spring extension experiment

Recording Results

The results were recorded in a table .

It is important to record all of the readings taken and to show clearly any calculations we do from those readings.

where g = gravitational field strength of Earth = 10 N/kg

As 'g' is given in N/kg we had to change the mass in grammes into a mass in kilograms before we could calculate the weight in newtons.

Results table (one was needed for each set of results)

Displaying results in a graph.

The amount the spring stretches plotted against the weight added to the hanger gives a straight line that goes through the origin. This means that the extension of a spring is directly proportional to the stretching force applied to it..

Hooke's Law states that the extension of a spring is directly proportional to the applied load (providing the elastic limit has not been exceeded)

We can e xpress the idea in an equation:

We can put this in an equation.

The constant 'k' (called the 'spring constant') shows it is a proportional relationship:

Follow me...

Cyberphysics - a web-based teaching aid - for students of physics, their teachers and parents....

PhysicsTeacher.in

High School Physics + more

Extension-Load graph of Spring with Lab set-up and Analysis of the graph

Last updated on October 3rd, 2021 at 09:49 am

The Extension-Load graph of spring is a graphical representation of its extension versus applied load. This Extension-Load graph is drawn to see how the extension of a spring depends on the applied load . It is also known as the Load-Extension graph.

Here we will see 1. How to prepare the Lab set-up required to do this graph plotting, 2. How to take the experiment data set and 3. How to interpret a sample extension-load graph of a spring

Read these posts on Elasticity and Hooke’s Law for a quick revision.

Result table for Extension-Load graph

Drawing extension-load graph, how to set up the lab experiment to prepare an extension-load graph of a spring.

Here is a sample lab setup to carry out an experiment on the stretching of a spring. The spring is hung from a rigid clamp and its top end is fixed. A weight or load is attached to the open end of the spring. The spring is suspended as shown in the diagram beside. Now as the load is attached the spring extends i.e. its length increases. As the load is increased, the spring stretches, and its length increases.

It is observed that as the load is increased in regular steps, the length of the spring also increases in regular steps. At this stage, the spring will get back to its original length if the load is removed.

The observations are to be noted in a tabular form with 3 columns which will be used to draw the extension-load graph of the spring. The 3 data columns are (1) Load in Newton (2) Current length of the spring in centimeter (3) Extension of the spring in centimeter. The first row will be for zero load i.e. with no load attached.

However, beyond a certain limit of the applied load, the spring becomes permanently stretched and will not return to its original length when the load is removed. Here we can say that the spring has been inelastically deformed .

Here is one such sample results table.

Now it’s time to draw the load versus extension graph for the given spring according to the experiment result set listed in the table in the previous section of this post.

Analysis of the Extension-Load graph

We have drawn extension versus load in a graph to find out how the extension of length depends on the applied load for a spring. We can observe that the graph has 2 visibly distinct parts.

1 ] In the beginning, the graph slopes up uniformly in a straight line up to a point. This means that the extension of length increases in equal steps as the load increases. And when the load is removed the extension becomes zero and the spring gets back to its original length. This point is known as the limit of proportionality.

2 ] Then after a certain limit of the applied load, the graph bends. Here the extension is no more in equal steps with the load. The spring here has become permanently damaged, as when the load is removed the extension doesn’t become zero and the spring doesn’t return to its original length.

Here we have covered the concept of extension load graph of spring and the limit of proportionality. If you like this post share this using the share buttons on this page.

If you want to revise the fundamentals then read these posts on Elasticity and Hooke’s Law .

Related Posts:

• Stress-Strain Graph & stress-strain analysis
• The oscilloscope & its signal attribute, AC and DC graph
• Ductile and Brittle materials beyond elastic limit & their force-extension graph
• Connecting ammeter and voltmeter in physics lab
• Shape change by Forces & stretching a spring
• How to Determine g in laboratory | Value of acceleration due to gravity -…

An Example of An Accurate Hooke’s Law Laboratory

Table of Contents

Learning Objectives

• Gain confidence and experimental care in making accurate measurements.
• Understand the relationship between force and spring stretch.
• Use a neat and orderly lab notebook in which data are recorded.
• Execute a specific experimental procedure to test a specific hypothesis.
• Analyze the acquired data with a spreadsheet and graphing program to test the hypothesis.
• Explain in one’s own words whether the experimental data supported the hypothesis.

