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P5 G) Elasticity
P5 G) Elasticity
When a force is applied to an elastic object, the object will stretch/ change its shape and store energy in its elastic potential energy stores. When the force is removed, the elastic object will revert back to its original shape; when the elastic object reverts back to its original shape, energy is transferred from the object’s elastic potential energy store to the object’s kinetic energy store. As energy has been transferred from one store to another store, work has been done.
Applying a force to an elastic object can result in 3 different types of deformation; compressing, stretching and bending. In order to stretch, compress or bend an elastic object, we need to apply multiple forces; this is because if we only applied one force, we would just move the elastic object. There are a few diagrams below for the compressing, stretching, and bending of a spring.
Applying a force to an elastic object can result in 3 different types of deformation; compressing, stretching and bending. In order to stretch, compress or bend an elastic object, we need to apply multiple forces; this is because if we only applied one force, we would just move the elastic object. There are a few diagrams below for the compressing, stretching, and bending of a spring.
Elastic & Inelastic Deformation
If you have an old clickable pen with a spring that no longer works, it may be worth taking the pen apart and using the spring to help you understand elastic and inelastic deformation.
If a spring has been elastically deformed by a force, the spring will go back to its original shape after the force has been removed. For example, with a pen spring, if you apply a small force to the spring, the spring will stretch. When you remove this force, the spring will go back to its original shape.
If a spring has been inelastically deformed by a force, the spring will not go back to its original shape after the force has been removed. This happens when a very large force is applied to the spring. For example, with a pen spring, if you apply a very large force, the spring will extend by a considerable amount. If you then remove this force, the spring will not return to its original shape and this is because the spring has been inelastically deformed. The force where the spring will no longer return to its original shape is known as the “elastic limit” for the spring.
If you have an old clickable pen with a spring that no longer works, it may be worth taking the pen apart and using the spring to help you understand elastic and inelastic deformation.
If a spring has been elastically deformed by a force, the spring will go back to its original shape after the force has been removed. For example, with a pen spring, if you apply a small force to the spring, the spring will stretch. When you remove this force, the spring will go back to its original shape.
If a spring has been inelastically deformed by a force, the spring will not go back to its original shape after the force has been removed. This happens when a very large force is applied to the spring. For example, with a pen spring, if you apply a very large force, the spring will extend by a considerable amount. If you then remove this force, the spring will not return to its original shape and this is because the spring has been inelastically deformed. The force where the spring will no longer return to its original shape is known as the “elastic limit” for the spring.
Stretching Springs
We can see the effect that force has on the extension of a spring by attaching a spring to something that is fixed and then adding weights on to the bottom of the spring. A diagram of this is shown below.
We can see the effect that force has on the extension of a spring by attaching a spring to something that is fixed and then adding weights on to the bottom of the spring. A diagram of this is shown below.
The extension of a spring is the difference between the length of the natural spring (when no forces are applied) and the length of the spring when a force is applied.
The extension of an elastic object is directly proportional to the force applied; direct proportion means that the variables move in the same direction by the same proportion and that the graph starts from 0. For example, if we double the force applied to the spring, the extension of the spring would also double. Variables that are in direct proportion have a linear relationship to each other.
The equation and formula triangle that links force, extension and spring constant is shown below.
The extension of an elastic object is directly proportional to the force applied; direct proportion means that the variables move in the same direction by the same proportion and that the graph starts from 0. For example, if we double the force applied to the spring, the extension of the spring would also double. Variables that are in direct proportion have a linear relationship to each other.
The equation and formula triangle that links force, extension and spring constant is shown below.
In the above equation, force is measured in Newtons (N), extension is measured in metres (m) and spring constant is measured in Newtons per metre (N/m).
Different springs will have different spring constants. The stiffer a spring is, the greater the spring constant will be; this is because a stiffer spring will require a greater force for the same extension. Extension in the above formula can either be extension or compression (extension is where the spring gets longer, and compression is where the spring gets smaller).
The graph below shows how the extension of a spring changes as we apply different forces to the spring.
