Experiment 5: Newton’s Second Law

1 Experiment 5: newton s Second LawFigure : newton s Second Law SetupFigure : Note: String from cart to pulley must behorizontal and aligned with the CartPulley and StringTriple-Beam BalanceDigital BalanceStopwatchMeter StickMass Hanger(1) 10 g Mass(2) 20 g Masses(1) 50 g MassPaper Clips (small masses)Plumb BobWastebasket2728 Experiment 5: newton s Second LawFREE-BODY DIAGRAM SOLUTION METHOD: INSTRUCTIONSStep 1:Sketch the problem/situation and specify the coordinate system for each object in your 2:Draw all forces (arrows that represent these vectors) acting oneach objectin the system you are forces should extendaway fromthe object in the direction of the force. Remember that the length of the arrowis an indication of the magnitude of the : Free-Body Diagram of Modified Atwood s Machine (Example for~vconstant, ~F=m~a= N).Step 3:Write newton s 2ndLaw ( ~F=m~a) in component form ( Fx=maxand Fy=may) foreachobject inthe system.

2 For this example,mAandmB:mA: FAx=mAaAx FAy=mAaAymB: FBx=mBaBx FBy=mBaByStep 4:Refer to your diagram to sum the forces for each object as instructed by Sir Isaac newton . For this example: FAx=mAaAx=T Ff FAy=mAaAy=FN mAg= N(aAy: Constant velocity means this acceleration m/s2) FBx=mBaBx= N(mB: No forces acting in the horizontal direction.) FBy=mBaBy=T mBg(Note that sincemAandmBare connected and mov-ing together,Tis the same for each object, andaAx= aBy.)Step 5:Write the known quantities. Write the write equations algebraically first, then insert the known do the math! That s all there is to 5: newton s Second Law29 Advance ReadingText: newton s Second Law, acceleration, velocity, dis-placement, Manual: Appendix CObjectiveThe objective of this lab is to explore and analyze therelationship between force, mass, and to newton s Second Law, the acceleration,~a, of a body is directly proportional to the vector sumof the forces, ~F, applied to the body: ~F=m~a( )where m is the mass of the experimental configuration for this Experiment isa variation of Atwood s machine (Fig.)

3 , Fig. ).A forceT(tension) will be applied to the cart,mA, bymeans of a string with an attached mass,mB. If onecan ignore the force of friction acting on the cart, thenEq. in the direction of motion simplifies to: FAx=mAaAx=T( )Thus, if the mass of the cart is doubled whileTisheld constant, the acceleration of the cart is halved(Part 1). Correspondingly, ifTis doubled whilemAisheld constant, the acceleration of the cart is doubled(Part 2).This analysis assumes a frictionless environment. Forsimplicity,Ffwill be counterbalanced by a small mass,mf, hanged from one end of the system. When theweight ofmfis equal to the force of friction (mfg=Ff), the system will be in equilibrium. F= 0 Na= 0 m/s2In equilibrium, the cart set in motion continues mov-ing with constant velocity. A new massmfmust befound each time the cart s mass is adjusted inPart 1,asFfwill have been counteracted, any additional masswill be directly related to the acceleration of the sys-tem as in Eq.

4 The added mass,mB, exerts a forceequal to its weight on the cart/mass the cart is accelerating, derivingTandaof thecart is more involved. The relevant equations for thisexperiment are provided:a=mB gmA+mB+mf( )T=mA mB gmA+mB+mf+mf g( )We will compare the acceleration from Eq. to theacceleration obtained from thekinematic equations forconstant acceleration(Page 22, Experiment 4).In this Experiment , acceleration will be found exper-imentally tracking the cart s motion across a set dis-tance. The time of travel will be carefully measuredusing a that since the cart andmBare connected, theiracceleration, velocity, and distance traveled are equalat all times. Thus, the horizontal distance the carttravels, x, is equal to the vertical drop of the at-tached mass, +v0xt+12axt2( )We now define calculated and measured accelerationsasaT :aT determined by Eq. ; determined by Eq. 5: newton s Second LawName:1. State newton s First and Second Laws (qualitative explanations).

5 (20 pts)2. How is tension applied to the cart in this Experiment ? (15 pts)3. How is friction compensated for in this Experiment ? (15 pts)4. Should the acceleration determined inStep 5(or any part of this Experiment ) be greater than, less than, or equalto the acceleration of gravity? Explain. Assume friction is negligible; refer to Eq. (20 pts)5. Complete the free-body diagrams for the two situations shown below. Draw to scale ( , your diagrams shoulddelineate between ~F=m~a= N and ~F=m~a> N). (Refer to the lab manualTheory) (30 pts)Situation 1: ~F=m~a= NSituation 2: ~F=m~a> NExperiment 5: newton s Second Law31 PROCEDUREPART 1: Vary the Mass of the Cart,maTrial #11. Measure the mass of the cart,mA, using the triplebeam balance. Record it in the table Measure the frictional force acting on the cart:Add small masses to the string until the cart main-tains a constant velocity when tapped. The weightofmfis equal toFf. Recordmfin the table AttachmB( kg) to the end of the string.

6 [Mea-sure its actual mass and record it]4. Use a stopwatch to measure the time it takesfor the cart to travel a distance x(or formBto fall the same distance y). Your data willbe more accurate if xis as large as not allow the cart to hit the Determine theoretical and measured accelerationfor the #26. RemovemBfrom the system. Add kg to thecart and measure its total Determine the new force of friction on the cart ReplacemBand measure time and distance of thecart s Determine acceleration for this heavier #310. RemovemBand add kg to the cart. Measurethe force of friction and adjustmffor this ReplacemBand determine acceleration for 2: Vary the Applied Force12. Keep the weight of the cart (approx. kg) andkeep the samemfas in the previous Trial #1:IncreasemBto kg, findaT Trial #2:IncreasemBto kg, findaT Trial #3:IncreasemBto kg, findaT 3: GraphingThe entire cart/hanging mass system follows thesame law, F=ma.

7 This means that plottingforce vs. acceleration yields a linear relationship (ofthe formy=mx).16. Open Graphical force(mBg) (aMeas.) for theVaryingForcetrials. Apply a linear fit to the three datapoints. Print this Create a similar graph ofmBg vs. aT : Use the method specified on Page 5 forQuestion 21. Assume a modified Atwood s Machine arrangementsimilar to today s Experiment and a frictionless cartthat continues moving after the hanging mass hasreached the floor, thus no longer exerting a forceon the cart. Qualitatively sketchv vs. tfor thisarrangement, starting from rest att= s, andinclude times after the hanging mass has reachedthe floor (long table!).2. Draw a free-body diagram for the cart/hangingmass system shown in Fig. ,ignoring this diagram to derive an equation of force,T,that has only masses and acceleration due to grav-ity,g( , an equation similar to Eq. ).