Hooke S Law Gcse Coursework Math

Hooke's Law

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This is a basic physics tutorial that is targeted at GCSE (grade 9 and grade 10) standard reviewing Hooke's Law and Springs. The video for this written tutorial is on its way.

What is Hooke's Law?

Robert Hooke was an English physicist who first described elasticity. He identified that there is a relationship between force size (magnitude) and the amount of resultant deformation. Hooke's law tells us that the elastic deformation of a substance is proportional to the force that's applied to it. That is, the greater the force, the greater the elastic deformation.

Up until the elastic limit (or yield strength), this relationship is linear (as seen below).

Because the relationship is linear, we can say that the extension of the spring is proportional to the force applied to it.

extension α force

Mathematically we can describe this as:

F = k x e


  • F is the force measured in newtons (N),
  • k is the spring constant, measured in Newtons per meter (N/m), and
  • e is the extension, measured in metres (m).

The spring constant varies between different springs. It can be calculated by the gradient of Force-Extension graphs, as shown below. Just make sure you're always working with the right units and that force is on the y-axis and extension is on the x-axis.

Knowing this, have a look at the below graph, and work out the spring constant for each line - then roll your mouse over the graph for the answer.

The spring constants are 667 N/m, 454 N/m and 200 N/m.

Hooke's Law and compression

Hooke's Law also applies to the compression of an elastic object; you simply need to change e to refer to the compression of the spring. NB: Some texts will use x instead of e. This is demonstrated with the hanging spring below.

The spring constant is calculated in the same fashion as above, however compression is measured instead of extension (mouse over the graph below for calculations).

The spring constant is 231 N/m.

Varying Forces The elastic deformation of a substance is proportional to the force that's applied to it. That is, the greater the force, the greater the elastic deformation (up until its yield or ultimate strength). As you roll your mouse over the image below, you'll note that a doubling in the forces applied in either direction (from +/- 10 N to +/- 20 N) results in a doubling in deformation (from 0.75 cm to 1.5 cm). img src="/content/1-physics/1-grade-9-10-gcse-hsc/2-forces/5-different-types-of-forces/1-contact-forces/3-deforming-forces/2-hooke-s-law/Hooke%27s-Law1.png" onmouseover="this.src='/content/1-physics/1-grade-9-10-gcse-hsc/2-forces/5-different-types-of-forces/1-contact-forces/3-deforming-forces/2-hooke-s-law/Hooke%27s-Law.png'" onmouseout="this.src='/content/1-physics/1-grade-9-10-gcse-hsc/2-forces/5-different-types-of-forces/1-contact-forces/3-deforming-forces/2-hooke-s-law/Hooke%27s-Law1.png'" br h2What is Hooke's Law?/h2 Robert Hooke was an English physicist who first described elasticity and the relationship described above between force magnitude and amount of deformation. You'll often hear this relationship described in terms of a spring. One of the most common ways to explore tension and compression is to study how these forces affect a spring. This is covered in the next tutorial.

AQA's ISA (Individual Skills Assignments)

The Controlled Assessment unit consists of two ISA papers, worth up to 50 marks. They will be worth up to 25% of your GCSE overall. That's a lot, so the ISA is something you should work hard at - it will help your final grade!

Using AQA's Specimen ISA, here we reveal the different sections, leading to our detailed advice.

Stage 0 - Glossary

You will need to be clear in your use of scientific language. Our carefully written AQA Glossary Guide provides you with a significant advantage. Start here!

Stage 1 - Planning

Before you carry out the practical, your teacher will introduce the experiment to you in a context - e.g. if asked to investigate how springs stretch under different loads, the context could be a child's toy which bounces up and down on a spring.

You then write research on the topic, using a Candidate Research Notes sheet, and plan what to do, coming up with a suitable hypothesis. e.g. you find out about the behaviour of springs, read about Hooke's Law and come up with a hypothesis that the extension of the spring will depend on the force added.

You must find two methods for your investigation as you may need to explain why you chose it.

Your Candidate Research Notes must not contain draft texts for Stage 2, so keep your research brief and in note form. You could scribble down the table headings and possible units, but don't draft a table - that's not allowed.

Stage 2 - Reporting on Planning

This is Section One of the ISA and is a written paper, done under exam conditions. In it you will have to:

  1. state and explain your hypothesis
  2. consider variables (independent, dependent and control) that you will manage
  3. use your research to show how to test your hypothesis
  4. write a detailed plan of your chosen method
  5. identify possible hazards and write a short risk assessment
  6. draw a blank table ready for results from your planned experiment.

Section One sounds really nasty, but it will always consist of the above parts, so concentrate on understanding each piece first and you should find that you quite enjoy completing the paper - if you can enjoy exams, that is!

There are two marks for the table and they're dead easy. Click here for our simple advice!

Stage 3 - Practical Work

At last, your practical! Don't worry too much about having to get "perfect results". What really matters here is that you get enough results and record them properly in a table.

You might be the best experimenter since Richard Feynmann, or as clumsy with a stopwatch as a bear unscrewing a jar of marmalade... you can still get the same marks!

Stage 4 - Processing Results

Having done your practical, you will be given some time to process the results from your table into a graph. In Physics, most graphs you do will be line graphs, but this needn't always be the case and you must decide!

There are four marks for the graph and some are really easy. Click here for our simple advice!

Stage 5 - Analysing Results

This is Section Two of the ISA, the final written paper, done under exam conditions. In it you will have to:

  1. analyse your own results
  2. draw a conclusion
  3. compare your results to your hypothesis
  4. evaluate the method of collection and the quality of the data
  5. analyse secondary data about the same topic as your investigation
  6. relate your findings to the context of the ISA.

So again there's a lot to do, but it will be in nice little sections and with practice you will do okay!

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