms. They are mahemaically equal, bu hey look differen and conain differen variables. They are useful for differen problems, depending on wha is given in he problem. W P = Fd P = P = F v Relaes Power o Work and Time. Relaes Power o Force, Disance and Time. Relaes Power o Force and Velociy. How long will i ake a moor, raed a 200 W, o do 1800 Joules of work? P = W 200 = 1800 = 9sec How much power is used o lif a 15 N objec upward 4 meers in 20 seconds? P = Fd P = Fd 15 4 P = = 3Was 20 A wha speed can a 1000 W moor lif a 25-kg mass? P v = 4m s = F v 1000W = 245N v 1 N is abou ¼ pound FYI May be helpful someday 12