Flipping Physics Lecture Notes: AP Physics 1 Review of Kinematics

Transcription

1 Flipping Phyic Lecture Nte: AP Phyic 1 Review f Kinematic AP i a regitered trademark f the Cllege Bard, which wa nt invlved in the prductin f, and de nt endre, thi prduct. Intrductry Cncept: Vectr: Magnitude and Directin Magnitude mean the amunt f the vectr r the value f the vectr withut directin. Scalar: Magnitude nly, n directin Cmpnent Vectr Theta wn t alway be with the hrizntal, the cmpnent in the x directin wn t alway ue cine. inθ O H Ax A A x Ainθ Kinematic: Ditance v. Diplacement Ditance i hw far mething mve and it include the path travelled. Ditance i a calar. Diplacement i the traight-line ditance frm where the bject tarted t where it ended. Diplacement i a vectr. Speed Ditance Time Velcity, v Δ x Acceleratin, a Δ v Diplacement i the change in pitin f an bject. Δ x x f x i, i a calar., i a vectr., i a vectr. The lpe f a pitin v. time graph i velcity. The lpe f a velcity v. time graph i acceleratin. On an acceleratin v. time graph, the area between the curve & the time axi i change in velcity. On a velcity v. time graph, the area between the curve & the time axi i change in pitin which i al called diplacement. In Free Fall, a y g 9.81 m. An bject i in free fall if the nly frce acting n it i the frce f gravity. In ther wrd: the bject i flying thrugh the vacuum yu can breathe and nt tuching any ther bject. Vacuum yu can breathe n air reitance Lecture Nte - AP Phyic 1 Review f Kinematic.dcx page 1 f

2 The Unifrmly Accelerated Mtin Equatin (UAM Equatin): AP Phyic 1 Equatin Sheet Flipping Phyic v x v x 0 + a x t v f v i + a x x 0 + v x t + 1 a x t Δx v i + 1 a v x v x 0 + a x ( x x 0 ) v v f i + aδx The AP Phyic 1 UAM Equatin aume t i 0; t f t i t f 0 t Δx 1 ( v + v f i ) Prjectile Mtin: An bject flying thrugh the vacuum yu can breathe in at leat tw dimenin. x directin y directin Free-Fall a x 0 Cntant Velcity v x Δx a y g 9.81 m Unifrmly Accelerated Mtin i the ame in bth directin becaue it i a calar and ha magnitude nly (n directin). Remember t break yur initial velcity int it cmpnent if it i nt directly in the x directin and if the initial velcity i directly in the x directin, then the initial velcity in the y directin equal zer. Relative Mtin i Vectr Additin. Draw vectr diagram. Break vectr int cmpnent uing SOH CAH TOA. Make a right triangle. Ue SOH CAH TOA and the Pythagrean therem t determine the magnitude and directin f the reultant vectr. Center f ma. Only need t knw center f ma qualitatively, in ther wrd, withut number. Fr the purpe f tranlatinal mtin, which i eentially nn-rtatinal mtin, the whle bject r ytem f bject can be cnidered t be lcated at it center f ma. Fr example, an bject r grup f bject in prjectile mtin i decribed by nly analyzing the mtin f the center f ma nt each individual part f the bject r ytem. page f