Introduction

Robert Hooke was a 17th-century scientist who made notable discoveries in a wide range of fields from astronomy to biology (discovery of the cell). His discovery of the linear relationship between the extension of a spring and the applied force has broad application in engineering and physics because it has been shown to apply in a wide array of circumstances for sufficiently small displacements. Most of Hooke’s discoveries resulted from careful observations and measurements. Hypothesis: Spring stretch and applied force are linearly related. This hypothesis can be tested by hanging known masses (which create known downward forces) to a spring and measuring the resulting displacements. The slope of the line from plotting Force (in N) vs. position (in m) is a characteristic of the spring known as the spring constant (in units of N/m).

Note, that Hooke’s law is most commonly expressed as a direct proportionality between force and spring stretch. However, many simple coil springs are wound such that the coils physically prevent the spring from contracting to the true unstretched position that would correspond to zero displacements for zero applied force. Consequently, it takes some finite applied force to overcome the resulting internal tension and produce a measurable displacement. To accommodate these springs, it is convenient to frame the hypothesis as a linear relationship rather than a direct proportion. This also allows students to simply record the position for each hanging weight rather than computing the displacement from the position corresponding to zero hanging weight.

Materials * A spring that has a significant and easily measurable stretch with the available masses. Here, a composite spring is constructed from 3 #84 springs arranged in series. These springs were purchased at an Ace hardware store. * Electronic balance (if masses are unknown). * A range of test masses (6-8) that can be hung to stretch the spring. Masses should have a range of values so that the heaviest mass is 3-4 times the lightest mass, and the range has (approximately) equal steps over the interval.

Likewise, it is essential to position your eye looking as near as possible to exactly horizontal when making the position measurement. Looking slightly upward or downward when lining up the position of the spring coil with the position scale will introduce parallax error. Repeat this measurement for each of your test masses until the table in your lab notebook is complete.

Procedure for Analysis

Make four columns in a spreadsheet with headings of Mass (g), Position (mm), Position (m), and Force (N). The first two columns contain the numbers for your original measurements, the same as they are recorded in your lab notebook. The third column contains the position converted to meters with an appropriate spreadsheet formula, something like = B3/1000 (assuming the position in mm was in cell B3). The fourth column computes the applied force for each given mass, with a spreadsheet formula something like = A3*9.81/1000 (assuming the mass in g was in spreadsheet cell A3).

Now, copy the third and fourth columns for Position (m) vs. Force (N) (data only, no headers) into Graph.exe (downloadable for free from https://www.padowan.dk/download/ ) or other suitable graphing program and make a scatter plot of the data. Adjust the level of zoom as needed and take care to properly label the horizontal (x) axis as Position (m) and the vertical (y) axis as Force (N). You may also make other aesthetic adjustments to improve the appearance of the graph. Now, use the trendline menu option to insert a linear trendline. Do not check the box setting the y-intercept to zero. Make aesthetic adjustments to improve the appearance of the graph. Save your work as a graph file. Now, you may also save the graph as an image so that it can be imported into your lab report later. The slope of the trendline provides an accurate estimate of the spring constant, k, of your spring. It has units of N/m (newtons per meter) and is a characteristic of the spring.

The Rationale for Extended Analysis The goal of low-cost quality experiments tends to put more of the burden on the analysis side than on the experiment side because most people have already invested in computers and the analysis software can be obtained for free. Further, extended and careful analysis is excellent training in scientific thinking, builds skills that will be useful in college and reinforces skills that will increase scores on standardized tests like the ACT. Don’t give the analysis efforts short shrift. These tools and techniques will be used often and careful attention to these details is essential preparation for later laboratories.

