ork & c Energ eew of Preou Lecture New polc for workhop You are epected to prnt, read, and thnk about the workhop ateral pror to cong to cla. (Th part of the polc not new!) There wll be a prelab queton whch to be anwered on the workheet before cong to cla. The prelab queton wll be graded durng the quz. (Th polc replace the penalt for not prntng the workheet n adance.) lud retance, ternal peed f D at hgh peed f g Unfor crcular oton: g / D Tangent to crcle ; = cont adall nward ; a = cont If force on object perpendcular to : a r a a r ar Net force caue radal acceleraton a Newton nd law. Object path becoe crcular wth radu : The forcepontngto the center called radal or centrpetal force. The centrpetal force a be ade up of weght, frcton, tenon, noral force actng on object t not an addtonal force! block gen a kck and then freel lde up an nclned plane at angle wth the horzontal. There frcton between the block and plane. The agntude of the acceleraton of the block occer ball dropped fro a hot ar balloon. Durng the fall, ar retance cannot be neglected. hch of the followng graph bet repreent the acceleraton. te graph? (Chooe down drecton a pote.). g. gn C. gco D. larger than g n E. aller than g n C 4
ball attached to the end of a cord of length eter. The ball whrled n a ertcal crcle. hch correct? kg ball attached to the end of a cord of length eter. The ball whrled n a ertcal crcle. The tenon n the cord at the top of the crcle 0 N. hch correct?. The tenon at the botto and at the top greater than the weght of the ball..the tenon at the botto and the top le than the weght of the ball. C.The tenon at the botto greater, and at the top le than the weght. D. The tenon at the botto greater than the weght, and at the top t a be greater or le than the weght. E. The tenon at ether locaton a be greater or le than the weght, dependng on the peed.. The acceleraton at the top of the crcle zero.. The acceleraton at the top of the crcle 9.8 /, upward. C. The acceleraton at the top of the crcle 9.8 / downward. D.The acceleraton at the top of the crcle ha agntude 9.6 /. E. The acceleraton at the top of the crcle cannot be deterned. VECTO MULTIPLICTION: SCL PODUCT Vector ddton: hat doe ean? Scalar Product (= Scalar) (projecton of on ): Note: co co co co Scalar product of two ector COMMUTTIVE. co co SCL PODUCT USING COMPONENTS Dot product dtrbute ( C) C Conder: ( ˆ) j ( ˆ) j Ue dot product to fnd angle between ector. Eaple: kˆ ; ˆ ˆ j k ; ( kˆ) ( j kˆ) co co co 60 ( z z ) C C C! o ĵ î 0
Suppoe block of a le on horzontal plane. Cae : horzontal force act contnuoul a block dplaced b ork done b force: Cae : orce and dplaceent are not collnear O ork = (dplaceent) (coponent of along dplaceent) ( co ) ork done (b a force) a be: EMPLES: Pote Negate Zero Pote: e.g. block on preou ewgraph Negate: rnold lower the barbell EMPLE: : Let (5N)ˆ, (3)ˆ [(5N)ˆ] [(3)ˆ] 5 N5 J : (5N co )ˆ (5Nn ) [(5N co )ˆ (5N n ) ˆ] j (3)ˆ (5co )(3) J Zero: Unfor crcular oton C c d radal tangent EMPLE: block of a lde a dtance down an nclne plane. How uch work done b frcton? n gco = 0 n = gco gn f f = n = gco f g co f gco f gco n gn g How uch work Gra w done b grat? w gn g g n g co hat the work done b all force actng on the block a t lde? ( )ˆ ( ) g(n co )ˆ ( n g co ) S g n co k n g T Contant peed!!! Net force = 0 ork = 0
block puhed o that t oe dtance L up a rap (nclne angle ) at contant peed. If there frcton, the work done on the block b the hand block puhed o that t oe dtance L up a rap (nclne angle ) at contant peed. The work done on the block b the noral force of the rap. g n L.. le than g n L. C. greater than g n L. D. could be greater of le. E. zero.. g co L.. le than g co L (but > 0) C. greater than g co L. D. could be greater of le. E. zero. I the work pote or negate? block puhed o that t oe dtance L up a rap (nclne angle ) at contant peed. If there frcton, the agntude of the work done on the block b frcton block puhed o that t oe dtance L up a rap (nclne angle ) at contant peed. If there frcton, the agntude of the work done on the block b grat. g n L.. le than g n L. C. greater than g n L. D. could be greater of le than g n L. E. zero. I the work pote or negate?. g n L.. le than g n L. C. greater than g n L. D. could be greater of le than g n L. E. zero. I the work pote or negate?
block puhed o that t oe dtance L up a rap (nclne angle ) at contant peed. If there an unknown aount of frcton, the work done on the block. zero.. le than zero. C. greater than zero. D. could be pote or negate. E. need to know the frcton force. O ND INETIC ENEGY Conder collnear force and dplaceent: here NET force ECLL: If contant acceleraton a change to oer a dtance Defne c Energ: a a ork-energ Theore: ork done b a force on an object of a = change n kc energ of the object EMPLE: ecall the ellow lght Car wth Ma of,000 g ong at 30 / ut top n 30. How uch force ut be appled? 000 kg30 / 30 500 900 30 4.50 30.50 4 5 kg / kg hat the correpondng acceleraton??? N EMPLE: Drop a bowlng ball fro the top of the Epre State uldng. How fat t gong jut before t ht the ground? Ue ork-energ Theore: S g( ˆ); j (30 ) g( 30 ) g(30 ) 6400 / 80 / 30.50 a 000 4 N kg 5 /
Two dentcal block are releaed fro ret at the ae heght on two eparate frctonle rap. The block reach the ae fnal heght labeled fnh. hch tateent correct regardng the work done on the two block b the gratatonal force? Two dentcal block are releaed fro ret at the ae heght at the ae te. lock lde down a teeper rap than lock. oth rap are frctonle. The peed of lock a t croe the fnh lne :. lock trael further, o ore work done on block b the gratatonal force than on block.. oth block fall the ae ertcal dtance, o the work done b grat the ae. C. Newton Thrd Law, the force eerted on the block b the earth eactl cancelled b the force eerted on the earth b the block. The work done zero. D. The angle between force and dplaceent aller for block than for block, thu the work done on block greater. E. None of the aboe.. greater than the peed of lock at the fnh lne.. le than the peed of lock at the fnh lne. C. equal to the peed of lock at the fnh lne. D. Not enough nforaton. O DONE Y VYING OCE Conder arng force along lne or contant force: = = rea under orce. dplaceent cure or arng force: ( ) () l ( )! 0 ( ) d EMPLE: orce to tretch prng Contant force = k Sae contant force act oer ae dtance = = k = prng contant [N/] Hooke Law
ork done b to tretch prng: In General: ork done on prng to etend fro to : () ( ) d k kd o k k kd k ( ) d o 0 EMPLE: It take 4.00J to tretch a prng fro equlbru to 0.0 c. How uch work ut be done to tretch t an addtonal 0 c? 0 c Intal etenon: = 4.00 J k( k k = 800 N/ ) #( 0.0 ) (0.0 $ ) k( NOTE: ork-energ theore ald for arng force on cured path! ) ddtonal etenon: k ) ( 0 c) (0 c ( 800 N/) 0.040 0.00 =.0 J New polc for workhop You are epected to prnt, read, and thnk about the workhop ateral pror to cong to cla. (Th part of the polc not new!) There wll be a prelab queton whch to be anwered on the workheet before cong to cla. The prelab queton wll be graded durng the quz. (Th polc replace the penalt for not prntng the workheet n adance.) 7