Experiment ELA: Elasticity and Hooke s Law. Eksperiment ELA: Elastisiteit en Hooke se wet. Introduction: Inleiding:

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1 Experiment ELA: Elasticity and Hooke s Law Introduction: In this experiment you will investigate the elastic properties of a spring and compare them to those of an elastic rubber band. Experimental Aims: The aim of this experiment is to: 1. Investigate the relationship between the applied force and the extension (stretching) for a helical spring. 2. Determine the spring constant of a spring. 3. Repeat point 1 with a rubber band 4. Determine the mass of an object by suspending it from a spring and measuring the extension. Skills Developed: 1. Observation and measuring skills 2. Data collection and data processing 3. Plotting of graphs 4. Determining slope of a graph. 5. Interpreting of data and graphs 6. Drawing conclusions from results. Theoretical background: You need to read up on the theoretical background of the practical beforehand. All the required information is in Halliday Resnick & Walker (use the index to find it). Your knowledge on the topics will be tested in the pre-practical test. You should be able to do the following: Explain the difference between mass and weight, and describe how they are related. Write down Hooke s law both in words as well as a formula and explain what quantity each of the symbols represent and state the SI units in which they are measured. Explain the difference between elastic and plastic deformation. (Look this up on the Internet.) Eksperiment ELA: Elastisiteit en Hooke se wet Inleiding: In hierdie eksperiment sal u die elastiese eienskappe van ŉ heliksveer vergelyk met diè van ŉ rubberrekkie. Eksperimentele Doel: Die doel van die eksperiment is om 1. Die verband tussen die toegepaste krag en die verlenging vir beide n heliksveer te bepaal. 2. Die veerkonstante van n veer te bepaal. 3. Herhaal punt 1 met ŉ rubberrekkie. 3. Die massa van n voorwerp te bepaal deur die uitrekking van n veer a.g.v. die massa te meet. Vaardighede Ontwikkel: 1. Waarneming- en meetvaardighede 2. Dataversameling en verwerking 3. Teken van grafieke 4. Bepaling van die helling van n grafiek 5. Interpretasie van data en grafieke 6. Gevolgtrekkings maak van gegewe resultate. Teoretiese agtergrond: U moet oor die teoretiese agtergrond van die eksperiment oplees. Al die nodige inligting is in Halliday, Resnick & Walker (gebruik die indeks om dit te vind). U kennis oor die werk sal deur middel van ŉ vooraf-toets bepaal word. U moet in staat wees om die volgende te doen: Verduidelik wat die verskil tussen massa en gewig is en noem wat die verband tussen die twee is. Skryf Hooke se wet beide in woorde asook as ŉ formule neer, en verduidelik watter grootheid deur elke simbool voorgestel word. Noem ook die SIeenhede van elke grootheid. Verduidelik wat die verskil tussen plastiese en elastiese vervorming is. (Soek dit op die internet op.)