3 Inertial Ma v. Gravitatinal Ma Flipping Phyic Lecture Nte: AP Phyic 1 Review f Dynamic AP i a regitered trademark f the Cllege Bard, which wa nt invlved in the prductin f, and de nt endre, thi prduct. Inertial ma: the meaure f an bject inertia r a meaure f it reitance t acceleratin. Gravitatinal Ma: ued t determine the frce f gravity r weight f an bject. F g m g Inertial Ma and Gravitatinal Ma are experimentally identical. Newtn Firt Law: An bject at ret will remain at ret and an bject in mtin will remain at a cntant velcity unle acted upn by a net external frce. Cmmn mitake: an bject in mtin will remain in mtin i wrng. It will remain at a cntant velcity which mean it will have a cntant peed and a cntant directin. Cmmn mitake: unle acted upn by an external frce. D nt leave ut the wrd net. It i the um f all the frce that need t be zer fr an bject t remain at ret r at a cntant velcity. Newtn Secnd Law: F m a It i arranged differently n the equatin heet: a F m, but it i the ame equatin. When yu ue Newtn Secnd Law, yu mut identify bject() and directin. Free Bdy Diagram: alway draw them t ue Newtn Secnd Law. On the AP Tet, d NOT break frce in t cmpnent in yur initial Free Bdy Diagram. The Frce f Gravity r Weight f an bject i alway dwn. F g m g The Frce Nrmal i caued by a urface, i nrmal r perpendicular t the urface and alway a puh. Dimenin fr Frce are Newtn, N: F m a N kg m The Frce f Frictin i parallel t the urface, ppe mtin and independent f the directin f the frce applied. On equatin heet: F f µ F n, which wrk ut t be three equatin becaue we have tw type f frictin. Static r nn-mving frictin: the tw urface d nt lide relative t ne anther. F f µ Fn and F fmax µ Fn Kinetic r mving frictin: the tw urface d lide relative t ne anther. F kf µ k Fn Fr tw urface, the cefficient f kinetic frictin i alway le that the cefficient f tatic frictin. µ k < µ F 1 F 1, Fr every frce frm bject ne n bject tw there i an equal but Newtn Third Law: ppite frce frm bject tw n bject ne where bth frce are vectr. Newtn Third Law Frce Pair r Actin-Reactin Pair: Act n tw different bject. Act imultaneuly. Incline: Break the Frce f Gravity in t it cmpnent that are parallel and perpendicular t the incline. F g mg inθ & F g mg cθ Tranlatinal Equilibrium: F 0 m a a 0 The bject i either at ret r mving with a cntant velcity Lecture Nte - AP Phyic 1 Review f Dynamic.dcx page 1 f 1

4 Flipping Phyic Lecture Nte: AP Phyic 1 Review f Wrk, Energy and Pwer AP i a regitered trademark f the Cllege Bard, which wa nt invlved in the prductin f, and de nt endre, thi prduct. ΔE W F d Fd cθ : In term f an bject r a grup f bject which we call the ytem, the change in energy f the ytem equal the wrk dne n the ytem which i equal t frce time diplacement time the angle between the frce and the diplacement. Wrk caue a change in energy f the ytem. F F cθ : The frce parallel t the diplacement i the frce time the cine f the angle between the frce and the diplacement f the bject. Identify which frce yu are uing in the wrk equatin. Ue the magnitude f the frce and the diplacement. Dimenin fr Wrk are Jule r Newtn time meter: Three type f mechanical energy: Kinetic Energy: KE K 1 mv (can t be negative) Dimenin fr energy are al Jule: ( ) KE 1 mv kg m kg m kg m m ( ) N m J Elatic Ptential Energy: PE e U 1 kx (can t be negative) Gravitatinal Ptential Energy: PE g mgh r ΔU g mgδy PE g Can be negative. If the bject i belw the hrizntal zer line, then h, the vertical height abve the zer, i line negative. Wrk and Energy are Scalar Cnervatin f Mechanical Energy: ME i ME f Valid when there i n energy cnverted t heat, light r und due t frictin. Identify the initial and final pint. Identify the hrizntal zer line. Subtitute in mechanical energie that are preent. If there i frictin & yu need t ue energy: W f ΔME (De nt wrk when there i a frce applied.) Pwer, the rate at which wrk i dne r energy i tranferred int r ut f the ytem. Hke Law: P ΔE W Fd cθ Fv cθ Dimenin fr Pwer are Watt which are Jule per ecnd: P ΔE J watt & 746watt 1hp F k x : The frce f a pring i linearly prprtinal t the diplacement frm equilibrium pitin. The lpe f a graph f Frce f a Spring v. diplacement frm equilibrium pitin i the pring cntant. lpe rie run F x k Typical dimenin fr the pring cntant are Newtn per meter: F x k N m 0108 Lecture Nte - AP Phyic 1 Review f Wrk, Energy and Pwer.dcx page 1 f 1

