⇒ Materials can be characterised by the properties they show when forces are applied to them

⇒ In 1678, Robert Hooke wrote about his discovery of elasticity

⇒ Hooke realised that the extension of some springs shows a linear region gor a range of applied forces

⇒ How mich a spring extends will also depend on the spring constant of the spring

⇒ A spring that extends a large amoung for a force of 1N is not as stiff as a spring that extends only a small amount for the same force

⇒ The spring constant, k, defines the stiffness of a spring as the force required for a unit extension of the spring

⇒ Using the simple equipment shown below, the spring constant of a spring can be measured

⇒ When the results from the experiment are plotted, the graph initially has a linear region, as seen above

⇒ Here the spring is still coiled and the extension is directly proportional to the load

⇒ The elastic limit of a material is the point below which the spring will return to its original length when the load is removed

⇒ The spring on the left is showing elastic deformation – above the elastic limit, the spring will be stretched out of shape and will not return to its original length

⇒ This is known as plastic deformation

⇒ If you want to learn about how to calculate the spring constant with springs in series and parallel, I highly recommend this video:

⇒ Nearly all materials show Hooke’s law behaviour up to a point

⇒ The applied force beyond which materials no longer obey Hooke’s law will be different for each material

⇒ Wires obey Hooke’s law because the bonds between the metal atoms act like springs

⇒ The dotted line on this graph represents the extension measured once the force is removed from the loaded wire

⇒ Some materials do not show plastic behaviour but are brittle and break when the elastic limit is exceeded

⇒ The way in which ductile and brittle materials fracture is also different

⇒ The exercise equipment shown here makes use of springs

⇒ The energy stored is eequal to the work done stretching the strings

⇒ The work done depends on the average force appliedand the extension of the springs: Work done = average force x extension

⇒ For a material that does not fully obey Hooke’s law, we can still calculate the elastic strain energy by calcuilating the are under the load-extension graph

⇒ For any graph, we can choose small echanges in the extension, δl, and calculate the work done by the load to produce that small extension. The total work done is then the sum of all these values:

⇒ This shows how this is doene for a simplified force-extension graph

⇒ For the second region of the graph, AB, the material no longer obey’s Hooke’s law

⇒ However, energy is still required to stretch the material, so work is still being done

⇒ The elastic strain energy stored is equivalent to the work done in stretching the material

⇒ When a material is stretched or compressed its elastic strain energy is altered

⇒ Below shows two common toys that make use of stored elastic strain energy…

The spring jumper toy is compressed by pushing the suction cup on to the stand. When the suction cup releases the toy ‘jumps’ to a height of 65cm. The toy has a mass of 16g. The spring is originally 3.6cm long, and is compressed to 0.9cm long.

Assuming that no energy is dissipated as heat and sound when the toy jumps, calculate:

⇒ The classic properties of some materials, such as rubber, can be complex

⇒ Initially, there is only a small amount of extension as the force is applied

⇒ Then, as more force is applied, the rubber band stretches easily

⇒ Finally, just before it breaks (which isn’t shown in the graph) it becomes harder to stretch again

⇒ The graph also shows that the extension for a given force is different when the rubber band is being loaded (top curve) or unloaded (bottom curve)

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