Results (50 points total)

Your results should be a well-ordered and labeled table (15 points), as well as a figure (15 points) with the trendline and data produced in a graphing program. The above figure and table are illustrative examples, but yours must be created with your original data.  Pay attention to formatting and communication. The Table needs to be properly captioned and should also have a paragraph of text (10 points) describing its contents, but saving discussion relative to the hypothesis for the discussion section. Pay careful attention to include all the specific accuracy estimates in your table that are shown below. These are important in the discussion of whether the hypothesis is supported, and the uncertainty in the spring constant may also be important in later lab testing predictions for the period of simple harmonic oscillators. The Figure also needs to be properly captioned and should be described in a paragraph of text (10 points).

Table 1: Data and analysis for Force vs. Position for our Hooke’s Law experiment.

Discussion (50 Points)

Your written discussion should be from 1 to 3 paragraphs discussing the following questions in complete sentences: * Was your hypothesis supported? Why or why not? (20 points) * What was the relative uncertainty of your spring constant? (10 points) * Other than the accuracy of the electronic balance, what else may have caused variations in your measurements? (10 points) * Can you say your hypothesis was proven (or disproven)? Or is it better to say supported (or unsupported)? (10 points)

Note on lesson plans: Teachers should consider a multi-day approach to this lab. Day 1: Discuss the theoretical background and read the lab instructions. Day 2: Experiment. Day 3 (possible homework): Analyze the data. Day 4 (best as homework): Write lab report. A good lab science course uses 30-40% of class time on lab activities and completes at least 15 different lab experiments in a school year.

I grew up working in bars and restaurants in New Orleans and viewed education as a path to escape menial and dangerous work environments, majoring in Physics at LSU. After being a finalist for the Rhodes Scholarship I was offered graduate research fellowships from both Princeton and MIT, completing a PhD in Physics from MIT in 1995. I have published papers in theoretical astrophysics, experimental atomic physics, chaos theory, quantum theory, acoustics, ballistics, traumatic brain injury, epistemology, and education.

My philosophy of education emphasizes the tremendous potential for accomplishment in each individual and that achieving that potential requires efforts in a broad range of disciplines including music, art, poetry, history, literature, science, math, and athletics. As a younger man, I enjoyed playing basketball and Ultimate. Now I play tennis and mountain bike 2000 miles a year.

You might also like

You mention downloading a graphing program. An alternate suggestion is just train the students to use Excel’s x-y scatter plot. You have the option to “add trend line” and display the equation of the trend line on the graph. Along with correlation coefficient indicating “goodness of fit”. Probably also helpful for students to know about the array formula “linest”. I might sound a bit like a Microsoft salesman here but I have found Excel a great “all in one” tool for data analysis generally.

This is a great introductory Science prac – many thanks for your insights article.

Pick any functional form, and any data, and there exists a best fit. This is the basis of politically motivated “science”.Sure, but in teaching science we can do better. We can have an honest look at how well a hypothetical functional form "fits" the data – R2, residuals, p-values, and so on. Not that every intro lab needs it, but most intro courses would do well to have several labs where students are required to compare their residuals to their instrumental accuracy. Most intro courses would also do well to have a few labs where students fit alternate functional forms to their data. If a power law, square root, quadratic, or exponential fits the data better than a straight line, what does this say about the hypothesis that predicted a linear fit? These data analysis steps help students see beyond their possible confirmation bias if only the hypothetical model is tried. It also gives students experience and analysis tools to help them see through "junk science."

Pick any functional form, and any data, and there exists a best fit. This is the basis of politically motivated “science”.

That's why I like the way we run our class here. We basically used the concept of "Studio Physics", where we really do not have an assigned session for "labs". Rather, the lab is considered as part of the lesson, where I often stop discussing the material and let the students check out something that is relevant to the topic. This works especially well when we do Lenz's law, where everyone has a bar magnet, a galvanometer, and a solenoid. I actually let them discover the property themselves as we go through various combinations of the magnet going in and out of the solenoid.

And since writing ability is included as part of our Syllabus, the students had to find the most accurate way to describe what they learned and to try to come up with a "rule" of what would happen under any circumstances.

But coming back to the non-Hooke's law experiment, during our class session, I had some of the best in-class discussion among the students based on this part of the experiment. It sets up perfectly for the rest of the semester what is expected out of the students, and they get a very early wake-up call that this is not going to be your normal, boring "labs". Even if they don't learn anything else, that realization by itself is worth doing this experiment.

