Can We Use a Spring To Accurately Measure Force?
Kaiya Yamada
Physics 10
Hypothesis: If we add weight (force) in increasing increments to a spring, then the extension of
the spring will be directly proportional to the weight added. According to Hooke’s Law, up to the
elastic limit, the extension of a spring is proportional to the tension force (Kirk, 2007, p. 16).
Variables: The independent variable in the experiment is the weight (force) added to the spring.
It is the variable we are manipulating. The dependent variable is the extension of the spring. It
depends on the amount of weight added. The controlled variables are the spring and weights
used. They remain constant throughout the experiment. The only variable that determines the
extension of the spring is the amount of weight added.
Materials: Spreadsheet, clamp stand, spring, six 0.5N weights, meter stick
Method: We used a simple method to measure the size of a force by using the extension of a
spring. We set up a clamp stand and attached a spring to it. We then added six 0.5N weights one
at a time and measured the corresponding extensions of the spring with a meter stick. We did
three trials and recorded our data in a spreadsheet. Finally, we added a mystery object to the
spring and measured the extension of the spring.
Photo showing the method we used:
Data: Table showing the extension of the spring as weight is added
Weight (N)
Extension of the spring when mass added (±0.5)cm
(±0.05 )
Trial 1
Trial 2
Trial 3
Mean
Range
1/2 Range
0.5
10.0
10.4
9.9
10.1
0.5
0.25
1.0
20.5
20.5
20.1
20.4
0.4
0.20
1.5
27.7
30.6
30.2
29.5
2.9
1.45
2.0
37.9
40.9
40.4
39.7
3.0
1.50
2.5
48.2
51.0
50.6
49.9
2.8
1.40
3.0
58.2
60.5
60.9
59.9
2.7
1.35
Mystery object: The extension as a result of adding the mystery weight to the spring is 46.2 cm.
Our estimated weight is 2.28N.
The real value of the weight was 2.27N.
Associated qualitative data: When we put the first 0.5N weight on the spring, the spring was
pulled down. The weight was a constant downward force. When we let the spring go, it
accelerated upwards, meaning that there was an upward force in the spring. The spring bobbed
up and down many times before coming to rest as the spring tried to balance the added weight.
Once the spring reached equilibrium (where the downward force was balanced by the upward
force), the spring came to rest. Each time we added an extra weight, the spring stretched longer
and the weight sank lower. Another thing I noticed was the sound the metal weight made as it
bounced.
Graph: Force vs Extension Graph for the Spring Experiment
Extension (cm)
Note: This graph shows the mean of our three trials.
66.0
63.0
60.0
57.0
54.0
51.0
48.0
45.0
42.0
39.0
36.0
33.0
30.0
27.0
24.0
21.0
18.0
15.0
12.0
9.0
Graph showing the relationship between the
force added to a spring and the resulting
extension of the spring.
(Error bars represent ± 1/2 the range)
Extension of spring with mystery object: 46.2cm
Estimated weight
of mystery object:
2.28N
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Force (N)
Interpretation of Results: Increasing increments of weight were added to the spring causing an
increased downward force on the spring. As the graph indicates, this caused the spring to extend
in proportion to the weight added. When 0.5N of weight was added, the extension was 10.1cm.
The ratio is 10.1cm/0.5N which is 20.2cm/N. When 1.0N of weight was added, the extension
was 20.4cm. The ratio is 20.4cm/1.0N, which is 20.4cm/N. When 2.0N of weight was added, the
extension was 39.7cm. The ratio is 39.7cm/2.0N, which is 19.9cm/N. Basically, we see a pattern
or trend. The ratio of force to extension is constant. This is indicated by the straight line of the
graph. As force increases, the extension of the spring increases in direct proportion.
Calculations: Because the ratio of force to extension is constant, we can easily find out the
mystery weight because if we know the extension the weight causes, we just find the extension
on the graph and go straight across until we hit our slope line and then straight down and read the
corresponding weight. If our extension is 46.2 cm +/- 0.5 cm, then the corresponding weight is
about 2.28N +/- 0.05N. Please see conclusion for further calculations related to the “spring
constant.”
Validity and Reliability of Data: Our results for the experiment are valid. We collected enough
data. We did three trials with 6 weights each time. The tools we used were appropriate. We used
the same spring and the same weights each time so we controlled our variables. The extension of
the spring depended only on the weight being added to the spring. The meter stick we used to
measure was also the same each time. The uncertainty range due to the readability of the meter
stick would be +/- half the smallest scale division on the ruler. Our results could have been more
accurate if we had measured more precisely. For example, we had a range of data when we
added the 2.0N weight of 3.0cm. This is a big difference. To improve our method next time, we
should clamp the meter stick to the stand to ensure more accurate measurements. We stated that
our measurements for the extension of the spring are accurate to within +/-0.5cm, but with some
of our readings for the heavier weights there seemed to be a bit more inaccuracy.
