Back to P5 Home
P5 H) Investigating Springs
P5 H) Investigating Springs
We are now going to have a look at how we can investigate the link between force and extension of an elastic object. The elastic object that I am going to investigate is a spring and we set up the apparatus like what is shown below.
The first step is to measure the natural length of the spring, which is the length of the spring when no forces are applied to the spring. We measure the natural length of the spring by attaching a ruler to the stand and reading across to the ruler at eye level. We can also add a piece of tape to the end of the spring to make our reading for length more accurate/ to make reading the length easier.
We then add some weights/ masses to the end of the spring. If we are adding weights that have newton values on them, the force will be the weight that is applied to the spring. If we are instead adding masses on the end of the spring, we would need to work out the weight, which we can do by using the equation: weight = mass x gravity (click here for more information about this); the weight will then be the force applied to the spring. After we have added our weight/ mass to the end of the spring, we wait for the spring to come to rest (after it has stopped bouncing up and down). We then work out the extension of the spring (the extension is the change in length between the natural length and the new length with the weight/ mass added).
We then add some more weight/ mass and work out the extension. We keep doing this until we have at least 6 readings. I completed this experiment and did 8 readings. My results are shown in the table below.
We then add some weights/ masses to the end of the spring. If we are adding weights that have newton values on them, the force will be the weight that is applied to the spring. If we are instead adding masses on the end of the spring, we would need to work out the weight, which we can do by using the equation: weight = mass x gravity (click here for more information about this); the weight will then be the force applied to the spring. After we have added our weight/ mass to the end of the spring, we wait for the spring to come to rest (after it has stopped bouncing up and down). We then work out the extension of the spring (the extension is the change in length between the natural length and the new length with the weight/ mass added).
We then add some more weight/ mass and work out the extension. We keep doing this until we have at least 6 readings. I completed this experiment and did 8 readings. My results are shown in the table below.
We then plot our results on a graph and draw a line of best fit. I am going to plot extension on the x-axis and force on the y-axis (you could have had the axis’ the other way around with force on the x-axis and extension on the y-axis). My graph is shown below.
The line of best fit for the first part of the graph will be straight. The straight part of the graph tells us that there is a linear relationship between force and extension. It also tells us that force and extension are in direct proportion. We are able to use the equation “f = ke” for the straight part of the graph. The value of k in this equation is the gradient of the straight line.
When our line of best fit starts to curve, the relationship between force and extension becomes non-linear, which means that the two variables will no longer be in direct proportion to each other. We can use our graph to estimate where the limit of proportionality ends, which is where the line of best fit goes from being straight to curved. On the above graph, it looks like the limit of proportionality ends after 11 Newtons (any value between 10 N and 12 N would get you the marks for a question about where the limit of proportionality is).
When our line of best fit starts to curve, the relationship between force and extension becomes non-linear, which means that the two variables will no longer be in direct proportion to each other. We can use our graph to estimate where the limit of proportionality ends, which is where the line of best fit goes from being straight to curved. On the above graph, it looks like the limit of proportionality ends after 11 Newtons (any value between 10 N and 12 N would get you the marks for a question about where the limit of proportionality is).
Calculating the Spring Constant
We can use the graph to find the spring constant for the spring (the value of k). We find the spring constant by choosing any point on the straight part of the line of best fit. We then sub the values into the “f = ke” formula. I am going to choose the point that has a force of 10 N and an extension of 15 cm. We find the spring constant (k) by dividing the force by the extension. The force needs to be in newtons, which it is as the force is 10 N. The extension needs to be in metres, but currently the extension is in centimetres. We convert centimetres to metres by dividing by 100; the extension is 0.15 metres (15 ÷ 100 = 0.15). We now have the force (10 N) and the extension (0.15 m) in the correct units, so we can sub them into the formula to find k.
This tells us that the spring constant is 66.7 N/m to one decimal place. We could have chosen any point on the straight part of the line of best fit as all of these points would have given us the same value for spring constant.
We could have also worked out the spring constant by finding the gradient of the straight part of the line of best fit. We work out the gradient of a line by dividing the change in y by the change in x. This method is slightly trickier because we need to make sure that the units are correct for the spring constant; the force needs to be in newtons (which it will be from the graph), and the extension needs to be in metres (which it won’t be from the graph because the units are centimetres; we would need to convert the extension into metres before subbing the value into the gradient formula). To be honest, I wouldn’t worry too much about finding the value of k by finding the gradient – instead, I would focus on the other method (using the “f= ke” formula).
We could have also worked out the spring constant by finding the gradient of the straight part of the line of best fit. We work out the gradient of a line by dividing the change in y by the change in x. This method is slightly trickier because we need to make sure that the units are correct for the spring constant; the force needs to be in newtons (which it will be from the graph), and the extension needs to be in metres (which it won’t be from the graph because the units are centimetres; we would need to convert the extension into metres before subbing the value into the gradient formula). To be honest, I wouldn’t worry too much about finding the value of k by finding the gradient – instead, I would focus on the other method (using the “f= ke” formula).
Energy Stored
When a force is applied to an elastic object, the elastic object will stretch or compress and store energy in it’s elastic potential energy stores. When the force is removed, energy from the object’s elastic potential energy store is transferred to the object’s kinetic energy store and the object will revert back to its original shape.
Providing that a spring is not stretched beyond its limit of proportionality, we can work out the amount of energy in an elastic object’s elastic potential energy store by using the formula below:
When a force is applied to an elastic object, the elastic object will stretch or compress and store energy in it’s elastic potential energy stores. When the force is removed, energy from the object’s elastic potential energy store is transferred to the object’s kinetic energy store and the object will revert back to its original shape.
Providing that a spring is not stretched beyond its limit of proportionality, we can work out the amount of energy in an elastic object’s elastic potential energy store by using the formula below:
Ee is elastic potential energy measured in joules (j). This is also the amount of work done by the spring being stretched or compressed.
k in the above formula is the spring constant, which is measured in newtons per metre (N/m). The spring constant tells us the force that we have to put in to extend the spring. All springs are different and therefore have different spring constants (different values for k). For example, a spring that is on a clickable pen will have quite a low spring constant, and a spring that is in a mattress will have a greater spring constant.
e in the above formula is extension, which is measured in metres (m). Springs can be stretched and compressed. Stretching and compression go in as positive values for e into the formula.
There is more information on this equation in a separate section; click here to be taken to that section.