I think you missed my scenario. I included a non-Hooke's law spring. I didn't say that that was the only spring that the students were given. They were given 2 springs to find the spring constant. One was straight-up Hooke's law behavior. The other was not.I caught your scenario. The next lab (immediately after Hooke's law) in my lab course is usually the simple harmonic oscillator, where the hypothesis is basically the formula for the SHO period, using the previously measured spring constant. Using Tracker as the timer and timing 10 periods usually yields an accuracy comparable to that of k in the original experiment for linear springs. Of course, this hypothesis will not be supported for a non-linear spring.

Since my labs are designed for 1 hour experiments, there is insufficient time to do multiple springs. But with a long enough class period, one could keep the fun going by having students perform the SHO experiment with the same set of springs as used in the Hooke's law experiment.

But the whole propensity to allow students to "eyeball" whether data is linear feeds their disposition to conclude data is linear when it really is not. Even high school students can learn how R-Squared and the uncertainty in the slope can be used to determine that one spring is a lot less linear than the other. If one has an estimate on the uncertainty in k, students can see how the SHO formula for period becomes a garbage in – garbage out exercise for the non-linear spring. A careful experiment with a linear spring can yield a 1% or better uncertainty in k, which can yield a 1% or so support for the SHO period formula. The uncertainty in k for a nonlinear spring is going to be much larger.

Good point. A well designed lab course should include a number of cases where the hypothesis is not supported. But I prefer to put most of these later in the semester for several reasons: 1. Students tend to ascribe the lack of experimental support for a hypothesis to human or experimental error. I design most earlier labs to develop skills and build confidence in measurement accuracy to empower them to consider the possibility that the hypothesis might simply be wrong. 2. In cases like Hooke's law, the rule is more important than the exceptions for downstream courses. I would only present an experimental exception after the rule has been verified. There is probably time for cases that include both the rule and exceptions to Hooke's law in a 3 hour college lab once students are reasonably skilled and efficient. But this is unlikely in most 1 hour high school physics and physical science classes. 3. If a hypothesis will not be supported, I like students to have built enough analysis skills to suggest a different hypothesis. At some point in a lab course, students will be familiar with the most common functional forms: linear, quadratic, power law, square root, etc. and will have tested various data sets against multiple possibilities. If one hypothesis is not supported (such as a linear relationship), it is nice if students can explore other possibilities and suggest an alternative hypothesis from their data.I think you missed my scenario. I included a non-Hooke's law spring. I didn't say that that was the only spring that the students were given. They were given 2 springs to find the spring constant. One was straight-up Hooke's law behavior. The other was not.

Whatever the situation, we have sit back and figure out what we are trying to accomplish here. Our Syllabus for this class includes training the students with the skills and ability to perform experiments and analyze data, including systematic and analytical evaluation of experimental results. So seeing them respond to something that was completely unexpected is part of it. I made it a point to discuss this situation when I return their lab reports.

Here's the thing. If they were walking down the street, and I show them a random graph that looks like the non-Hooke's law graph, none of then would say that the straight line is a good representation of the data. Yet, many of them seem to throw out this sensibility when they walk into a physics class! I want them to learn (often, the hard way) that they need to bring that sensibility into the physics classroom, and that just because we are learning physics, it doesn't mean that all their worldly experiences no longer apply.

I find that they learn more when they make the mistake without my warning them first, rather than if I talk till I'm blue about it before hand.

You may not believe it, but part of my Hooke's law experiment that I gave to my students were DESIGNED to not work "as expected". I gave them springs that had been abused and no longer exhibit the linear behavior, but I never told them that. Looking at the F versus x graph will show that this wonky spring did not show the same behavior as the Hooke's law spring.

You'd be surprised how many students IGNORED this, and blindly fit a straight line to something that clearly could not be accurately represented by a straight line.

Part of doing an experiment is the ability to handle things when something unexpected happens. You cannot be oblivious to what the data are telling you and simply forced it into ways that you expect them to be, or if there was something weird going on that may be attributed to error in the measurement or setup. I repeatedly have told to my students that they can get away with getting unexpected result and still get very good grade for the lab report, IF they are able to account for the strange result and were cognizant to the fact that something unexpected was obtained.

