Module 3.4 - Hooke's law ✓ Flashcards
State Hooke’s law?
The force applied to a spring is directly proportional to the extension of the spring provided the elastic limit is not exceeded
What is the Hooke’s law equation?
F = Kx
What is the limit of proportionality (P)?
The limit of proportionality is the point at which a material stops obeying Hooke’s law, but will still return to its original shape if the stress is removed
What is the elastic limit (E)?
The elastic limit is the point at which, if exceeded, a material starts to behave plastically (will be permanently stretched).
How do you combine force constants of springs in series?
1/Kt = 1/K1 + 1/K2
How do you combine the force constants of springs in parallel?
Kt = K1 + K2
Explain elastic deformation (in terms of the atoms in the material)?
1) When the material is under tension, its atoms are pulled apart from one another
2) Atoms can move slightly relative to their equilibrium positions, without changing position in the material
3) Once load is removed, the atoms return to their equilibrium distance apart
Explain plastic deformation (in terms of atoms in the material)?
Some atoms in the material move relative to one another, so when the load is removed the atoms don’t return to their original positions
What is Tensile stress?
Tensile stress - the force applied per unit cross-sectional area
What is the equation for tensile stress?
σ = F/A stress = force / cross-sectional area
What is stress measured in?
Pascals (Pa). or newtons per square metre (Nm^-2)
What is tensile strain?
Tensile strain - The extension per unit length of a material`
What is the equation for tensile strain?
ɛ = x/l strain = extension/original length
What are the units for tensile strain?
No units :)
What is breaking stress (B)?
Breaking stress is the stress at which a material breaks.
What happens at the breaking stress point B?
Eventually the atoms in the material are pulled so far apart that they separate completely and the material breaks.
What is the Ultimate Tensile Stress (UTS) of as material?
Ultimate Tensile Stress - The maximum stress that a stretched material can withstand before breaking
How do you find work done to deform a stretched/compressed material?
Work done to deform a material is the area under the force/extension graph.
NOT the same as F*x. It’s actually W = ½Fx
How is energy transferred when work is done to stretch a material?
Before the elastic limit, work done is stored as elastic potential energy in the material (except for rubber)
Therefore area under force-extension graph = EPE
What is the equation for elastic potential energy for an extended/compressed material?
E = ½Kx^2 E = ½Fx
Derive the equation E=½kx^2
1) W = Fx, however the force on a material being stretched isn’t constant so you need to use the average force applied between 0 and F (i.e. ½F). So W = ½Fx
2) Therefore EPE, E = ½Fx
3) Because Hooke’s law is being obeyed (before limit of proportionality) then F = kx. So E=½kx^2
What is the Young’s modulus of a material?
Young’s modulus - A measure of the stiffness of a material. The ability of a material to withstand changes in length under tension/compression
What is the equation for the Young’s modulus?
Young’s modulus = stress/strain
E = σ/ɛ
What are the units for Young’s modulus?
Pascals or Newtons per square metre (Pa/Nm^-2)
How do you calculate the elastic potential energy per unit volume from a stress/strain graph?
The elastic potential energy per unit volume for a material is the area under the material’s stress strain graph
What is the equation for elastic potential energy per unit volume?
Energy per unit volume = ½σɛ
PROVIDED HOOKE’S LAW IS OBEYED
What is the Yield point Y of a material?
Yield Point - The stress at which a large amount of plastic deformation will take place without any extra load
What does the graph for a ductile material look like?
E.g. a metal wire. It has ALL ZE POINTS
P, E, Y1 (yield point), Y2(lowest point after yield point), UTS, B
What happens after the yield point?
Beyond the yield point, at y2, a small increase in stress causes a large increase in strain. The wire undergoes ‘plastic flow’
What does the stress-strain graph for a brittle material look like?
It has a limit of proportionality then a breaking point soon after. It DOES NOT undergo plastic deformation.
Why do brittle materials have no elastic limit?
When stress is applied to a brittle material, tiny cracks at the material’s surface get bigger and bigger until the material breaks completely. < Called brittle fracture!
What is the difference between a stiff and strong material?
Stronger materials have higher breaking stresses, however stiffer material will have lower strain. A strong and stiff material will have high breaking stress but low strain, whereas a weak and less stiff will have a low breaking stress but a large strain.
Why do different polymeric materials have different stress-strain graphs?
The molecules making up polymeric materials are arranged in long chains which have a range of properties so different polymers have different stress-strain graphs.
What is the stress-strain graph for polythene?
Look in book because hard to describe
What type of material is polyethene?
Polyethene is a ductile material despite behaving plastically when stretched
How does rubber behaved when stretched?
Rubber behaves elastically, returning to its original length when the load is removed
Explain why the loading and unloading curves for rubber are different?
Some of the elastic potential energy stored in stretched rubber is converted to heat, meaning the energy released when the rubber is unloaded is less than the work done to load/stretch it.
What does the area between the loading and unloading stress-strain curves for rubber give you?
The amount of energy converted to heat per unit volume is given by the area between the loading and unloading curves