2 Van: Surname: Voorletters: Initials: PHY 114 Praktikum / Practical ELA Datum: 2014 Date Handtekening van student: Signature of student: Van van TA: Surname of TA: Studentenommer: Student Number: Elastisiteit / Elasticity [I] *ELAI* * * Mm dd MEMO Praktikumsessie: Practical session: Groepnommer: Group number: TA Paraaf: TA Initial: Praktikum: Practical: Vooraftoets (/10): Pre-test is plotted (/10): Praktikum (/40): Praktical (/40): Note to TA: The approach in this experiment differs significantly from the approach followed in the FSK 116 and PHY 131 texts. Main differences are that y as a function of y (correct choice of axes for dependent and independent variables) and the y 0 value is measured with neither mass nor hanger on the spring. ELA Part A: Elasticity of a helical spring Deel A: Elastisiteit van ŉ heliksveer Theory According to Hooke s law, the magnitude of the force exerted by a spring extended by a distance y from its equilibrium length, is given by F = ky, where k is the spring constant of the spring. [A1] In this experiment, the extension of the spring will be measured as a function of the applied force. Rewrite the above equation, making the extension (y) the subject of the equation. Teorie Volgens Hooke se wet word die grootte van die krag wat deur ŉ veer uitgeoefen word, wanneer dit met ŉ afstand y van sy ewewigslengte uitgerek word, gegee deur F = ky waar k die veerkonstante van die veer is. [A1] In hierdie eksperiment sal u die uitrekking van die veer as ŉ funksie van die toegepaste krag meet. Herskryf die vergelyking hierbo, en maak die uitrekking (y) die onderwerp van die vergelyking y = F/k [A2] Draw rough graph of the extension of the spring (from its unstretched length) as a function of the force exerted on it. Clearly show the quantity plotted on each axis, and where your graph intersects the axes. Also write down an expression for the spring constant in terms of the slope of the graph. [A2] Teken ŉ rowwe grafiek van die uitrekking van die veer (van sy onuitgerekte lengte) as ŉ funksie van die krag dat daarop uitgeoefen word. Toon duidelik wat op elke as gestip word, en waar die grafiek die asse sny. Skryf ook ŉ uitdrukking neer vir die veerkonstante van die veer in terme van die helling van die grafiek. Extension on the y- (vertical) axis Force on the x- (horizontal) axis A straight line graph with positive slope going through the origin. slope = m = 1/k (From previous question), therefore k = 1/m. [4]

3 Apparatus Helical spring Stand with ruler to measure the spring s length Mass hanger with known mass (to suspend from spring) 5 50 g mass pieces fitting on hanger Mirror (fixed to ruler or separate) Experimental Consider the equipment available and devise a plan to find the relationship between the extension and the force applied to a spring. [A3] How can a known force be applied to the spring? Give a formula and explain how the magnitude of the known force may be calculated. Also show one numerical example (with correct units!) (Note: you do not know the spring constant of the spring.) Apparaat Heliksveer Staander met ŉ lineaal om die veer se lengte te meet Massahanger met bekende massa om aan die veer te hang g massas wat op die hanger pas. Spieëltjie (aan lineaal vas of appart) Eksperimenteel Beskou die toerusting wat beskikbaar is en bedink ŉ plan om die verband tussen die uitrekking van die veer en die krag daarop toegepas te vind. [A3] Hoe kan ŉ bekende krag op die veer uitgeoefen word? Gee ŉ formule en verduidelik hoe die grootte van die bekende krag bereken kan word. Gee ook een numeriese voorbeeld (met korrekte eenhede!) (Let wel: U weet nie wat die veerkonstante van die veer is nie.) The weight of a mass may be used as a constant, known force. W = mg. E.g. a 50 g piece will have a weight of: 50/ = = 0.49N [3] [A4] Using the given apparatus, how can the extension (stretching) of the spring from its unstretched length be measured? What point on the spring will you use for measurements? Explain (with the aid of a picture) how a mirror may be used to avoid parallax errors. [Note: the extension of the spring is the amount by which the spring stretches from its length with no mass attached.] [A4] Deur die gegewe apparaat te gebruik, hoe kan die uitrekking van die veer van sy onuitgerekte lengte bereken word? Verduidelik (met behulp van ŉ skets) hoe ŉ spieël gebruik kan word om parallaksfoute uit te skakel. [Let wel: Die uitrekking van die veer is die hoeveelheid waarmee die lengte van die veer toeneem van sy lengte as geen massa aan die veer hang nie.] Note: strictly speaking the zero mass length of the spring should be measured with no mass (not even the hanger) hanging on the spring, therefore the most reasonable point on the spring to use as reference point is the bottom of the hook of the spring. Place a mirror against the back of the scale. At zero parallax, you should see an image of your eye line up with the hook of the spring. [2]

