Calculate the efficiency associated with one rotation of the axle

Transcription

1 We cn clculte the efficiency of one rottion of the xle by exining the work one. k Mx Your Rie: Workheet hi ctivity will tke you through the tep neee to optiize the work ue in your ouetrp cr. ollow thi workheet in orer. Refer to previou ctivitie experientl eureent n clcultion where poible. You y nee to repet thi ctivity. Clculte the efficiency ocite with one rottion of the xle You eure the ttic frictionl force,, in Drgge Rcer. We cn clculte the work one by the frictionl force for one rottion if we know the length of the pth tht thi force ct. he pth i relte to the ize of the wheel it i the circuference. Copute the circuference you eure the riu in Quntify It : C π r (π ) ( ) W f Copute the work one by the frictionl force, W f : C ( )( ) Mx Your Rie 1

2 Clculte the orque cue by lo: In Spinner, we turne the xle by uing known force weight. When et into otion, the ouetrp provie the force tht propel the cr. You ight hve eure the force previouly in Quntify It or Convert It, but o o now before continuing. Recor the force below. Mouetrp force, We lo nee to know the itnce tht the force ct in orer to clculte the torque reulting fro the force. hi itnce i the riu of the xle. Axle riu, r xle orque fro ouetrp force: r ( )( ) xle Clculte the Work one by orque: W θ ow tht we know the torque cue by the ouetrp force,, the work cn be clculte if we know the ngle, θ, tht the torque ct through. Since we re eling with one rottion (or revolution), the ngle i equl to 360, or π rin. orque fro ouetrp force: W θ ( )(π r) Mx Your Rie

3 Clculte the Efficiency of Mouetrp Cr: Let ue tht the cr only ue energy to overcoe friction. hen we coul reon: (Work out) (riction Work); (Work in) (Mouetrp Ar Work) Since the work of the ouetrp i expene on ttic friction. he efficiency of the ouetrp cr i the rtio of the output to the input work. Efficiency Work out Work in E Work out Work in Iprove the Efficiency If we know the externl force cting on the cr (friction, norl force), we cn optiize the length of prt on the cr o tht it oe not wte energy. Since we re only coniering ttic friction n externl force, we houl tune the cr o tht the force of the ouetrp eqully oppoe thi force. We hve to fin the ccelertion of the wheel neee to ct gint the frictionl force. Wht eqution relte orce n Accelertion? ewton n lw:. Ue the of the cr (clculte in Drgge Rcer ) n the frictionl force to clculte the necery ccelertion for the wheel: cr kg Mx Your Rie 3

4 Relte liner ccelertion to ngulr ccelertion: α r We h to o relte liner n ngulr ccelertion in Spinner : we re oing the e opertion in thi clcultion. α cr rxle / r/ in the necery orque: I α In Spinner, we foun the oent of inerti, I, of the rer xle be on how it ccelerte in repone to n pplie torque. Ue the oent of inerti clculte in Spinner n the ngulr ccelertion clculte bove to eterine the torque necery to ove the cr without the wheel overcoing ttic friction n lipping reult. xle I xle α wheel ( kg )( r/ ) xle in the force neee to prouce xle : We re trying to rotte the xle, n now tht we know the torque neee to cue the eire rottion, we cn fin the force tht ut be trnferre fro the ouetrp. ouetrp r xle xle Mx Your Rie 4

5 Scle the orce, Scle the orque We cn ue the ie of echnicl vntge to lift the ouetrp r if we ttch ro to the r, it tke le effort to oppoe the pring force. How will the extene ouetrp r pply force on the xle? Hint: ewton 3 r Lw: or every ction there i n equl n oppoite rection Accoring to ewton 3 r lw, extening the ouetrp r will reult in lower force being pplie to the rive xle. hi i goo thing if we hve too uch force trnferre fro the ouetrp pring to the xle: we cn cle the force be on the itnce wy fro the ouetrp be. Ue proportion! If you know the force ( r ) eure t certin point fro the pring ( r ), you cn fin the itnce, extenion, tht the ouetrp r ut be. r r ouetrp extenion extenion r ouetrp r ( ) extenion Mx Your Rie 5