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Physics A level revision resource: Introduction to Young's Modulus

One of the most important tests in engineering is knowing when an object or material will bend or break, and the property that tells us this is the Young’s modulus. It is a measure how easily a material stretches and deforms.

Will it bend or will it break?

Wires obey Hooke’s law, just like springs do. When a force F is applied, it will extend some distance x, which can simply be described by the equation F = kx

Whereas k for a spring is the spring constant, the amount of extension for a wire depends on its cross sectional area, length, and the material it is made from. The Young’s modulus (E) is a property of the material that tells us how easily it can stretch and deform and is defined as the ratio of tensile stress (σ) to tensile strain (ε). Where stress is the amount of force applied per unit area (σ = F/A) and strain is extension per unit length (ε = dl/l).

Since the force F = mg, we can obtain the Young’s modulus of a wire by measuring the change in length (dl) as weights of mass m are applied (assuming g = 9.81 metres per second squared).

The equation for youngs modulus
A woman in a science lab
Is Young's modulus relevant to research?

What are the key things to know?

For different types of materials, the stress-strain plots can look very different. Brittle materials tend to be very strong because they can withstand a lot of stress, they don’t stretch very much and will break suddenly. Ductile materials have a larger elastic region where the stress-strain relationship is linear, but at the first turnover (the elastic limit), the linearity breaks down and the material can no longer return to its original form. The second peak, is the ultimate tensile strength and it tells us the maximum stress a material can withstand before breaking. Plastic materials are not very strong but can withstand a lot of strain. Young's modulus is given by the gradient of the line in a stress-strain plot.

A graph showing stress against strain

In the experiment in the video above, we measured the Young’s modulus of some copper wire which does not extend very much. So a fiducial marker such as some tape can be used to help identify the original and extended lengths. Making multiple measurements with a variety of masses will increase the number of points on the stress-strain plot and make the calculation of Young's modulus more reliable. Another thing to take care of is measuring the cross-sectional area of the wire. Imperfections of the wire may mean that the diameter is not perfectly constant along its length, so taking the mean of several readings with the micrometer could help.

How is this applicable to me?

Studying of the mechanical properties of materials is important because it helps us understand how materials behave, and allows us to develop new products and improve existing ones. One example research topic at Birmingham looked at developing vaulting poles used by high jump athletes to maximise performance. These poles need to be light to allow a fast run-up, but also must be able to store elastic strain energy as the pole bends. The pole has to convert elastic energy to kinetic energy as the pole straightens out, and be able to withstand the stress caused by the weight of the vaulter - and withstand repeated uses by the athlete.

An athlete doing the high jump mid air on a cloudy day

On small scales, there are many products that contain biological (e.g. pharmaceutical drugs, fertility treatments, tissue engineering) and non-biological microparticles (e.g. chemicals, agriculture, household care). Through understanding their mechanical properties we can predict their behaviour in manufacturing and processing, maximise their performance capabilities.

The Young's modulus of a material is a useful property to know in order to predict the behaviour of the material when subjected to a force. This is important for almost everything around us, from buildings, to bridges to vehicles and more.