# A LEVEL PHYSICS Year 1 Stress and Strain

- Slides: 9

A LEVEL PHYSICS Year 1 Stress and Strain Review and Elastic Energy A* A B C Be able to calculate the elastic strain energy stored in a stretched material using the area under a force extension graph or the formula. Understand how energy is conserved in B/C Target A/A* Target EP EP AEP EP

If you increase the force past the elastic limit the material will become permanently stretched. Materials obey Hooke’s law up to the limit of proportionality/Hooke’s law limit. It is the point beyond which the force is not proportional to the extension. If a deformation is elastic the material returns to its original shape after all force is removed. Metal deformation is elastic when it obeys Hooke’s law. If a deformation is plastic the material is permanently deformed after all force is removed. Not just plastic materials! The atoms do not return to their original equilibrium position.

Tensile Stress Breaking Stress: A stress that is big enough to break the materials apart (tears the atoms apart from each other). Ultimate Tensile Stress: The maximum stress a material can withstand Tensile Strain

Elastic Strain Energy • Work has to be done to stretch a material. • Before the elastic limit all this work done is stored as potential energy. • This stored energy is called elastic strain energy.

Calculating energy stored Deriving the formula • The energy stored is equal to the work done. • W = F x d = (½ F) x ∆L The force is not constant so you need to take the average from 0 to F. • So the elastic strain energy is: E = ½ F ∆L • Because the material obeys Hooke’s Law (F = k∆L), F can be replaced in the equation. • E = ½ F ∆L = ½ k ∆L 2 In the exam you may be 2 asked to derive this • E = ½ k ∆L formula from the graph.

Conservation of Energy • When the stretching force is removed after an elastic deformation the stored energy is transferred to other forms (elastic band fires across a room). • If the deformation is plastic work is done to separate atoms therefore energy is not stored as strain energy, it is dissipated as heat. Gravitational potential energy In reality there is always some energy transferred as heat but you can usually ignore this in conservation calculations. Kinetic energy Elastic strain energy

Conservation of Energy • When the stretching force is removed after an elastic deformation the stored energy is transferred to other forms (elastic band fires across a room). • If the deformation is plastic work is done to separate atoms therefore energy is not stored as strain energy, it is dissipated as heat. Therefore, Change in kinetic energy = Change in potential energy Both elastic strain energy and gravitational potential energy

Energy Conservation in Transport Design (again) Modern cars must have crumple zones that deform plastically in a collision. The car’s kinetic energy goes into changing the shape of the vehicle, so less is transferred to passengers. In trains this has to be balanced with the fact that the driver has to sit at the front

Practice Questions • A/A*Target • Qs. 3 -6 Pg. 178 • Q. 1 & 2 Pg. 187 • B/C Target • Qs. 1 -6 Pg. 178 • Q. 1 Pg. 187