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# Hooke's Law / Young's Modulus - trying to find out what factors effect the stretching of a spring.

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Introduction

## Hooke's Law / Young's Modulus

I am trying to find out what factors effect the stretching of a spring.

Things, which might affect this, are:
· Downward force applied to spring.
· Spring material.
· Length of spring.
· No. of coils in spring.
· Diameter of spring material.
· Cross sectional area of spring.
I have chosen to look at the effect of the weight applied, as it is a continuous variation.
I predict that the greater the weight applied to the spring, the further the spring will stretch. This is because extension is proportional to load and so if load increases so does extension and so stretching distance.

Extension = New length - Original length

To see if my prediction is correct I will experiment, and obtain results using Hookes Law. He found that extension is proportional to the downward force acting on the spring.

Hookes Law
F=ke
F = Force in Newtons
k = Spring constant
e = Extension in Meters

My method of experimentation will be to use a clamp stand and boss clamp to suspend a spring from. A second boss clamp will hold in place a metre rule starting from the bottom of the spring to measure extension in mm. I will then add weights to the spring and measure extension.
Before deciding on the range of experimentation I carried out a preliminary test to find the elastic limit of the springs we had.

Middle

y=mx+c <THORN> e = mf <THORN> e = f
m

Hookes Law

F=ke

By comparison

K = 1 <THORN> 1 = 28.7769
m 0.03475

This shows the spring constant is 28.7769 N/m
To check that my spring constant from hooks law was correct I am going t experiment again using Simple Harmonic Motion. If both experiments are correct the spring constant from both experiments will be almost identical.
The Simple Harmonic Motion experiment requires measurements of time over an oscillation of the spring being acted on by different forces.
My method of experimentation for simple harmonic motion will be to suspend the spring as in the first experiment and place on the required weight. I will then stretch the spring a further 15mm and then release the spring and take a time measurement for an oscillation in the spring. This however will be inaccurate due to the response time of starting and stopping the timer, because of this I have decided to time 10 oscillations and then divide the result by 10 this will reduce the experimental error. Only one test is needed to find the spring constant but I will take 5 tests each with a different weight. The equation used uses a weight measurement in Kg so the 1N masses I have available will each be 0.1Kg.

Simple Harmonic Motion

T = 2p m
T = Time in seconds k
M = Mass in Kg
K = Spring constant

Conclusion

In the Simple Harmonic Motion test the timing of the oscillations could be taken over a greater number to help reduce experimental error.
Further investigations could use Young´s Modulus This was created by Thomas Young and gives a number representing (in pounds per square inch or dynes per square centimetre) the ratio of stress to strain for a wire or bar of a given substance. According to Hooke´s law the strain is proportional to stress, and therefore the ratio of the two is a constant that is commonly used to indicate the elasticity of the substance. Young´s modulus is the elastic modulus for tension, or tensile stress, and is the force per unit cross section of the material divided by the fractional increase in length resulting from the stretching of a standard rod or wire of the material. This would be useful as after the limit of proportionality had been reached using Hooke´s law; Young´s modulus would give results until the spring became straight until eventually breaking. However the change in length at this stage is very small and special measuring equipment would be needed in order to conduct a reasonable experiment.

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