5 Flipping Phyic Lecture Nte: AP Phyic 1 Review f Linear Mmentum and Impule AP i a regitered trademark f the Cllege Bard, which wa nt invlved in the prductin f, and de nt endre, thi prduct. Mmentum: p m v (remember, mmentum i a vectr) Dimenin fr mmentum have n pecial name: p m v kg m p i p f (during all clliin and explin) Cnervatin f mmentum: Clliin in tw dimenin: different equatin; p xi p xf & p yi p yf Type f clliin: Type f Clliin I Mmentum Cnerved? I Kinetic Energy Cnerved? Elatic (bunce) Ye Ye Perfectly Inelatic (tick) Ye N Many clliin are in between Elatic and Perfectly Inelatic. They are called Inelatic clliin. During inelatic clliin the bject bunce ff f ne anther, mmentum i cnerved hwever Kinetic Energy i nt cnerved. Elatic and Perfectly Inelatic clliin are the tw ideal extreme. Rearranging Newtn Secnd Law in term f mmentum: F m a m Δ v v m f v i m v f m v i p f p i Δ p Give u the equatin fr impule: Δ p F J Impule F Δ p The Impule Apprximatin give u the equatin n the equatin heet: F F impact Δ p F impact J Impule On a Frce f Impact v. time graph, the area between the curve & the time axi i impule. Dimenin fr impule: Δ p F impact N kg m 0109 Lecture Nte - AP Phyic 1 Review f Linear Mmentum and Impule.dcx page 1 f 1

6 Angular Velcity: ω Δ θ Flipping Phyic Lecture Nte: AP Phyic 1 Review f Rtatinal Kinematic AP i a regitered trademark f the Cllege Bard, which wa nt invlved in the prductin f, and de nt endre, thi prduct. rad r rev min Remember fr cnverin: 1 rev 360 π radian Angular Acceleratin: α Δ ω rad Unifrmly Angularly Accelerated Mtin, UαM, i jut like UAM, nly it ue angular variable: Equatin are valid when α cntant Unifrmly Accelerated Mtin, UAM Unifrmly Angularly Accelerated Mtin, UαM v x v x 0 + a x t ω ω 0 + αt x x 0 + v x t + 1 a x t θ θ 0 + ω 0 t + 1 αt v x v x 0 + a x ( x x 0 ) ω ω f i + αδθ Δx 1 ( v + v f i ) Δθ 1 ( ω + ω f i ) v t r ω Tangential velcity i the linear velcity f an bject mving alng a circular path. The directin f tangential velcity i tangent t the circle and nrmal t the radiu. Tangential velcity i a linear velcity it ha the ame dimenin a linear velcity: Centripetal Frce and Centripetal Acceleratin: Centripetal mean Center Seeking Centripetal frce i the net frce in the in directin r the center eeking frce which caue the acceleratin f the bject in tward the center f the circle which i the centripetal r center eeking acceleratin. Centripetal Frce, F in m a c : Nt a new frce. Never in a Free Bdy Diagram. The directin in i pitive and the directin ut i negative. Centripetal Acceleratin, a c v t r rω The Perid, T, i the time fr ne full cycle r revlutin. Dimenin fr perid: ecnd r ecnd per cycle. The Frequency, f, i the number f cycle r revlutin per ecnd. Dimenin fr frequency are cycle per ecnd which are called Hertz, Hz: Frequency and Perid are inverely related: T 1 f We can ue the equatin fr angular acceleratin t derive an equatin n the equatin heet: ω Δ θ π rad T π T ω 1 f m f cyc ec Hz 0110 Lecture Nte - AP Phyic 1 Review f Rtatinal Kinematic.dcx page 1 f

7 The Cnical Pendulum Example: O FTin in θ FT FT in θ in H FT A FT c θ y FT FT c θ y H FT F y () FT Fg may m 0 y FT FT c θ mg y vt F F F in θ ma m in Tin T r c v t rω r v t Δx C π r T T We culd even ubtitute further: FT c θ mg FT mg c θ π r v t mg T 4π r 4π r FT in θ m g tan θ in θ m r T T r r c θ And lve fr the radiu in term f the length f the tring. O r r L in θ H L 4π r in θ 4π L in θ g 4π L 4π L c θ g tan θ g T c θ g c θ T T T in θ And we end with an exprein fr the perid f the circular mtin. page f

