Materials

Materials

1. Springs and Hooke's law

   • Tensile and compressive forces
     • Force that produce extension are known as tensile forces
     • Forces that shorten an object are known as compressive froces
   • Hooke's law
     • The extension of the spring is directly proportional to the force appiled
       • This is only as long as the elastic limit of the spring hasn't been exceeded
     • F=kx
       • k is the force constant
         • Nm^-1
         • Can be determined by the gradient of the linear region of the force-extension graph
       • F is force
         • N
       • x is extension
         • m
     • Can be applied to any object
   • Investating Hooke's law
     • Need spring and some standard masses
     • Attach the spring at one end using a clamp, boss, and clamp stand secures to the bench using a G-clamp or a large mass
     • Set up a metre ruler with a precision of 1mm or better
     • Add masses to the spring and record the extension
     • Plot the data on a graph and the gradient is the force constant for the linear region

2. Elastic potential energy

   • When work is done on object stretching/ compressing it the energy is transferred into elastic potential energy which turns into kinetic energy once the force is taken away
   • Workdone and springs
     • When a material has work done on it as long as it is below the elastic limit the energy can be fully recovered
       • After the elastic point the energy can't be fully recovered
     • W=Fx
       • x
         • Extension
       • F
         • Force
       • W
         • Work done (energy)
     • The aarea under a force -extension graph=work done
   • E=1/2Fx
     • F=kx
     • E=1/2kx^2

3. Deforming materials

   • Bungee cords
     • Jumper falls at free fall (9.81ms^-2)
     • This stretches the cord and jumper slows down due to the tension
     • The elastic potential energy is then converted into GPE and KE as the jumper accelerates back upwards
   • Loading/ unloading
     • Polythene
       • Doesn't obey Hooke's law
       • They are very easy to stretch and suffer plastic deformation under relatively little force.
       • Shopping bags do not return to their original size after being stretched
       • Plastic deformation
         • Not a bad thing
         • Steel is pressed into car body parts, which must retain their new shape after manufacture
     • Rubber
       • Don't follow hooke's law at all
       • In the elastic region the rubber band will return to it's orginal length
       • The loading and unloading graphs are both curved and are different
       • The 'loop' formed by the graph is called a hysteresis loop
       • More work is done when stretching a rubber band than is done when its extension decreases again
         • Thermal energy is released when the material is loaded then unloaded, this is the hysteresis loop
     • Metal wire
       • Follows Hooke's law till the elastic limit
       • Beyond the elastic limit the unloading is the parallel to the loading graph but not equal to it
       • After elastic limit, the wire is permanently extended after the force is removed.
       • It suffers plastic deformation

4. Stress-strain, and the Young modulus (YM)

   • Stretching materials
     • Strain
       • Tensile strain is defined as the fractional change in the original length of the wire
       • = extension/ original length
       • • Change in l is symboled by x in the formula book
     • Stress
       • Tensile stress is defined as the force applied per unit cross-sectional area of the wire
       • = force/ cross-sectional area
       • =F/A
     • The extension of a wire will depend on the original length of the wire, diameter, the tension in the wire, and of the material of the wire.
       • There are two helpful terms for the behaviour of materials under tensile forces
         • Stress
         • Strain
   • Cobwebs
     • It is very elastic and it is as strong as steel but has one-sixth the density
     • A single strand of spider silk can be stretched up to 40% of its length before it breaks
   • Stress-strain graph
     • A ductile material can easily be drawn into a wire or hammered into thin sheets
     • The stress is directly proportional to the strain from the origin to the elastic limit
     • It follows Hooke's law
     • Plastic deformation is where the material extends rapidly.
     • Look at pg 93 figure 2 and below
     • A strong material is one with a high ultimate tensile strength
   • The Young modulus (E)
     • Stress is proportional to strain
       • YM is the ratio between stress and strain
     • =stress/strain
     • Nm^-2 or Pa
     • It is the gradient of the linear region of a stress-strain graph
     • The Ym is the same for a block of copper and a wire of copper
       • Depends on the material only not the shape or size
       • A material with a larger YM is stiffer than one with a smaller YM
   • Determining the YM of a wire
     • Set up equipment as shown
     • Have a wire os starting length greater than 1.00m is clamped securely at one end
     • Measure the diameter using a micrometer and work out the cross-sectional area of the wire
       • Make more accurate by repeating the measuring of the diameter at different points across the wire
     • Hang masses from the wire
       • Work out force from this by doing F=mg
       • Measure the extension
     • Record the length of the wire before masses are added
     • Plot a stress-strain graph and work out the YM

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