mechanics力学-30作用在摆上向心力

实验ExperimentP30:CentripetalForceon作用在摆上(ForceSensorPhotogate)（力传感器，光门Time:30mSWInterface:500&Macintosh_File:P30CentripetalForceWindows_File:P30_CENT.SWSEQUIPMENTNEEDED所需仪ScienceWorkshop_horizontalrod_50Newtonforcesensor力传感masssetforcalibration)pendulume.g,metalcylinder)摆（例如，金属圆桶rightangleclamp直角baseandsupportrodstring细calipers测径PURPOSEThepurposeofthislaboratoryactivityistomeasurethecentripetalforceexertedon bobdirectlyusingtheforcesensorandtocomparethemeasuredforcetothecalculatedforcebasedonthespeedofthependulum.本实验的目的是用力传感器来测量直接作用在一个摆锤THEORYndulumbobfollowsacircularpath.Therefore,itisactedonbya(“center-seeking”)force.Inthecaseofthependulum,thetensioninthestringcausesthebobtofollowthecircularpath.Atthebottomofthependulum’sswingthenetforceonthebobisthecombinationofthetensioninthestringandtheforceofgravity.摆锤沿着一个圆形路径运动。T=m=mg=AccordingtoNewton’sSecondLaw,根据第二定律，FTmgmawhereTisthetensioninthestring,misthemassofthependulumbob,gistheaccelerationdueTheforcesensorwillbezeroedwhenthependulumisatrestinitsequilibriumposition(orT=mgThustheforcemeasuredbytheforcesensorwhenthependulumisinmotionisequaltothecentripetalforceFcasthependulumbobpassesthroughthelowestpointoftheswing.当摆锤静Thecentripetalforcecsobefoundusingthespeed,v,ofthebobasitpassesthroughthelowestpointoftheswingusing:向心力也可以根据摆锤通过摆动最低点时的速度，由下式求vFrwhereristheradiusofthecircularpathwhich,inthiscase,isequaltothelengthofthePROCEDUREForthisactivity,theforcesensorwillmeasurethecentripetalforceon ndulumbobasitswingsback-and-forth.Thephotogatewillmeasurethetimethatthependulumbobblocksthephotogatebeam.Youwillenterthevalueforthediameterofthependulumbob.TheScienceWorkshopprogramcalculatesanddisplaysthespeedofthependulumbobandthecentripetalforceonthependulum.YoucanusetheScienceWorkshopprogramtocalculatecentripetalforce动时，作用在摆锤上的向心力。光门将测量摆锤阻断光门光束的时间。ScienceWorkshop程序将计算并显示摆锤的速度和作用在摆上的向心力。你也可以使用ScienceWorkshop程Thecalculatedandmeasuredvaluesofcentripetalforcewillbecompared.向心力的计算值和测PARTIComputerSetup计算机设ScienceWorkshopConnecttheScienceWorkshopinterfacetothecomputer,turnontheinterface,andturnonthecomputer.Connecttheforcesensor'sDINplugintoogChannelAontheinterface.Connectthephotogate’sstereophoneplugintoDigitalChannel1ontheinterface.OpentheScience titledasWindows:P30_CENT.SWS willopenwithaGraphdisplayofForce(Newtons)andVelocity(m/sec).文件将打开并带一个力（N）——速度(m/sec)图表显示。TheExperimentSetupwindowhasbeenresized.IfyouwanttoexpandtheExperimentSetupwindowtoitsoriginalsize,clickonthe“Zoom”boxintheupperrighthandcornerofthewindow.(Note:Tobringadisplaytothetop,clickonitswindoworselectthenameofthedisplayfromthelistatoftheDisplay The“SamplingOptions_”areasfollows:PeriodicSamples=Fastat100Hz(onehundredsamplespersecond)andStartCondition=Channel1,Low(recordingbeginswhenthephotogateconnectedtoDigitalChannel1isblocked).PARTII:SensorCalibrationandEquipmentSensorTocalibratetheforcesensor,changetheExperimentSetupwindowtofullsizebyclickingonthe“Zoom”boxortheRestorebuttonintheupperrighthandcornerofthatwindow.要IntheExperimentSetupwindow,double-clickonSensorA’sicontoopentheForceSensorsetupwindow.在实验设置窗口中，双击传感器A的图标来打开力传感器设置窗TheForceSensorsetupwindowforSensorAshowsthedefaultcalibrationvalues(i.e.,apushof50Newtonsproduces8Volts;apullof-50Newtonsproduces-8Volts).Theforcesensorissetupsothatapullawayfromthesensorisa‘negative’force.Forexample,ifaonekilogramobjectishungverticallyfromthehook,theforcesensormeasures-9.8Newtonssincetheforceisdownward).传感器A的力传感器设置窗口显示了一系列缺省Mounttheforcesensoronahorizontalrodsothehookispointingdown.Donotputanobjectonthesensor’shookyet.将力传感器安装在一个水平杆上，则力传感器的钩子朝下。还任何物体挂在力传感器的钩子上。