Different springs will have different spring constants. The stiffer a spring is, the greater the spring constant will be; this is because a stiffer spring will require a greater force for the same extension. Extension in the above formula can either be extension or compression (extension is where the spring gets longer, and compression is where the spring gets smaller).
The graph below shows how the extension of a spring changes as we apply different forces to the spring.
There are two different parts of this graph; the straight part at the start and the curved part at the end. Point P on the graph is known as the limit of proportionality.
Between 0 and point P (the straight part), the extension of the spring and the force applied to the spring are directly proportional to each other. We can use the equation “f = ke” for this part of the graph. We can also say that there is a linear relationship between force and extension for this part of the graph.
After point p (the curved part), the force and extension are no longer directly proportional to each other. We are unable to use the equation “f = ke” for any point after point P. After point P, the relationship between force and extension becomes non-linear; the spring now stretches more for each additional unit of force.
Sometimes there is another point labelled on the graph called the elastic limit. If a force greater than the elastic limit is applied to the spring, the spring will become inelastically deformed, which means that the spring will no longer return back to its original shape after the force has been removed. I have added the elastic limit on the graph below.
Between 0 and point P (the straight part), the extension of the spring and the force applied to the spring are directly proportional to each other. We can use the equation “f = ke” for this part of the graph. We can also say that there is a linear relationship between force and extension for this part of the graph.
After point p (the curved part), the force and extension are no longer directly proportional to each other. We are unable to use the equation “f = ke” for any point after point P. After point P, the relationship between force and extension becomes non-linear; the spring now stretches more for each additional unit of force.
Sometimes there is another point labelled on the graph called the elastic limit. If a force greater than the elastic limit is applied to the spring, the spring will become inelastically deformed, which means that the spring will no longer return back to its original shape after the force has been removed. I have added the elastic limit on the graph below.
Sometimes force and extension graphs for springs can be shown with the axis the other way around (force on the x-axis and extension on the y-axis). When this is the case, the graph will look like what is shown below.
Some Calculations
We are now going to have a look at a few calculations involving forces, spring constants and extension. The equation and formula triangle are shown below.
We are now going to have a look at a few calculations involving forces, spring constants and extension. The equation and formula triangle are shown below.
Example 1
A spring has a spring constant of 40 N/m. When an unknown force is applied to the spring, the spring extends by 5 cm. Work out the force applied to the spring.
We can find the force applied to the spring by multiplying the spring constant by the extension of the spring.
A spring has a spring constant of 40 N/m. When an unknown force is applied to the spring, the spring extends by 5 cm. Work out the force applied to the spring.
We can find the force applied to the spring by multiplying the spring constant by the extension of the spring.
The spring constant needs to be measured in Newtons per metre (N/m) and the extension needs to be measured in metres. The spring constant is in the correct units; the spring constant is 40 N/m. The extension is not currently in the correct units; the extension is 5 cm. There are 100 cm in 1 m, so we convert centimetres to metres by dividing by 100; this tells us that the extension in metres is 0.05 m (5 ÷ 100 = 0.05). We now sub the spring constant in as 40 N/m and the extension in as 0.05 m into the equation.
The force applied to the spring is 2 N.
Example 2
A 5 N force causes a spring to extend by 4 cm. Find the spring constant for this spring.
We find the calculation that we undertake to find the spring constant by covering up k in the formula triangle. When we do this, we see that we find the spring constant by dividing the force by the extension.
A 5 N force causes a spring to extend by 4 cm. Find the spring constant for this spring.
We find the calculation that we undertake to find the spring constant by covering up k in the formula triangle. When we do this, we see that we find the spring constant by dividing the force by the extension.
In the above calculation, the force needs to be in Newtons and the extension needs to be in metres. The question tells us that the force is 5 N, which is in the correct units. It also tells us that the extension of the spring is 4 cm, which is not in the correct units. We convert centimetres to metres by dividing by 100; this tells us that the extension is 0.04 metres (4 ÷ 100 = 0.04). We now have everything in the correct units; the force is 5 N and the extension is 0.04 m – we sub these values into the calculation.
Therefore, the spring constant is 125 N/m.