# Investigation on how putting springs in series and parallel affects their extension.

Gemma Hillidge                                                               G.C.S.E Physics Coursework

Investigation on how putting springs in series and parallel affects their extension

### Planning

#### Introduction

##### In order to find out how putting springs in series of parallel affects the extension of the spring I will use Hooke’s law. Hooke’s law states that the force applied to a spring is proportional to its extension, so long as the limit of elasticity is not exceeded. This can be written Tα . This statement of proportionality can be used to write an equation of proportionality: T=k. k represents the spring constant or stiffness of the spring. To find out how the extension of the springs is affected by putting the springs in series or parallel I will set up an experiment involving putting weights on a single spring, two springs in parallel and two springs in series.

Single Spring       Two Springs in Series        Two Springs in Parallel

Prediction

I researched this topic in the textbook “Advanced Physics by Keith Gibbs” and I found that the equation used to find the spring constant is

k =

l        ,

which means the spring constant can be calculated by dividing the modulus of elasticity by the length of the spring. All springs have a different spring constant and the higher the spring constant, the lower the extension. Two springs put into series have a different spring constant than two springs in parallel. I predict that the springs put in series will extend much more than the springs in parallel. This is because springs in series should have a much higher spring constant as they have the properties of a very long spring. If the springs have the same modulus of elasticity then the springs in series’ spring constant will be higher than the spring constant of the springs in parallel as the modulus of elasticity will be divided by a much bigger value as the spring acts as a longer spring, thus making the constant a lower value. For example two springs in series with a force of 1N applied to them would extend double the amount of one of the springs on its own with a force of 1N being applied to it because they act like a single spring with a greater length therefore their constant will be lower making their extension greater. So I predict that the extension of two springs in series will be double the extension of a single spring.

I predict that the springs in parallel will have a smaller extension than a single spring. I believe this to be true as two springs in parallel have different properties than a single spring and therefore have a different spring constant. As the springs are alongside on another they will have the properties of a spring with the same length as a single spring however as there are two springs together rather than just one single spring so their modulus of elasticity should be double that of one single spring. This means that their spring constant should be double that of a single spring as the equation for the spring constant would contain a value twice as big for the modulus of elasticity being divided by a length value the same as the length of a single spring which would make the constant work out to be double that of a single spring. As the spring constant should be double that of a single spring, and stronger springs have higher spring constants, the extension of the two springs in parallel should be half the extension of a single spring with the same force being applied to it.

#### How I will conduct my experiment

I will set up a clamp stand with my springs on it, attach weights of 1N,2N,3N,4N,5N,6N and 7N to a single spring and then to two springs in parallel. When I attach weights to the two springs in series however I shall only go up to 4N as anymore force than this may exceed the limit of elasticity of the springs in series, causing the springs to have plastic properties and not behave as a spring thus making any further readings inaccurate. I will then measure the extension of the springs ...