Newton s Lws II PES 6 Advnced Physics Lb I Purpose of the experiment Exmine two cses using Newton s Lws. Sttic ( = 0) Dynmic ( 0) fyi fyi Did you know tht the longest recorded flight of chicken is thirteen seconds? Newton s Lws II -
Tble of Contents Bckground 3 Sttic Forces 3 Dynmic Forces 6 Procedure 8 Equipment List Prt A Force Bord Lrge Wshers (0) Protrctor Prt B Super pulley Threded rod Ring stnd Ring stnd clmp C-clmp String Lrge wshers Motion sensor LbPro Interfce Protective metl cge Crdbord trget Newton s Lws II -
Bckground Sttic Forces Newton s lws re some of the most fundmentl descriptions of clssicl mechnics. The beutiful thing bout them is their simplicity. The simplest cse to investigte is one in which nothing is ccelerting. Keeping the ccelertion t zero mens the forces must blnce out. This is clled the sttic cse. The specific sttic cse we will be looking t tody is digrmmed below: Experimentl Setup m m m 3 This is the vector nlysis of this setup. T T T T F F T T m m g F 3 T 3 m 3 m m g m 3 g This is the interesting prt we will be concentrting on tody. Newton s Lws II - 3
The experiment presented is network of msses ech exerting its force in seprte direction. Choose the forces such tht the msses re sttionry (velocity = 0 therefore ccelertion must = 0). Forces nd ccelertions, s you know from your lecture clss, re vector quntities. Vectors hve mgnitude nd direction. Newton s lws del with forces nd ccelertions s vectors ( F = m ). In this prticulr lb we will del with only dimensions, x nd y. If we brek this eqution into its vector components we get: F x = m x nd F y = m y We use the summtion symbol () to represent tht this hlf of the eqution will contin ll the components of the forces in tht direction. y F F First let s del with the horizontl cse (the x direction). The only two forces tht hve 3 x components in the x-direction re F nd F. To find these components we hve to use some trigonometry. The x components of F x,f x nd F 3 x re given by the following F 3 equtions: Figure F x = F cos F = mgnitude, its length F x = F cos F 3x = F 3 cos 3 = 0 F 3 hs no x component. Cn you explin mthemticlly why F 3 hs no x component ( 3 =?). If you do not understnd how I got these force components review your physics nd mth book. Newton s Lws II - 4
Similrly, for the verticl components: F y = F sin F y = F sin F 3y = F 3 sin 3 = F 3 Note: For the reminder of this mnul the mgnitude of vector A will be written s A. Now to fill out our equtions of Newton s lw: 0 0 F x = m x nd F y = m y F cos + F cos = 0 nd F sin + F sin - F3 = 0 We now hve something we cn test with n experiment. Mss is esy to mesure. The ngles () will be little tricky but mesurble. By dding mss to the setup nd mesuring the ngles, ccording to Newton, ech direction should sum to zero. Let s find out! F string B F Note: Remember tht is reltive to the horizontl xis nd in the lb there is not some mgicl coordinte xis floting round. Therefore, we need something to mesure tht is A C t lest relted to. The only ngles tht re mesurble re the ngles between the strings () digrmed to the left. Your job is to find the F 3 s from the s. You cn sk your instructor for help. Newton s Lws II - 5
Dynmic Forces Consider the following sitution. A mssless string connects two msses over frictionless pulley. The msses re close to the sme mss m is slightly hevier thn m. Therefore the m will ccelerte upwrd while m will move down. pulley m m m > m This is clled the dynmic cse since the ccelertion is no longer zero. Therefore, the right side of Newton s equtions will not be zero. Now, to get mthemticl description of the system ccording to Newton. First thing is to brek the problem into smller more mngeble prts, let s look t the ech of the msses individully. Newton s Lws II - 6
T T y m g m g x F y = m F y = m T - m g = m T - m g = - m If you solve the expression for T from the left-hnd eqution (system ) nd substitute it into the right-hnd eqution (system ) we get: m g m - m g = m Now solve for : m = m - m + m g This is the expected (theoreticl) vlue of the ccelertion bsed on the setup nd Newton s Lws. Newton s Lws II - 7
