HOOKE'S LAW. THE RATE OR SPRING CONSTANT k.

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Wilfrid Farmer
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Practces Group Sesso Date Phscs Departmet Mechacs Laborator Studets who made the practce Stamp cotrol Deadle Date HOOKE'S LAW. THE RATE OR SPRING CONSTANT k.

1 Practces Group Sesso Date Phscs Departmet Mechacs Laborator Studets who made the practce Stamp cotrol Deadle Date HOOKE'S LAW. THE RATE OR SPRING CONSTANT k. IMPORTANT: Iclude uts ad errors all measuremets ad calculatos. I ever plot: ame the as ad ther uts, ad plot epermetal data pots wth error bars. Least-squares fts wll be draw o the same graph as epermetal data. 5.1 Relatoshp betwee stress ad stra a sprg Descrpto of the sprgs. Make a bref descrpto of the sprgs that allows detfg them (color, stffess ad equlbrum legth L 0 ). Sprg A. Sprg B Data acqusto. Whe we hag a weght o the sprg we see a stra takes place. Fg the zero pot of the graduated ruler after hagg the weght holder, complete the tables where ou should dcate the mass M of the weghts that hag o the sprgs as well as the legth L of the deformed sprgs. Use the mass values as show the tables provded together wth the sprgs. 1

2 Sprg A. M L Sprg B. M L Stud of the depedece of the sprg stra wth the stress. From epresso [1] the practce gude, we see that there s a lear relatoshp betwee the stra that a sprg udergoes ad the load that produces the aforemetoed deformato. We obta the load from the masses, ad, ths case, stra cocdes wth the legth of the deformed sprg sce we had supposed legth zero to be the oe correspodg to the sprg ad the holder. Epresso for the deformg load ad ts error.

3 Complete, for each sprg, the table that relates stra (legth) to load; make sure of cludg uts correctl. Sprg A. L F Sprg B. L F 3

4 4 Represet the stra as a fucto of load L(F), for each of the cases. Sprg A. Fd the least-squares le ft to the data of stra () versus load () for sprg A.

5 5 Results of the least-squares ft: - Slope: m A = - -tercept: b = Sprg B. Least-squares le ft cstra () versus load () for sprg B.

6 Results of the least-squares ft: - Slope: m B = - -tercept: b = Aaltcal terpretato of the ft parameters m ad b. Usg the prevous aaltcal terpretato ad the results of the ft, obta the force costats k A ad k B- Sprg A: Numerc value: k A = Sprg B: Numerc value: k B = 6

7 5. Relatoshp perod-mass Descrpto of the sprgs. Keep the order of the sprgs stated prevous epermet. 5.. Data acqusto. Whe we separate the mass hagg o the sprg from ts equlbrum posto (o more tha cm), t starts to oscllate wth a harmoc smple moto. Take three measuremets of the tme that t takes to the mass M to complete 5 oscllatos, for the mass values dcated the table, for each sprg. Sprg A. M Tme1 Tme Tme3 Sprg B. M Tme1 Tme Tme3 7

8 From data of prevous table, obta aaltc epresso of the perod T ad ts ucertat. Obta a epresso for the perod T. Obta a epresso for the ucertat ΔT. 8

9 Sprg A. M T Sprg B. M T 9

10 5..3 Stud of the depedece of the perod of oscllato wth the mass. Complete, for each sprg, the table that relates the square of the perod T to the mass M. Sprg A: T M Sprg B: T M Aaltc epresso used for the computato of the error the T colums. 10

11 11 Make a plot of the squared perod as a fucto of the mass T (M). Sprg A: To appl the least least-square method, set the varable = T ad the varable = M.

12 1 Results of the least-squares ft: - Slope: m A = - -tercept: b A = Sprg B. To appl the least least-square method, set the varable = T ad the varable = M.

13 Results of the least-squares ft: - Slope: m B = - -tercept: b B = Aaltcal terpretato of the ft parameters m ad b. Usg the prevous aaltcal terpretato ad the results of the ft, obta the force costats k A ad k B- Sprg A: Numerc value: k A = Sprg B: Numerc value: k B = 13

14 Compare, for each case, the rate of ever sprg obtaed b each method ad make a crtcal aalss of the results. Sa f the mass of the poter + weght holder have a fluece the results. From the epermetal measuremets that we have take, could we get the mass of the poter + weght holder? 14

Johns Hopkins University Department of Biostatistics Math Review for Introductory Courses

Johns Hopkins University Department of Biostatistics Math Review for Introductory Courses Johs Hopks Uverst Departmet of Bostatstcs Math Revew for Itroductor Courses Ratoale Bostatstcs courses wll rel o some fudametal mathematcal relatoshps, fuctos ad otato. The purpose of ths Math Revew s