4 Experiment [A5] We want to determine the relationship between the extension of the spring ( y = y y0 ) and the force applied to the spring ( F ). Here y is the position of the bottom of the spring with force applied, and y 0 is the position of the bottom of the spring with force applied. Collect the necessary data in a neat table and do the calculations to calculate F and y in SI units. (Use forces in the range 0 to 2.5 N, in approximately 0.5 N steps. Start with no mass hanging from the spring and add masses.) Don t forget units! Note: Leave some space for three columns to the right of your table for the next question. Eksperiment [A5] Ons wil die verband tussen die uitrekking van die veer ( y = y y0 ) en die toegepaste krag (F) bepaal. Hier is y die posisie van die onderkant van die veer met ŉ toegepaste krag en y 0 is die posisie van die onderkant van die veer met geen toegepaste krag nie. Versamel die nodige data in ŉ netjiese tabel en doen die nodige berekeninge om F en y in SI-eenhede te bepaal. (Gebruik kragte in die gebied 0 tot 2.5 N, in stappe van ongeveer 0.5 N. Begin met geen massa wat aan die veer hang nie, en voeg massas by.) Moenie eenhede vergeet nie! Let wel: Laat spasie vir drie kolomme aan die regterkant van u tabel vir die volgende vraag. Adding mass Removing mass Mass (g) Weight (N) Position y (mm) Extention y = y y ) ( 0 (m) Position y (mm) Extention y = y y ) ( 0 (m) 0 0 xxxx.x (this is y 0 ) = 0.49 Readings accurate to 1 mm = = = =2.45 Table with headings and correct units. Measurements while increasing mass Measurements while decreasing mass (Q5 & Q6) [4]

5 [A6] We want to test the repeatability of the results. Remeasure the results, but this time start from maximum mass, and reduce the mass each time. Put these results in the same table as for the previous question. Was there a significant difference between the two sets of measurements? What do you conclude regarding the repeatability of the results? [A6] Ons wil die herhaalbaarheid van die resultate toets. Meet al die uitrekkings weer, maar begin die slag van die maksimum massa en verminder die massa elke keer. Skryf die resultate in dieselfde tabel as wat u vantevore gebruik het. Was daar ŉ betekenisvolle verskil tussen die twee stelle metings? Wat is u gevolgtrekking aangaande die herhaalbaarheid van die metings? No significant difference. Conclusion: the results are repeatable. [A7] Which variable ( F or y ) is the independent variable and which one is the dependent variable? (The independent variable is the one whose value you choose, while the dependent variable is the quantity you measure.) [A7] Watter veranderlike (F of y ) is die onafhanklike veranderlike en watter een is die afhanklike veranderlike? (Die onafhanklike veranderlike is die een waarvan ons die waarde kan kies, waar die afhanklike veranderlike die een is wat gemeet word.) y is dependent variable and F is an independent variable. [A8] Draw a graph representing the relationship between the extension of the spring and the applied force. (Ensure that the independent variable is on the horizontal axis!). (Space on next page.) [A8] Teken ŉ grafiek wat die verband tussen die uitrekking van die veer en die toegepaste krag voorstel. (Verseker dat die onafhanklike veranderlike op die horisontale as gestip word!) (Plek op volgende bladsy.) [A8] What shape does your graph have? A straight line (linear) graph. [A8] Wat is die vorm van die grafiek? [A9] Does your graph go through the origin? Explain why it should. If the graph does not, explain why not. [A9] Gaan u grafiek deur die oorsprong? Verduidelik hoekom die grafiek deur die oorsprong behoort te gaan. Indien die grafiek nie deur die oorsprong gaan nie, verduidelik hoekom nie. Yes, because the length of the spring with zero force applied was taken as zero extension. (No with a good explanation is also OK.) [A10] What relationship between F and shape of your graph suggest? y does the [A10] Volgens u grafiek, wat is die verband tussen F en y? Extension is directly proportional to the applied force.