8 Flipping Phyic Lecture Nte: AP Phyic 1 Review f Rtatinal Dynamic AP i a regitered trademark f the Cllege Bard, which wa nt invlved in the prductin f, and de nt endre, thi prduct. Trque, the ability t caue an angular acceleratin f an bject: τ r F r F inθ The mment arm r lever arm i: r r inθ A larger mment arm will caue a larger trque. Maximize trque by maximizing r, the ditance frm axi f rtatin t the frce. Maximize trque by uing an angle f 90 becaue inθ ( ) in 90 max ( ) 1 Dimenin fr Trque are Newtn meter, N m, nt t be cnfued with Jule fr energy: Trque i a vectr. Fr directin ue clckwie and cunterclckwie. (adly, nt the right hand rule) Rtatinal frm f Newtn Secnd Law: Mment f Inertia r Rtatinal Ma: Fr a ytem f particle: I m i r i i τ I α Dimenin fr Mment f Inertia: I m i r i kg m Fr a rigid bject with hape the value r the equatin will be given t yu. Fr example: I lid cylinder 1 MR ; I thin hp MR ; I lid phere 5 MR ; I thin pherical hell 3 MR ; I rd 1 1 ML ; I rd abut end 1 3 ML With the exceptin f I rd abut end, thee are all abut the center f ma f the bject. Rtatinal Kinetic Energy: KE rt 1 Iω KE rt, like tranlatinal energy, i in Jule, J. i Rlling withut lipping: When an bject rll dwn a hill, it will gain nt nly tranlatinal kinetic energy but al rtatinal kinetic energy. Which mean, the higher the mment f inertia, the higher the rtatinal kinetic energy f the bject and therefre the lwer amunt f energy that will be left ver fr tranlatinal kinetic energy and therefre a lwer final linear velcity. Angular Mmentum: Uing Cnervatin f Mechanical Energy: ME i ME f PE gi KE rt f + KE t f Al need the equatin fr the velcity f the center f ma f a rigid bject rlling withut lipping: v cm Rω L I ω Dimenin fr Angular Mmentum: ( ) L I ω kg m Angular Impule: Δ L τ impact Angular Impule Dimenin fr Angular Impule: Δ L τ impact N m rad kg m 0111 Lecture Nte - AP Phyic 1 Review f Rtatinal Dynamic.dcx page 1 f 1

9 Flipping Phyic Lecture Nte: AP Phyic 1 Review f Univeral Gravitatin AP i a regitered trademark f the Cllege Bard, which wa nt invlved in the prductin f, and de nt endre, thi prduct. Newtn Univeral Law f Gravitatin: r G N m kg Univeral Gravitatinal Cntant: r i nt defined a the radiu, it i defined a the ditance between the center f ma f the tw bject which can be cnfuing becaue metime it de wrk ut t be the radiu. Fg mg i planet pecific. Fg We can cmbine the tw t lve fr the acceleratin due t gravity n Earth (r any large, Gm1m r i univerally true. Fg m g Gm me (R E + alt g ) (R GmE E + alt ) The gravitatinal field i apprximately cntant n the urface f the Earth becaue ur height i mall cmpared t the radiu f the Earth. hmr.p 1.8 m, RE 6,370,000 m The gravitatinal field i nt cntant frm a glbal perpective and decreae a altitude increae, thi can be hwn uing a vectr field diagram. Slving fr the peed f the atellite in rbit arund the Earth: F in Fg m ac vt Gm1m celetial bdy): Fg GmE r Gm me r GmE (R E + alt m vt r ) Univeral Gravitatinal Ptential Energy: Ug Gm1m r The equatin ued t find gravitatinal ptential energy in a nn-unifrm gravitatinal field. U g 0 : The zer line i infinitely far away. U g A ingle bject can nt have Univeral Gravitatinal Ptential Energy. Univeral Gravitatinal Ptential Energy i defined a the Gravitatinal Ptential Energy that exit between tw bject. " Technically Gravitatinal Ptential Energy in a cntant gravitatinal field: Gm1m 0 PE g mgh, i the gravitatinal ptential energy that exit between the bject and the Earth. S even PE g require tw bject. 011 Lecture Nte - AP Phyic 1 Review f Univeral Gravitatin.dcx page 1 f 1