Zz.Good point. A well designed lab course should include a number of cases where the hypothesis is not supported. But I prefer to put most of these later in the semester for several reasons: 1. Students tend to ascribe the lack of experimental support for a hypothesis to human or experimental error. I design most earlier labs to develop skills and build confidence in measurement accuracy to empower them to consider the possibility that the hypothesis might simply be wrong. 2. In cases like Hooke's law, the rule is more important than the exceptions for downstream courses. I would only present an experimental exception after the rule has been verified. There is probably time for cases that include both the rule and exceptions to Hooke's law in a 3 hour college lab once students are reasonably skilled and efficient. But this is unlikely in most 1 hour high school physics and physical science classes. 3. If a hypothesis will not be supported, I like students to have built enough analysis skills to suggest a different hypothesis. At some point in a lab course, students will be familiar with the most common functional forms: linear, quadratic, power law, square root, etc. and will have tested various data sets against multiple possibilities. If one hypothesis is not supported (such as a linear relationship), it is nice if students can explore other possibilities and suggest an alternative hypothesis from their data.

May I quote you on that and give it to my current students?

Zz.Certainly, but your students might not appreciate it. We get old too soon and smart too late , probably applies.

Zz, too bad I'm so old. It sounds like it would be fun to be one of your students.May I quote you on that and give it to my current students?

Zz, too bad I'm so old. It sounds like it would be fun to be one of your students.

I guess I was fortunate enough that most of the science labs were enjoyable to participate in. I do remember that sometimes we did not get the desired result. That was frustrating.

I like how you designed the experiment for the students to learn about the concept as well as the scientific method.You may not believe it, but part of my Hooke's law experiment that I gave to my students were DESIGNED to not work "as expected". I gave them springs that had been abused and no longer exhibit the linear behavior, but I never told them that. Looking at the F versus x graph will show that this wonky spring did not show the same behavior as the Hooke's law spring.

Wow ZapperZ, that’s a nice experiment to do…

I like how you designed the experiment for the students to learn about the concept as well as the scientific method.

That is a thoroughly enjoyable article. Thank you @Dr. Courtney .

I never did well in laboratory lessons in school, and I thought they were boring. Perhaps if I had a teacher who so clearly explained what we were doing and why, as you did in the article, that outcome may have been different.I have to confess, for my first 5 years as a teacher, I used canned laboratory exercises that had been written by others that had many of the flaws you mention. Student engagement was low due to the lack of excitement and interest, so the care they exercised and the learning they accomplished also tended to be low. I also viewed the point of the lab as reinforcing material from the lecture.

Eventually, I shifted in my view so that the main focus of labs became understanding and applying the scientific method itself. This naturally caused me to desire greater accuracy, since an experiment with 1% errors tests any hypothesis more rigorously than the experiments with 5-10% errors that I had been doing. I think the biggest part in motivating accuracy is showing it can be achieved with due care at a few important points along the way. But one also needs to avoid labs and equipment where the learning curve is just too steep for most students to have accurate results. Consequently, one needs to be content not having a lab that corresponds with every chapter in the book.

These days, I write my own labs and before being overly confident in student ability to achieve results, I pilot the experiments myself and also check out the lab equipment carefully. It is extremely demotivating for students to be expected to have accurate results using faulty equipment in the compressed time frame of most lab experiments.

Love how this Insight is laid out and especially the top “Learning Objectives” bit!

I never did well in laboratory lessons in school, and I thought they were boring. Perhaps if I had a teacher who so clearly explained what we were doing and why, as you did in the article, that outcome may have been different.

Leave a Reply

Leave a reply cancel reply.

You must be logged in to post a comment.

• TOP CATEGORIES
• AS and A Level
• University Degree
• International Baccalaureate
• Uncategorised
• 5 Star Essays
• Study Tools
• Study Guides
• Meet the Team
• Forces and Motion

Hooke's Law Lab

Devanshi Sodhani

PHYSICS LAB REPORT

VERIFYING HOOKE’S LAW

The aim of performing this experiment is to find out if the extension produced by a spring is directly proportional to the tension force applied to it and thus verifying Hooke’s law.

