Lab 4 PHYS 200
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Athabasca University, Athabasca *
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PHYS200
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Law
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Feb 20, 2024
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docx
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Athabasca University
PHYS 200: Introductory Physics
Lab Report 4: Hooke’s Law
Date: June 17th, 2023
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Introduction
This lab will examine Hooke’s Law, which states that the extension/compression of a spring and other elastic objects is directly proportional to the force that acts on it.
When the force applies to the spring (or other object) it stretches the spring. There are limitations to how much an elastic may stretch. The formula describing this relationship:
F = k x Where k represents the spring constant and x represents the amount it stretches, applies only when the spring does not break by surpassing its elastic limit. The following photos demonstrates this relationship:
Procedure
To begin this lab the materials required are a rubber band/elastic, a plastic bag, 10 identical coins, a ruler, and
a relatively strong tape. For this expirement the only rubber band I had available was a stretchy hair tie. I began by cutting that hair tie in half, so that I could use my tape to align both the elastic and the ruler to the wall as securely as possible. Secondly, I used a staple to fasten the plastic bag to the end of the elastic. At this
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point, taking note of the original length of the elastic with the ruler. The original length of the rubber band (Lo) was equal to 11.5cm long. The following photographs demonstrate the set up, where the photo on the left demonstrates the original length with no coins, and the photo on the right demonstrates the set up as coins were being added. One by one, I added loonies, each time taking note of the length of the elastic each time.
The following table represents the values as the procedure for the lab was followed. Number of coins (n)
Rubber band length (L +/- 0.2cm)
Rubber band stretch (x +/- 0.002m)
Weight of coins (w +/- 0.118N)
0
Lo = 11.5cm
0m
0N
1
11.8cm
0.003m
0.0686N
2
12.0cm
0.005m
0.1372N
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3
12.2cm
0.007m
0.2058N
4
12.4cm
0.009m
0.2744N
5
12.6cm
0.011m
0.343N
6
12.8cm
0.013m
0.4116N
7
13.1cm
0.015m
0.4802N
8
13.4cm
0.017m
0.5488N
9
13.6cm
0.019m
0.6174N
10
13.9cm
0.021m
0.686N
Analysis
The first step in the
análisis was to fill out the
third column in the table
from the previous section. Calulating the stretch in
the rubber band caused by
the weight of each
additional coin is done
using the following
formula:
X = L – Lo
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For the fourth column, w is the weight of n coins added after the original length of the rubber band. The equation to solve for w is:
W = nmg
M = mass of a single coin
The process for finding the value of the weight demonstrated in the photo to the write is repeated for each coin added and added to the fourth column of the table in the previous section.
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The graph demonstrates that the linear relationship between the weight and displacement is proportional. This means that the forcé applied increased everytime a coin was added, and the displacement of the rubber band
simeltanously increased as well. From the line of best fit, the slope of the graph was determined to be 32.7 N/m in
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the linear equation y = 32.7x. The relationship between the line of best fit equation and Hooke’s Law is that y values represent the force acting on the spring, the value
of 32.7 (the slope) represents the constant of the elastic used (k) and x values represent the distance the band is stretched. Overall, the graph does represent the relationship of Y = 32.7x and F = kx Possible errors: The accuracy of this experiment could have been impacted by the ruler used. When determining
the exact amount that the elastic had been displaced, there could have been human error in determining the exact amount that the elastic stretched. For that reason there is a limitation error margin of + or – 0.002m. Other aspects include the band or ruler not being fully straight when they are taped, thus making the amount measured off by a small amount. A solution to getting a more accurate measurement could be using a more accurate measurement device, and having multiple attempts to the experiment to ensure that the measurements are accurate.
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Questions
1. Based on your best-fit analysis, estimate the proportionality constant k for your rubber band.
The proportionality constant k for the band is amount of force needed to extend the elastic by a given distance, so
the value of k will be equal to the slope of the graph (weight(rise)/distance(run)). Using two points on the line of best fit the result is m = slope = rise/run = (0.525-0.100/0.016-0.003) = 32.69 N/m. So the proportionality constant k is approximately 32.7 N/m for the elastic used in this experiment. 2. How many coins are necessary to stretch the elastic band by 1.00m? Would this be possible with the rubber band you used in this lab?
If the formula F = kx is equal to the linear equation found from the graph, then the force used on the elastic will be equal to w W = n mg Nmg = kx N = (kx) / (mg) = (32.7N/m * 1.00m) / (0.007kg * 9.80m/s^2) = 476.67 It would take 477 loonies from 1987-2011 for the band to stretch 1.00m, which would not be possible with the rubber band used in this experiment, since it would not support that many.