Our results for the experiment are quite reliable for the lighter weights but not as much for the
heavier weights. Our data is not as consistent as it could be for the heavier weights.
Conclusion: Our hypothesis is valid. If we add weight in increasing increments to a spring, the
extension of the spring will be directly proportional to the weight added. We can predict the
weight (force) added to a spring simply by knowing the resulting extension when the weight is
added to the spring. For example, our mystery weight was added, and the extension was 46.2cm.
We can find our mystery weight on the graph by going across from the extension reading until
we hit the line of the slope and then going down to read the weight off the bottom axis. The
relationship between the extension of a spring and the force added is explained by Hooke’s Law,
which states that up to the elastic limit, the extension of a spring is proportional to the tension
force (Kirk, 2007, p. 16). This relationship is shown in the equation F=-kx.
F=force (weight)
x=extension
k=the spring constant
The negative sign just indicates that the force of the spring is in the opposite direction of the
force of the weight, so we will ignore that for our calculations. If we rewrite this equation as
k=F/x, we can see that the ratio of the force added to the extension of the spring is always
constant. k is actually called a “spring constant.” This explains why we get a straight line on our
graph. Another interesting thing is that if we look at the equation, we can see that to calculate the
spring constant all we have to do is take the inverse of the slope on our graph. Therefore, the
slope we calculated for our mystery weight was 46.2 cm/2.28N, which equals 20.3cm/N. The
spring constant would be the inverse of this, or 1/20.3cm/N, which is 0.05N/cm. (Of course, you
can also calculate it by putting 2.28N/46.2 cm from the beginning and get 0.05N/cm).
The percent error is easy to calculate. If we look at the answer we got from our graph, we got
the weight of 2.28N. The real value of the weight was 2.27N.
The % error would be found by:
1. subtracting the observed value from the accurate value
2.27N-2.28N=-0.01N
2. taking the modulus of the number
-0.01N becomes 0.01N
3. dividing this difference by the accurate value
0.01N
2.27N
= 0.0044
4. multiplying by 100%
=0.0044x100%=0.44%
Our percent error is 0.44%.
I would say we can use a spring to accurately measure force. We were very close to the
real value of the weight in this lab with only a 0.44% difference between the real weight value
and our estimated value arrived at by using the extension of the spring.
I have two suggestions for further related investigations. First, according to Hooke’s Law,
the extension in a spring, x, is proportional to the tension force, F. A “spring constant” can be
calculated by the formula F = -kx, where k is the spring constant (Kirk, 2007, p. 16). I wonder if
this law applies to elastic bands too. I think it does, and I would like to investigate this. Second, I
would like to measure the oscillation period of our spring to see if it depends on the mass of the
weight, the strength of the spring, or the amplitude of the motion. I think it depends on the first
two.
Sources:
Kirk, T. (2007). Physics: For the IB diploma. New York: Oxford University Press.
Self-evaluation rubric:
Level Descriptor
0
The student does not reach a standard described by any of the descriptors below.
The student collects some data and attempts to record it in a suitable format.
The student organizes and presents data using simple numerical or visual forms.
1-2
The student attempts to identify a trend, pattern or relationship in the data.
The student attempts to draw a conclusion but this is not consistent with the
interpretation of the data.
The student collects sufficient relevant data and records it in a suitable format.
The student organizes, transforms and presents data in numerical and/or visual
3-4
forms, with a few errors or omissions .
The student states a trend, pattern or relationship shown in the data.
The student draws a conclusion consistent with the interpretation of the data.
The student collects sufficient relevant data and records it in a suitable format.
The student organizes, transforms and presents data in numerical and/or visual
forms logically and correctly.
5-6
The student describes a trend, pattern or relationship in the data and comments on the
reliability of the data.
The student draws a clear conclusion based on the correct interpretation of the data
and explains it using scientific reasoning.
Reason for self-evaluation:
I would give myself a 5 or a 6. I think my write-up is good, and I think it shows an understanding
of the concepts. The data is presented logically. I have described the relationship between the
extension of the spring and the weight (force) added to it. I have shown how a spring can be used
to accurately measure force. I have interpreted the data properly and drawn a conclusion using
scientific reasoning. The area I could improve in is the accuracy of the measurements. We could
have found a more accurate way to measure the extension of the spring rather than using the
meter stick the way we did.