In 1676 the English physicist Robert Hooke discovered that elastic objects, such as metal springs, stretch in proportion to the force that acts on them. Despite all the advances that have been made in physics since 1676, this simple law still holds true.

This means that if a weight is added to a spring, it will stretch in proportion to that force and when the force is removed, the spring will return to its original shape. The extension or the strain will keep increasing as you increase the weight added as long as the spring doesn’t remain stretched permanently.  A point is reached where the spring can’t stretch any more when more tension force is applied to it and snaps. This is defined as the ‘elastic limit’ of the spring.

The force constant  ‘k’ of a spring is the force needed to cause unit extension, i.e. 5cm. If a force ‘F’ produces extension ‘e’ then,

       e

(Sourced from: Microsoft ® Encarta ® Reference Library 2005. © 1993-2004 Microsoft Corporation. All rights reserved.)

HYPOTHESIS:

Hooke’s Law states that the extension produced by the spring is directly proportional to the tension force applied to it. Therefore, in this experiment I hypothesize that the extension produced by the spring will increase as more weights are added. The graph for this extension will be as follows:

The Y-Axis shows the stretching force ‘F’ and the X-Axis represents the extension produced by the spring.  

• surroundings
• equipment used

Independent:

• Weights added (force applied)
• extension produced by the spring
• Clamp stand with a stable base.
• Uniform metre- rule.
• Metal spring with a pointer at the end.
• Uniform metal weights of 100g each.
• The same equipment must be used for all the trials so that the uncertainties remain constant for every reading taken.
• The surroundings must not be too breezy so that the spring which is suspended from the clamp stand doesn’t oscillate.
• The pointer of the spring must be completely horizontal so that correct measurements of the extension can be taken from the metre-rule.
• The metre rule used must be calibrated uniformly and it should be kept parallel to the suspended spring while taking the readings.
• All readings must be taken at eye-level.
• The clamp stand used must be very stable so that the suspended spring doesn’t oscillate during the experiment is being performed and thus to prevent anomalous results.
• There should be no contact of the spring with the hand which would apply an extra tension force to the spring and thus give inaccurate results.

SAFETY PRECAUTIONS:

• All the weights must be handled with care and should not fall on any part of the body causing injuries.
• The clamp stand should have a stable base so that when weights are added to the attached spring, the balance doesn’t shift and so the stand doesn’t topple over.
• Any rusted metal should be kept away from cuts in the body to prevent any contact with the bacteria present on the rust.
• The sharp edges of the metal spring must not poke any part of the body causing any injuries.

MODIFICATIONS TO THE EXPERIMENT:

This is a preview of the whole essay

• Instead of using one spring, the experiment was carried out using two springs with different elasticity.
• The metre rule was held in a straight position by attaching it to the clamp stand. Thus the data could be recorded more efficiently.
• Since the base of the clamp stand was not very stable, loads were put on the base to make it more stable.

DIAGRAM OF THE SET-UP APPARATUS:

Length after adding weights on spring 1:

Length after adding weights on spring 2:

PROCESSED DATA:

Weights added = force applied

100g = 0.1kg

Gravity= 10m/s 2

Weight= 0.1 X 10

            = 1N

Extension caused by adding weights on spring 1:

Extension caused by adding weights on spring 2:

Table to calculate the spring constant for spring 1:

             = shows an anomalous result

Average value for the spring constant= (2.22+0.72+0.46+0.34+0.33)/5

                                                            = 0.81

Table to calculate spring constant for spring 2:

GRAPHS OF RESULTS ATTACHED AS PAGES 7 AND 8.

Gradient of the l.o.b.f= spring constant.

