Period & Frequency. Work and Energy. Methods of Energy Transfer: Energy. WorkKE Theorem 3/4/16. Ranking: Which has the greatest kinetic energy?


 Allan Banks
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1 Perod & Frequency Perod (T): Tme to complete one ull rotaton Frequency (): Number o rotatons completed per second. = 1/T, T = 1/ v = πr/t Work and Energy Work: W = F!d (pcks out parallel components) F " Force on object d " dsplacement Drecton o orce relatve to moton matters! Unts: 1 Joule = 1 kg m /s Energy Several derent varetes o energy, dependng on what the object s dong, where t s located, what t nteracts wth, etc. Knetc Energy (moton): KE = ½ mv Rollng Knetc Energy: KE rot = ½ Iω Gravtatonal Potental Energy: U g = mgh Elastc Potental Energy (sprngs): U sp = ½ kx All have the same unts as work (Joules) Methods o Energy Transer: By work rom a orce By radatng heat By wave propagaton (ether physcal waves or electromagnetc waves) All energy comes rom/goes SOMEwhere! It s never destroyed, but can become less useul. WorkKE Theorem Work s done on or by objects/systems Energy s an nternal property that objects/ systems posess Rankng: Whch has the greatest knetc energy? W = ΔKE F! d = ½ m v ½ m v Work (+ or ) done on an object causes changes n ts KE (ncrease or decrease). 1
2 Types o Forces There are two general knds o orces Conservatve: Work and energy assocated wth the orce can be recovered (Example: Gravty Nonconservatve: orces are dsspatve and work done aganst t cannot easly be recovered (Example: Frcton) Conservatve Forces A orce s conservatve the work t does on an object movng between two ponts s ndependent o the path the objects take between the ponts The work depends only upon the ntal and nal postons o the object Any conservatve orce can have a potental energy uncton assocated wth t More About Conservatve Forces Examples o conservatve orces nclude: Gravty Sprng orce Electromagnetc orces Potental energy s another way o lookng at the work done by conservatve orces Nonconservatve Forces A orce s nonconservatve the work t does on an object depends on the path taken by the object between ts nal and startng ponts. Examples o nonconservatve orces knetc rcton, ar resstance Frcton Depends on the Path The blue path s shorter than the red path The work requred s less on the blue path than on the red path Frcton depends on the path and so s a nonconservatve orce WorkEnergy Theorem, Extended The workenergy theorem can be extended to nclude potental energy: W nc = (KE KE ) + (PE PE ) I other conservatve orces are present, potental energy unctons can be developed or them and ther change n that potental energy added to the rght sde o the equaton
3 Conservaton o Energy, cont. Total mechancal energy s the sum o the knetc and potental energes n the system E = E KE + PE = KE + PE Other types o potental energy unctons can be added to mody ths equaton Problem Solvng wth Conservaton o Energy Dene the system Select the locaton o zero gravtatonal potental energy Do not change ths locaton whle solvng the problem Identy two ponts the object o nterest moves between One pont should be where normaton s gven The other pont should be where you want to nd out somethng Problem Solvng, cont Very that only conservatve orces are present Apply the conservaton o energy equaton to the system Immedately substtute zero values, then do the algebra beore substtutng the other values Solve or the unknown(s) Example: Rollercoasters Where s the cart gong the astest? Could the cart ever get hgher than pont A on ts own? Example: Problem 7.4 A 0.14kg pnecone alls 16m to the ground whle eelng sgncant ar resstance, where t lands wth a speed o 13 m/s. a. Wth what speed would the pnecone have landed there had been no ar resstance? b. Dd ar resstance do postve or negatve work on the pnecone? c. How much work dd ar resstance do on the pnecone? Conservaton o Energy Energy cannot be created or destroyed; t may be transormed rom one orm nto another or low n/out o objects, but the total amount o energy never changes 3
4 Power Oten also nterested n the rate at whch the energy transer takes place Power s dened as ths rate o energy transer P = W t SI unts are Watts (W), 1 W = 1 J/s and Impulse : p = mv p has unts o [kg m/s] p tot = m 1 v 1 + m v + m 3 v 3 + Impulse: I = F avg Δt Unts o mpulse: [kg m/s] " same as momentum! Impulse relatonshp Impulses cause changes n the momentum o an object or system: F avg Δt = p p A crate s pushed across the loor or 3 seconds, startng at rest wth net orce shown. Whch crate has the largest mpulse delvered? Ths s an alternatve way o expressng the same concept n Newton s second law. s a vector quantty, so we can wrte ths or x and y drectons. A crate s pushed across the loor or 3 seconds, startng at rest wth net orce shown. Whch crate ends up wth the astest nal speed? Conservaton o The prncple o conservaton o momentum states: When there s no net external orce on a system o objects, the total momentum o the system does not change. We say that the momentum o such a system s conserved snce t does not change. 4
5 A kg baseball s travellng at a speed o 30 m/s. The batter hts the ball, and the ball and the bat are n contact or 0.5 s. I the ball ends up gong the same speed n the opposte drecton, how strong was the orce that the bat exerted on the ball? Collsons When two objects collde, mpulse s equal and opposte or the two objects there s no net external orce. Beore Collson Impact Ater Collson Each object has equal and opposte change n momentum. The momentum o the system o objects s conserved. Collsons The change o momentum o the two objects n a collson s equal and opposte  the momentum ganed by one object s the amount lost by the other. Object A beore collson Object B Beore collson Object A ater collson Object B ater collson Collsons 1. Elastc collson: Objects rebound wthout deormng or generatng heat Bllard balls. Inelastc: objects ht, but deorm and/or generate heat Tenns ball beng ht by a racket 3. Perectly nelastc: Objects ht and stck together s conserved, whether collson s elastc or nelastc, as long as there s no net external orce! M x v Recol: Also explaned by conservaton o momentum m x V Example Two hockey players, one 7 kg travellng at.3 m/s and the other 58 kg travellng at 3.1 m/s are skatng towards each other. I the angle between ther ntal drectons s 10º and they stck together ater the collson, what s ther speed ater the collson? 5
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