Mrosopi nd Mirosopi Springs Proedure OBJECTIVE Purpose In this l you will: investigte the spring-like properties of stright wire, disover the strethiness of mteril, independent of the size nd shpe of n ojet, relte mrosopi strethiness of mteril to mirosopi stiffness of the intertomi onds. Some useful equtions nd onstnts re given here 1. Questions to Explore 1 Is solid metl, stright wire like spring? If so, in wht wys? If you onsider the wire to e spring, how does spring stiffness ompre to the oiled springs used in the previous l? 2 How n one express the spring-like properties of the prtiulr metl in wy tht is independent of the size, shpe, nd physil dimensions of the wire (Young s modulus)? 3 How n one relte the mrosopi spring-like properties of the prtiulr metl to the stiffness of tht metl s intertomi onds (intertomi spring stiffness). EQUIPMENT stright metl wire strethed on frme, with hnger for weights millimeter sle for determining the position of the end of the wire Vernier liper (for how to red see the Mesuring with Vernier Clipers setion elow) PROCEDURE Plese print the worksheet for this l. You will need this sheet to reord your dt. Experimentl Setup Reording Dt 1 Right lik on the Exel R file youngs modulus.xls 2, nd sve it to My Douments. Doulelik the file to open it in Exel R. 1 Useful Equtions nd Constnts.pdf 2 youngs modulus2008 09.xls 2013 Advned Instrutionl Systems, In. nd North Crolin Stte University 1
2 You should see disply tht inludes ples for your group informtion, mesured vlues, nd lulted vlues, s well s spe for your grph. 3 You will reord ll of your dt nd nlysis on the Exel R sheet nd sumit it to WeAssign to e grded y your TA. Mesuring with Vernier Clipers In this lortory exerise, you will e using Vernier liper, whih is omprised of two teeth, one tthed to fixed sle nd the other tthed to sliding (Vernier) sle. In order to mesure n ojet s width, the ojet is simply pled etween the liper s two teeth. The sliding tooth is then moved until the ojet is pressed tightly etween the teeth. Using oth sles, the width n e red to the nerest 0.005 m (or 0.05 mm). The sles re red s follows (refer to the figure). Figure 1: Vernier Clipers 4 Find where the 0 mrk of the sliding sle lines up on the fixed sle. In this se, it is just pst the 5.3 m mrk. So, the first reding is 5.3 m. 5 Find the mrk on the sliding sle tht most losely lines up with one of the mrks on the fixed sle. Here, 5.0 nd 6.0 re very lose, ut 5.5 lines up est with one of the mrks on the fixed sle. This vlue is the numer of hundredths of entimeters (or tenths of millimeters). So, the seond reding is 0.055 m. 6 Add the two vlues together to get the totl reding: 5.3 m + 0.055 m = 5.355 m. To get more prtie reding lipers, visit this wesite 3 whih hs n intertive Jv pplet. At this wesite, the lel on the sliding sle is misleding. The sle is leled mm, whih leds the user to think tht the numers on tht sle represent millimeters. This is NOT orret. As desried ove, the numers on the sliding sle represent tenths of millimeters. 3 http://physispm.ukzn..z/onlineexerises/vernier10/vernier.html 2013 Advned Instrutionl Systems, In. nd North Crolin Stte University 2
Mesurements Dimensions of the Wire One of the gols is to desrie the strethiness of mteril independent of the size nd shpe of the wire. To do this, we first need to know the physil dimensions of the wire. 1 Mesure the following nd enter your dt into your Exel R sheet. Entire length of the wire without ny weights on it Dimeter of the wire using the liper (see setion ove Mesuring with Vernier Clipers) Using the mesured dimeter of the wire, lulte the ross-setionl re of the wire. CHECKPOINT: Compre your dt with nother group to mke sure it is resonle. Stiffness of the Wire To determine if the stright wire ehves like spring, you need to mesure the position of the end of the wire s you dd different mounts of weight. 2 Remove the kinks in the wire. Add 6 kg to the pltform hnging from your wire. Remove the 6 kg. Repet. This helps get smll kinks out of the wire, so the stright wire doesnt t like oiled spring. If the wire hs kinks in it, you will mesure the springiness of the oiled wire insted of the stiffness of stright wire. Remove the kinks efore strting your mesurements. 3 Tke the following mesurements nd reord your dt in your Exel R sheet. Look t the sle on the pprtus, nd mke sure you know wht the divisions re nd how to red the sle. You should e le to mesure to the nerest 0.1 mm. You need to mke three sets of mesurements, so tht you n get verge vlues. i Tke mesurements with 0 kg, then 2 kg, 4kg, 6kg. ii Tke ll the msses off nd strt from zero gin, tking the sme mesurements twie more. iii Tke the verge of your three sets of mesurements. Clulte the vrition of your mesurement. i The vrition in the mesurements (the reproduiility ) gives you n indition of how meningful the individul mesurements re. Reord your estimte of the vrition. 2013 Advned Instrutionl Systems, In. nd North Crolin Stte University 3