The Lb The gol of this lb is to investigte the vlidity of Newton s clims. F = m, if force cts on ny mss, then tht mss will ccelerte. Remember to include the uncertinty nd the units in your mesurements Prt A Force bords The experiment should be set up s follows: pulleys Leveling feet msses Newton s Lws II - 8
Experimentlly it is difficult to mesure the ngles, nd 3. The problem rises when we try to mesure these ngles reltive to the horizontl xis, which only exists on pper. So, we need to find something else. How bout mesuring the ngles mde between the strings, A, B, nd C. You will notice tht the force tble hs two sets of ngles lbels. When mesuring the ngles mke sure you use the sme lbels for ll your mesurements. Level the tble by djusting the feet. Set the x-y coordinte system. You hve mesured the ngles between the strings ( A, B, nd C ) t this point you need to clculte, nd 3. Hint: set one of the strings to zero degrees nd ssign it the x or y xis the other will be t 90 degrees (perpendiculr) to this one. DO NOT WRITE on the force tble. Apply rndom ngle nd msses to two of the three pulleys nd djust the thirds ngle nd mss until you rech equilibrium. Mke sure the system is in F 3 complete equilibrium, by this I men the ring should be centered on the peg in the middle of the tble nd smll movement to the ring should result in the ring retuning to the center. Weigh ech of the msses nd record their vlues. Clculte the forces F, F, nd F 3. Note: The hooks count s prt the msses! We would now like to test Newton s lw. You hve direct mesurements nd n eqution tht reltes them. Hint: Py specil ttention to how you set up you coordinte system, you cn mke things much simpler through creful selection. Ech cse will be different so you my hve to reorient you xis for ech seprte cse. Fill in both hlves of these equtions with the mesurements you hve tken. How does Newton s lw hold up? If both side re equl then Newton s lw is vlid. Record ll of your results nd your work. Also, list ny sources of error tht my hve contminted these results. Repet prt A two more times using different msses nd ngles. Newton s Lws II - 9
Prt B Atwood Mchine Open the Logger Pro progrm. Connect the Motion Detector to the DIG/SONIC chnnel of the interfce. Lod the progrm PES6/Newtons Lws II/Atwood.cmbl. Plce the motion detector on the floor, under the protective cge, to mesure the ccelertion. A trget (crdbord sheet) is provided for good sound reflections include this in the mesurement of the mss. Set msses somewhere round 50g ech. Mke sure tht m is no more thn 0 g hevier thn m. m m The strting position will be with m t the bottom of its trvel nd no closer thn 0 cm to the motion sensor. As shown bove. Strt the progrm nd then give m short nd very light push down. Poor results will occur if the msses re ccelerted too quickly. The lighter mss should come within few centimeters of the hevier mss before going bck up. Mke sure tht the msses ren t swinging or spinning, tht they don t collide, nd tht the Motion Sensor only mesures the distnce to the hevier mss. It is importnt tht you get clen dt. There should be no spikes, nd the Motion Sensor should not pick up the lighter mss, the tble or your hnd. The computer will monitor the distnce nd show the results on the grph. Newton s Lws II - 0
Prctice this mny times. Ask your instructor if you re unsure wht good dt looks like. The grph of the position vs. time should be qudrtic, Right?! Remember the kinemtic equtions, x = t + vo t + x. This is qudrtic eqution. o Fit the position vs. time grph to qudrtic eqution using the modeling softwre within the Logger Pro progrm from this find the experimentl vlue for ccelertion. Clculte the theoreticl vlue of using the msses involved. Are these two vlues in greement? List ll possible sources of error. Perform % difference clcultion on your results. Newton s Lws II -