Solve Physics Lab: Hooke's Law & Simple Harmonic Motion

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SUMMARY

The forum discussion centers on a physics lab focused on Hooke's Law and Simple Harmonic Motion, where the user struggles with calculating the spring constant (k). The user initially misapplies the conversion of mass from grams to Newtons, incorrectly using 9.18 m/s² instead of the correct 9.81 m/s². The accurate calculation for k, derived from the slope of the graph using the correct values, results in k = 20 N/m, aligning with the professor's expected answer. The primary error lies in the misunderstanding of the units and conversions involved in the calculations.

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  • Understanding of Hooke's Law and its mathematical representation.
  • Knowledge of unit conversions, specifically from grams to kilograms and Newtons.
  • Familiarity with graphing techniques, including calculating the slope.
  • Basic principles of Simple Harmonic Motion.
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  • Review the principles of Hooke's Law and its applications in physics experiments.
  • Learn about unit conversions in physics, focusing on mass and force.
  • Study how to accurately calculate the slope of a graph and its significance in experimental data.
  • Explore the concepts of Simple Harmonic Motion and its relationship with spring systems.
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Students in physics courses, educators teaching mechanics, and anyone involved in experimental physics labs focusing on spring dynamics and harmonic motion.

kashmirekat
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I had a physics lab for Hooke's Law and Simple (ha!) Harmonic Motion. I am not pleased with my grade, but my professor did not indicate what I did wrong and I am banging my head against the wall trying to figure it out (btw, it's not helpful). So if any of you all can take a gander at it and tell me hey! You did this wrong! That would be great. Thank you.

First Section: Spring Elongation

weight(grams)*9.18m/s^2 | Scale reading (mm)
m1g = 114.26                  | y1 4.7
m2g = 124.26                  | y2 = 5.2
m3g = 134.26                  | y3 = 5.9
m4g = 144.26                  | y4 = 6.3
m5g = 154.26                  | y5 = 6.7
m6g = 164.26                  | y6 = 7.3
m7g = 174.26                  | y7 = 7.8
m8g = 184.26                  | y8 = 8.2

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Okay, the first thing I did was convert the grams to kg and multiply by g (9.8m/s^2).
For these values I got:
mg1=1.12N, mg2=1.22N, mg3=1.3157N, mg4=1.414N, mg5=1.512N, mg6=1.61N, mg7=1.708N, mg8=1.806N

Then I converted mm to m...0047, .0052, .0059, .0063, etc.

It's asking for k and in parentheses next to it has slope of graph. [ie k(slope of graph)] So k=slope of graph. Slope equals rise/run, (delta y)/(delta x). So I choose two points 1 & 4.
(1.12N - 1.414N) / (.0047m - .0063m) = -0.294N / -.0016m = 183.75 N/m.

His answer is k = 20. Where did go wrong to get a value so far from the answer?
 
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uh I'm not math head but I would recon that you didn't label something correct on your graph...20 what? perhaps he wants you to label everything, and I thought weight was in Newtons therefor you don't have to say weight * 9.8 m/s² because 9.8 m/s² is already included in the Newton measurement...yes? no?
 
According to your table:
weight(grams)*9.18m/s^2 | Scale reading (mm)
m1g = 114.26 | y1 4.7
m2g = 124.26 | y2 = 5.2
m3g = 134.26 | y3 = 5.9
m4g = 144.26 | y4 = 6.3
m5g = 154.26 | y5 = 6.7
m6g = 164.26 | y6 = 7.3
m7g = 174.26 | y7 = 7.8
m8g = 184.26 | y8 = 8.2

"m1g" is ALREADY multiplied by 9.81 (not "9.18") m/s^2. In order to convert that to Newtons, you only need to multiply by 0.001 to convert grams to kg. If that is correct, then m1g is 0.11426 Newtons and m8g is 0.18426. For those two values, y1= 0.0047 m and y8= 0.0082 m so the "slope" of your graph is (0.18426-0.11426)/(0.0082- 0.0047)= 20.
 
Coughlan, k is suppose to be 20N/m.

HallsofIvy, oh if that were only true, but those values did not include the multiplication of g. My masses were 114.26, 124.26, but were not already multiplied by g. Sorry, I should have written g next to them, but that could also be mistaken for grams (which they are in). I would convert to kg before multiplying with 9.8 anyhow, right? The m1g tells us to multiply m by g, ergo .11426kg*9.8m/s^2=1.12N.

Just in case I didn't clear it up, 9.8m/s^2 is not included in the measurement of 114.26, 124.26, etc...those are all masses in grams.

Any more suggestions?
Thank you.
Christina
 
Eh sorry about that...I'm fresh out of ideas...
 

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