6 Ensure that graph conforms to the requirements as set out in the Graphs experiment: Heading Axis labels with units Appropriate scale Experimental points indicated as a circled dot Points correctly plotted. [5] [A11] Draw a best fit line through your experimental data points and find its slope. Don t forget the units! [A11] Teken die beste passingslyn deur u eksperimentele punte en verkry die helling van die lyn. Moenie eenhede vergeet nie. y m = = use big triangle and show on graph how done = 0.1_ m/n (check units!) F [2] [A12] From your answer in the previous question, write down the empirical (observed) relationship between F and y. [We call this equation an abstract model.] [A12] Gebruik u antwoorde in die vorige vraag om die empiriese (waargenome) verwantskap tussen F en y neer te skryf. [Ons noem hierdie vergelyking ŉ abstrakte model.] y = 0.10F

7 =1.96 [A13] Compare your answer in [A12] with Hooke s law, and determine the spring constant of the spring. [Hint: If you drew your graph as required, the spring constant is NOT equal to the slope of the graph.] y = m F [A13] Vergelyk u antwoord in [A12] met Hooke se wet en bepaal die veerkonstante van die veer. [Wenk: As u die grafiek geteken het soos vereis, is die veerkonstante nie gelyk aan die helling van die grafiek nie. F = ky Hooke s law Therefore, k = 1/m = 10.0 N/m [2] [A14] Summarise your conclusions in 2 3 sentences. [A14] Som u gevolgtrekkings in 2 3 sinne op. E.g.: We found that the spring obeyed Hooke s law, i.e. the extension of the spring was directly proportional to the applied force. [A15] Do you trust the results you have obtained? Discuss any deviations from expected results. [A15] Vertrou u die antwoord van u verkry het? Bespreek enige afwykings van die verwagte resultate. Discussion Part B: Elasticity of a rubber band Apparatus In addition to the equipment in part A: A rubber band Experimental: Repeat the experiment you did in Part A, but replace the spring with an elastic band. [B1]: Make a Table with the results of your measurements. Remember to record the measurements firstly when adding masses and secondly when removing masses (as in [A5] in Part A). Deel B: Elastisiteit van n rubber rekkie. Apparaat Addisioneel tot die apparaat in deel A: n rubber rekkie. Eksperimenteel: Herhaal die eksperiment wat u in deel A gedoen het, maar vervang die veer met ŉ rekkie. [B1] Maak ŉ tabel met die resultate van u metings. Onthou om eers metings te neem wanneer massa bygevoeg word en dan wanneer massa verwyder word (soos in [A5] in deel A). Mass (g) Weight (m/s 2 ) Extension or y (mm) = = =1.47

8 [B2] Draw a graph representing the relationship between the extension of the rubber band and the applied force. (Ensure that the independent variable is on the horizontal axis!). [B2] Teken ŉ grafiek wat die verband tussen die uitrekking van die rubber rekkie en die toegepaste krag voorstel. (Verseker dat die onafhanklike veranderlike op die horisontale as gestip word.) [4]

9 Now answer the following questions: [B3] Were the results repeatable? Explain. Beantwoord nou die volgende vrae: [B3] Was die resultate herhaalbaar? Verduidelik. No readings while adding mass differed from those when removing mass. [B4]: Do your results, as depicted on the graph, suggest a direct proportionality between F and y? Explain. [B4] Toon die resultate soos op die grafiek voorgestel, ŉ direkte afhanklikheid tussen F en y. Verduidelik. No the graph is not a straight line. [B5] Does it make sense to calculate a spring constant for the rubber band? Explain. [B5] Kan mens in die geval van ŉ rubber rekkie van ŉ veerkonstante praat? Verduidelik. No, there is no linear relationship. [B 6]: Conclusion: Would you say your rubber band obeys Hooke s law? Explain. [B6] Gevolgtrekking: Sou u sê dat die rubber rekkie Hooke se wet gehoorsaam? Verduidelik. A rubber band does not obey Hooke s law, as the extension is not repeatable and the graph is not linear. (Although, over a short distance, Hooke s law is obeyed.) Total marks / Puntetelling: 40