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Module 3 - Chapter 6 - Materials I - Coggle Diagram
Module 3 - Chapter 6 - Materials I
Hooke's law
Tensile deformation - force that extends a material
Compressive deformation - force that compresses a material
Force extension graph is a straight line from the origin up until the elastic limit
Spring undergoes elastic deformation up until the elastic limit, when the force is removed, it returns to its original shape/ length
Beyond elastic limit, spring undergoes plastic deformation, permanent structural changes to the spring occur, doesn't return to original shape when force is removed
For forces less than elastic limit, spring obeys Hooke's law
Force applied is directly proportional to the extension up to the elastic limit
K = force constant. Measure the stiffness of a spring
Spring with large constant is difficult to extend
Investigation
Attach the spring at one end using clamp, boss and clamp stand
Set up a metre rule (1mm resolution)
Suspend masses from the spring and after adding one, record the total mass added and new length
Accuracy
Measure length using set square
Take readings at eye level to reduce parallax errors
Measure mass of each slotted mass using digital balance
Draw a graph of force against extension and find the gradent of the straight section
Elastic potential energy
Work done and springs
When a material is stretched without going beyond its elastic limit, work done on the material can be recovered
Work done on a material goes into moving atoms to new permanent position when a material goes through plastic deformation, not recoverable
Area under a force extension graph = work done
Work done on a spring is transferred to elastic potential energy within the spring
Work done to an extensible object is transferred into stored energy in the band
Derivation
E = Area under graph = area of shaded triangle
Substitute Hooke's law into equation
E is directly proportional to e^2, doubling extension, quadruples energy stored
Deforming materials
Bungee cords
Jumper free falls, slack is taken up and cord stretched, jumper slows to a halt
EPE is converted into KE and GPE
Jumper accelerates upwards again
Loading and unloading
Loading and unloading curve might not be the same
Metal wire
Unloading graph will be identical for forces less than the elastic limit
Beyond the leatic limit, it is parallel to the loading graph
Wire is permanently extended after force is removed
Rubber
Rubber bands don't obey Hooke's law
Rubber band returns to original length after forces is removed, but loading and unloading graphs are curves and different
Hysteresis loop - more work is done when stretching a rubber band tha is done when its extension decrease again
Thermal energy is released when material is loaded then unloaded
Polythene
Polythene strip doesn't obey Hooke's law
Thin strips of polythene are very easy to stretch and suffer plastic deformation under relatively little force
Shopping bags made from polythene don't return to their original size after being stretched
Warming up
Rubber is made from squashed and tangled long-chain molecules
Once straightened, they require large force to extend
Rubbish is poor at storing energy
Basics
Forces that act away from the centre of the spring in both direction stretch it out
Forces that act towards the centre of the spring in both direction are called compressive forces and shorten the object