Gradient of the line= y2- y1

                                   x2- x1

                               = 3-2

                                  9-6

                               = 1/3

                               = 0.33

                               =   4-3  

                             38.45-28.4    

                             = 1/10.0

                               = 0.1

Tables 1.1 and 2.1 show the raw and processed data for the first spring. As observed, this spring was quite rigid and its coils were extremely close to each other. The total length of this spring was 13 cm and with the weights added, the spring did not show a large extension. Although a positive relationship is shown between the force applied an extension produced, it is not uniform since no trend can be seen between the two. When a force of 1N (100g) is applied, the extension produced is only 0.45 cm and when a force of 5N (500g) is applied, the extension produced is 14.95cm. This shows that the extension produced by the spring is over a very short range. The results of the first trial are anomalous because the value of the spring constant is way different from the values obtained with the other trials. After the experiment is performed with weights of 400g, the spring doesn’t return back to its original length of 13cm and it stops at 13.2cm. This shows that the spring has now been permanently stretched and the Hooke’s law can’t be applied to the spring anymore as the extension produced will not be proportional to the force applied.

However, the graph drawn for the results obtained is not a uniform straight line as it is supposed to be theoretically. This may have happened due to the inaccuracy in the experiment or because of changes in the surroundings which were supposed to be constant. The errors are identified in this report. The spring constant is calculated for the results obtained by using the formula k=F/e. This value is not a constant as it should have been due to the errors in the experiment. The average value is calculated as 0.814. The gradient of the graph of results also gives the spring constant. This value is found to be 0.33 and when this value is compared to the value obtained as the gradient of the graph, it can be seen that the two values differ.  The reason for this is that there were errors in performing this experiment and the results of the first trial were anomalous.

Tables 1.2 and 2.2 contain the raw and processed data for the second spring. This spring is very flexible and its coils are not extremely close to each other. This spring was longer than the first spring with a length of 14.8cm and this was because of its coils not being so close to each other. This spring being flexible, produced a large extension with every 100g weight added. There is a constant trend seen in the results. For every 100g added, the extension produced by the spring is approximately 10cm. this shows that the extension is proportional to the force applied. The extension shown by the spring ranges from 9.5 to 47.90cm which shows how flexible the spring is.

However, the Hooke’s law can’t be applied for the fifth reading. This is because after the fourth reading, the spring becomes permanently stretched because of which the extension produced in the fifth trial is not directly proportional to the 5N weight added.

The graph obtained for these results is a uniform straight line graph which shows the proportionality between the force and extension. The last point plotted on the graph for the extension produced when 5N force is applied doesn’t fall on the straight line since Hooke’s law is not applicable to the spring after the fourth trial. The gradient of the line gives a value of 0.1 which was same as the value obtained when the spring constant was calculated using the results. These results seem to be very accurate since there is an explanation related to the Hooke’s law for every trial performed.

When the two springs are compared, it can be said that the second spring produces more extension as force is applied to it. This happens because it is more flexible than the first spring and because its coils are further apart when compared to the first spring. Also, the second spring gives more accurate results than the first spring since the graph plotted for the second set of results is a uniform straight line graph with almost all of the points falling in the line of best fit.

SOURCES OF ERRORS:

• The springs used kept oscillating when the weights were added on them. This caused a lot of inconvenience while taking measurements and thus could have led to inaccuracy.
• The pointers of the springs were not exactly horizontal thus causing the measurements to be slightly incorrect.
• It was not possible to take all the readings at eye-level thus causing parallax errors.
• Since the pendulum was oscillating too much, I had to use my hand to hold the spring steady.
• The ruler attached to the clamp stand to make the experiment more efficient. However, it was not in a straight line thus causing some inaccuracy in measurements.
• This would have caused extra force to be applied and the exact measurements could not be taken.
• All the weights were assumed to be 100g and their exact weight was not taken. Thus it is possible that extra or inadequate force may have been applied.

SUGGESTED IMPROVEMENTS:

• More readings can have been taken to improve the accuracy of the experiment.
• All the weights used should be measured on a digital balance before using them so that the exact force applied can be calculated.
• The pointer of the spring should be totally horizontal to get accurate measurements of the extension.

CONCLUSION:

From the experiment performed above, it can be concluded that the Hooke’s law holds true for a metal spring. This is because the extension produced by the spring is directly proportional to the force applied on it. For the first spring, the results obtained are not very accurate due to the sources of errors identified above. However, the second spring gave very accurate results as I had hypothesized according to the theory. Therefore, this experiment is a reliable way of verifying Hooke’s law using a metal spring.