ii If the mesurements re 5.5, 5.7, 5.4, 5.6, 5.8, nd 5.6 mm, the verge is (5.5 + 5.7 + 5.4 + 5.6 + 5.8 + 5.6)/6 = 5.6, from minimum of 5.4 to mximum of 5.8. A ompt wy to report this verge with the pproximte vrition is 5.6 ± 0.2 mm. If the vrition is lrger thn 0.3 mm, you MUST repet your mesurements. Disrd erlier mesurements sine this ws proly getting more kinks out of the wire. 4 BEFORE grphing your dt, disuss the following questions with your group memers. If the wire ts like spring, wht would you expet grph of streth versus fore to look like? How ould you determine the spring stiffness of the wire from the grph? 5 Use your dt to mke grph in Exel R of the streth of the wire (on the y-xis) versus the fore exerted on the wire (on the x-xis). Both of these quntities will need to e omputed from your dt (either y hnd or using Exel R ). From the two olumns representing streth nd fore, highlight the ells with the dt for 2, 4, 6 kg. Do NOT inlude the dt for 0 kg, euse the wire my e kinked without lod. d e f Choose menu option Insert Chrt, nd hoose XY (Stter). (Do NOT hoose Line hrt.) Be sure to verify tht you hve the proper quntities on the proper xes. Fit your dt to Trendline. i Right lik on one of the dt points nd selet Add Trendline. ii Choose Liner under Type. iii Under Options, hoose Disply Eqution on Chrt this will disply the eqution of the line tht est fits your dt in the form y = mx +. You n reposition the eqution. From your dt, determine the spring stiffness of the wire. i Sine F = K s s, then s = 1 k s F, so the slope of your grph is equl to 1/k s. CHECKPOINT: Compre your mesurements, lultions, nd grph with nother group to verify tht they re resonle. 2013 Advned Instrutionl Systems, In. nd North Crolin Stte University 4
Strethiness of the Metl Clulting Young s modulus is wy to mesure the springiness or strethiness of the metl nd ftor out the size nd shpe of the prtiulr wire. 6 BEFORE lulting Young s modulus, disuss the following questions with your l prtners nd write your nswers on whiteord. d If the ross-setionl re of the wire were douled, would the wire streth more, less, or the sme mount when you hung 2 kg mss on it? Why? i ii Think out putting two of your originl wires together side y side. How does this ompre to pling two springs in prllel? If the wire were twie s long, would it streth more, less, or the sme mount when you hung 2 kg mss on it? Why? i ii Think out onneting two of your originl wires end to end. How does this ompre to pling two springs in series? The quntity F /A is lled stress. Wht re its units? The frtionl streth L/L 0 is lled strin. Wht re its units? CHECKPOINT: Compre your responses with nother group. 7 Use the mesurements for your wire to determine Young s modulus. At equilirium F = k s L = s, so: Y = (F/A) ( L/L 0 ) = (k s L/A) ( L/L 0 ) = k sl 0 A. (1) Use your mesurement for the initil length, your lulted vlue for the ross-setionl re, nd the vlue for the spring stiffness otined from your grph to determine Young s modulus for the mteril of whih your wire is mde. Show your lultion on your whiteord nd reord your result on your Exel R sheet. d How does your vlue for Young s modulus ompre to tht of luminum (6.2 10 10 N/m 2 ) or led (1.6 10 10 N/m 2 )? Given tht the wire is rss (n lloy of opper nd zin), is your vlue resonle? CHECKPOINT: Compre your results with nother group. Determining the Intertomi Spring Stiffness Young s modulus is wy to relte the mrosopi spring-like properties of the prtiulr metl to the stiffness of tht metl s intertomi onds (intertomi spring stiffness). 2013 Advned Instrutionl Systems, In. nd North Crolin Stte University 5
8 BEFORE determining the intertomi spring stiffness, disuss the following with your prtners. Assuming simple ll nd spring model for our solid, how ould we determine the length of the intertomi onds if we knew the density of the mteril? (Hint: You hve proly done something similr in your homework reently.) Using this ide nd the following informtion, determine the length of the intertomi ond for rss. Brss is n lloy of opper nd zin. The tomi mss of opper is 64 grms/mole; zin is 65 grms/mole. The density of opper is 8.94 grms/m 3, for zin, it is 7.14 grms/m 3. Note: ewre of your units. 9 Use your lultion of the intertomi ond length nd your vlue for Young s modulus to pproximte the stiffness of the intertomi onds, k s,i. In the Strethiness of the Metl setion ove, we showed: Y = k sl 0 A. (2) For our ll nd spring model, the ross-setionl re of the ond is A = d 2 nd the relxed length is L 0 = d (if you re unsure why this is, rered the Intertomi Spring Stiffness setion from Mrosopi nd Mirosopi Springs Conepts 4 ). Thus: Y = k sl 0 A = k s,id d 2 = k s,i d. (3) Show your lultion on your whiteord nd reord your result on your Exel R sheet. CHECKPOINT: Compre your results with nother group. 10 Sumit your Exel R sheet nd nswer the follow-up questions in WeAssign. 4../l 10 1/mnul.html 2013 Advned Instrutionl Systems, In. nd North Crolin Stte University 6