Forthe“HighValue”calibrationpoint,pressthetarebuttononthesideoftheforcesensortozerothesensor.Clickthe“Read”buttonfor“HighValue”.Sincethereisnoobjectonthesensor’shook,type“0”astheHighValue”.对于“高值”校准点，按下力传感器侧FortheLowValuecalibration,hanganobjectofknownmassonthesensor’shook.对于Clickthe“Read”buttonfor“LowValue”.Entertheobject’sweightinNewtons(massin••Remember,entertheobject’sweightasanegativevalue(aforcepullingawayfromtheInthisexample,theobjecthasamassof549.5grams(0.5495kg),oraweightof5.385ChangetheforcesensorSensitivity.Clickthe“Sensitivity ”button.Changefrom(1x)”改为“Med(10x)”。Click“OKtoreturntotheExperimentSetupwindow.单击“OKYoudonotneedtocalibratethephotogate.However,youdoneedtoenterthevalueofthediameterofthependulumbobintotheScienceWorkshopprogram.你无须校准光门。不过你一定要将摆锤的直径的值键入ScienceWorkshop程序中。Measurethediameterofthependulumbob.Recordthediameter.测量摆锤的直径并记录diameterofpendulum,摆锤的直径d IntheExperimentSetupwindowdouble-clickthephotogate’sicontoopenthePhotogateSetupwindow.在实验设置窗口中。双击光门的图标来打开光门设置窗口。ChangethedefaultvalueoftheObjectLength(0.100m)tothevalueofthediameterofthependulumbob.(Thediameteris0.0317mintheexample.)将物体长度的缺省值(0.100m)Click“OKtoreturntotheExperimentSetupwindow.单击“OKMounttheforcesensoronahorizontalrodwiththehookenddown.将力传感器安装在一Measurethemassofthependulumbob.RecordthemassintheDatasection.测量摆锤的massofpendulum,摆锤的质量，m Tomakethependulum,useapieceofstringthatisaboutonemeterlong.Tieoneendofthestringtothehookontheforcesensorandtietheotherendtothependulumbob.制作一Arrangethephotogatesothependulumbobblocksthephotogate’sbeamwhenthebobisatrest.Thecenterofmassofthependulumbobshouldbeapproximayatthesameheightasthephotogatebeam.调整光门的位置，使摆锤时可以阻断光门的光束。摆锤的Measurethelengthofthependulumfromtheforcesensor’shooktothecenterofthependulumbob.测量从力传感器的钩子到摆锤中心的摆的长度。length,长度，r ForceForceNOTE:NottoPreparingtoRecordData准备记录Whenalltheequipmentisready,practiceswingingthependulumbob.Pullthependulumbobtothesideabout15to20centimeters.Gentlyreleasethebobsoitswingsthroughthephotogateassmoothlyaspossible.Adjustthepositionofthephotogateifnecessary.当所有它尽可能光滑的通过光门摆动。必要，调整光门的位置。NOTE:NOTE:Don’tletthependulumbobhitthephotogate!PARTIIIDataRecording数据记Whilethependulumbobisatrest,zerotheforcesensorbypressingthetarebuttononthesideoftheforcesensor.当摆锤时，按下力传感器侧面的“tare”按钮使传感器归Setthependuluminmotion.Letthependulumswingback-and-forthseveraltimestoallowanyoscillationstodampenout.推动摆锤进行运动。让摆来回摆动几次，使摆动减弱。ClicktheREC”buttontobegin.Recorddataforabout20secondsClickthe“STOP”buttontoenddatarecording.记录数“Run#1”willappearintheDatalistintheExperimentSetupwindow“Run#1”将出现在YZINGTHEDATA分析数ClicktheGraphtomakeitactive.Clickthe“Autoscalebuttontorescalethegraphtofitthedata.单击图表使之活动。单击“Autoscale”来重新分度图表以适应数据。TheGraphwilldisplayaplotofthependulum’svelocityandaplotofthependulum’scentripetalforce.Theplotofspeedshouldbelinear.TheplotofcentripetalforceshouldbeClickthe“SmartCursor”button.Thecursorchangestoacross-hairsh whenyoumoveitintotheGraphdisplay.TheX-andY-coordinatesofthepositionofthecursoraredisplayednexttothehorizontalandverticalaxesoftheGraph.单击“灵敏光标”按钮。Movethecursor/cross-hairtotheorsecondpeakontheplotofcentripetalforce.TheY-coordinateatthatpointistheumcentripetalforceonthependulum.RecordthevalueofcentripetalforceintheDatasection.(Fc=0.2085Newtonsintheexample.)将光力的最大值。把这个值（本例中Fc=0.2085N）记录在数据一节中。PressandholdtheSHIFTkeyonthekeyboard.Thiswill‘freeze’thehorizontalpositionoftheSmartCursor.Movethecursorverticallyintotheplotofvelocityandplacethecursoratthepointthatcorrespondstothepeakyoumeasuredintheplotofcentripetalforce.TheY-coordinateatthatpointistheumspeedofthependulum.RecordthevalueofspeedintheDatasection(v0.84006m/secinthe