Encarta Reference library

IGCSE Physics- Hodder Murray

Physics class notes

Document Details

• Word Count 2259
• Page Count 7
• Subject Science

Related Essays

To determine the elasticity of an elastic band by applying Hookes law.

Do Elastic Bands Obey Hooke Law

SITEMAP  * HOME PAGE * SEARCH * UK KS3 level Science Quizzes for students aged ~13-14

UK GCSE level Biology *  Chemistry *  Physics  age ~14-16 * Advanced Level Chemistry age ~16-18

School-college Physics Notes: Forces Section 4.3 Hooke's law investigation

Above is an illustration of a simple instrument for weighing objects. It is essentially a 'force meter' calibrated to read in g and kg. (so it takes into account gravity at the Earth's surface, but it would be any good on the Moon or Mars with their different strength of gravitational fields)

Prior to taking a reading the pointer should be adjusted to read zero.

Different groups in a class can look at different springs, or if time permits each group of students can look at several springs. The class results can be pooled and graphs drawn. Instead of plotting force versus extension (which  I prefer) you can plot extension versus force. Since F = ke, e = F / k, so the gradient will be 1 / k, the reciprocal of the spring constant. In the 'idealised' right-hand graph of spring extension versus force, springs A and C results did not go beyond the limit of proportionality. However, the results for spring B showed a deviation from linearity and the graph curves upwards from point L, the limit of proportionality.

4.3b What happens if you keep on increasing the force applied to an elastic material?

In the above experiment, if you add even more weights to the spring then the resulting graph of results may not be linear for the higher weight readings. This is because the spring is overstretched beyond its elastic limit (the limit of proportionality). Beyond point L Hooke's Law is no longer obeyed. In other words the non-linear section of the graph is beyond L, the limit of proportionality - the spring stretches more than you expect and the graph begins to curve over. From zero force to L Hooke's Law is obeyed - the linear section of elasticity . After that, between point L and point D, the stretching is greater than expected - non-linear graph, but the spring will return to its original length - the spring is still behaving elastically , but only for a relatively small further increase in the applied force. Just because an object behaves elastically, it doesn't mean that Hooke's Law is obeyed. An elastic band is 'elastic' but it doesn't obey Hooke's Law!

Eventually at point D, called the elastic limit , the force is too great for spring will not return to its original length - permanent deformation beyond the limit of elasticity.

This happens with a repeatedly stretched elastic band - eventually it breaks!

From point D onwards the spring behaves with plastic deformation .

On the right-hand graph, an alternative representation of the graphical data, I've indicated the permanent extension showing the spring will NOT return to its original length.

Sub-index of physics notes: FORCES 4. Elastic potential energy

Keywords, phrases and learning objectives for elastic potential energy

Be able to describe an experiment to investigate the force applied to a spring and resulting extension. Explain  the experimental procedure to validate whether a stretched material obeys Hooke's Law - processing data with graphs and calculations. Know what happens if the material (e.g. a spring) is stretched beyond the elastic limit - interpret a graph to aid your explanation.

TOP of page

INDEX for physics notes on FORCES section 4

INDEX of all my physics notes on FORCES

INDEX of all my physics notes on FORCES and MOTION

INDEX of all my PHYSICS NOTES

email doc brown - comments - query?

BIG website, using the [ SEARCH BOX ] below, maybe quicker than navigating the many sub-indexes

Basic Science Quizzes for UK KS3 science students aged ~12-14, ~US grades 6-8

Biology *  Chemistry *  Physics  for UK GCSE level students aged ~14-16, ~US grades 9-10

Advanced Level Chemistry for pre-university age ~16-18 ~US grades 11-12, K12 Honors

Find your GCSE/IGCSE science course for more help links to all science revision notes

SITEMAP Website content � Dr Phil Brown 2000+. All copyrights reserved on Doc Brown's physics revision notes, images, quizzes, worksheets etc. Copying of website material is NOT permitted. Exam revision summaries and references to GCSE science course specifications are unofficial.

TOP OF PAGE