4.2 Flashcards
What is Hooke’s law?
The extension of the material is directly proportional to the applied force
(load) up to the limit of proportionality
What happens to a spring when it is stretched beyond its elastic limit?
doesn’t regain its initial length when the force applied is removed
What is the area underneath a force-extension graph equal to?
Strain energy (as work done = force x distance)
What is the breaking stress of a material?
The maximum stress it can withstand without fracture
On a stress-strain graph showing a stiff and a flexible material, which material has the line with the steepest gradient?
The stiff material
What are materials that permanently deform described as?
Plastic
What two words can plastic materials also be described as?
- ductile - can be drawn into wires
- malleable - they can be hammered into sheets
Describe the force-extension graph of a metal wire.
- loading - the line starts straight, and curves as it surpasses the limit of elasticity
- unloading - the line doesn’t come back along the same line as when loading
- difference between loading and unloading lines = permanent extension of wire
Describe the force-extension graph of a rubber band.
- loading - the line is curved
- unloading - the line is curved, but doesn’t follow the same curve as the loading line
- unloading line finishes at the origin - rubber returns to its original shape
What is the opposite of a tough material?
A brittle material
What happens when you try to deform a malleable material e.g. lead?
It deforms plastically - gives way gradually, absorbing a lot of energy before it snaps
Do brittle materials deform plastically?
No
What is the Young Modulus measured in?
Nm⁻² or Pa
What is work done per unit length measured in?
Jm⁻³
On a force-extension graph, what does it mean if the area of the unloading graph is smaller than that of the loading graph?
Some energy has been transferred
What is the reason for energy transference on a force-extension graph?
Some energy stored in the object (e.g. rubber band) becomes the internal energy of the molecules when the rubber band unstretches
On a force-extension graph, what does the area between the loading and unloading curve represent?
Difference between energy stored in the object when it is stretched and the useful energy recovered from it when it is unstretched
Brief explanation of experiment to find the Young Modulus of a wire?
- stress → wire with mass attached - measure mass using top-pan balance and use W=mg. measure diameter of wire using micrometer, then calculate area
- then stress = F/A
- strain → measure extension by measuring distance marker moves from original position, and length of wire. calculate strain
- vary mass for range of values - plot stress-strain graph
How to improve accuracy in the experiment to calculate the Young Modulus of a wire?
- use long thin wire and heavier weights → greater Δl so smaller % uncertainty
- measure diameter accurately using micrometer
- measure wire by holding ruler as close to the wire as possible
What types of forces does Hooke’s law work for?
- Tensile (stretching)
- Compressive
How is Hooke’s law illustrated on a graph?
- Graph of force (y) against extension (x)
- Gradient of straight part is the value of k
What is the limit of proportionality on a force-extension graph?
- The point at which the line starts to curve
- Hooke’s law works up to this point
What do X and Y represent?
- Area X is the work done in heating the rubber (or the increase in thermal energy)
- Area Y is the work done by the rubber when it is returned to its original shape
- Area X + Y represents the work done in stretching the rubber band originally
Describe elastic deformation in terms of atoms.
1) Under tension, the atoms in the material are pulled apart.
2) They move short distances relative to their equilibrium positions without changing positions in the material.
3) Once load is removed, atoms can return to their equilibrium distances apart.
Describe plastic deformation in terms of atoms.
1) Certain atoms move position relative to one another.
2) 2) When the load is removed, the atoms don’t return to their equilibrium position.
Describe the energy transfers when an object is deformed elastically.
- All the work done to stretch is stored as elastic strain energy
- When the force is removed, the stored energy is transferred to other forms (e.g. kinetic energy)
Describe the energy transfers when an object is stretched plastically.
- The work done to separate atoms is not stored
- It is mostly dissipated (e.g. as heat)
On a stress-strain graph, where is the breaking stress?
At the end of the line.
How can you find the (elastic strain) energy from a force-extension graph?
- It is the area under the straight part of the line.
The energy stored in a material by stretching it is equal to…
…the work done in stretching it.
What happens to a vertical spring when it has a mass suspended vertically?
It stretches
For vertical spring which has a mass suspended vertically, what is stored as it is stretched?
Elastic strain energy
What does a stress strain graph look like for brittle, ductile and polymeric materials?
Brittle: High UTS, low strain (doesn’t move much before it breaks)
Ductile: Curved after elastic limit (region of plastic deformation)
Polymeric: Small force (and stress) but long extension (and strain)
How do you find Young modulus from a stess-strain graph?
Gradient of line
Outline the energy charges that occur when a spring fixed at the top is pulled down and released
The work done in pulling the spring down is stored as elastic strain energy, when the spring is released this is converted to kinetic energy which is converted to gravitational potential energy as spring rises
How is the dissipation of energy in plastic deformation used to design safer vehicles.
- crumple zones plastically in a crash using the car’s kinetic energy so less is transferred to the passengers
- seat belts stretch to convert the passenger’s kinetic energy into elastic strain energy.
What is density defined as?
A substance’s mass per unit volume
Method for finding density of a regular solid?
- ruler - measure width, length and height
- top-pan balance - measure mass
- use ρ = m/v
Method for finding density of an irregular solid?
- top-pan balance - measure mass
- use a eureka can to measure water displaced by object
- volume of water = volume of object
- use ρ = m/v
What type of force is acting when a spring is squashed?
Compressive
What type of force is acting when a spring is lengthened?
Tensile
In materials, what does the stiffness depend on?
Material, length and cross-sectional area
What is the definition of stress on a material?
The force acting per unit cross sectional area
What is stress measured in?
pascals (Pa)
What can breaking stress also be referred to as?
Ultimate tensile stress
What is strain defined as?
The extension produced per unit length
What is strain measured in?
Has no units
What does the gradient represent on force-extension and stress-strain graphs?
- force-extension → spring constant (Nm⁻¹)
- stress-strain → Young Modulus, E (Nm⁻² or Pa)
Describe the forces acting on a metal wire being stretched by a load.
- Load pulls down on the end of the wire with force F
- Support pulls up on the top of the wire with an equal reaction force R
- F = R
What things obey Hooke’s law?
- Springs
- Metal wires
- Most other materials
(Up to a point!)
How do you investigate extension?
Support the object being tested (the spring) from above with a clamp.
Measure it’s original length with a ruler - use a set square to make sure the ruler is parallel with the stand.
Add weights one at a time to the end of the object (the spring).
After each weight is added find new length then do: New length - original length = extension.
Make sure you can add a good number of weights before the object breaks to get a good picture of force-extension.
Plot a graph of load-extension.
On a stress-strain graph, where is the ultimate tensile stress?
For vertical spring which has a mass suspended vertically, what happens to the elastic strain energy when the end of the spring is with the mass is released from suspension?
Elastic Strain energy converts to kinetic energy (as the spring contracts) and gravitational potential energy (as the mass gains height).
The spring begins to compress and the kinetic energy is transferred back to stored elastic strain energy.
What is the equation for the overall spring constant in parallel
k(T) = k(1) + k(2)
What is the equation for total spring constant in series?
1/k(T) = 1/k(1) + 1/k(2)
What happens if you have two identical springs in parallel and 1 spring below in series experiencing a force?
Group the top springs together and think of them as 1 big spring : kT = k1 + k2 = 2k.
There are now two springs in series: use the equation:
Are strain and stress on a material proportional?
Only up to the limit of proportionality.
Name some ways in which the experiment to find the Young modulus of a wire is made more accurate.
- Using a long, thin wire -> Reduces uncertainty
- Taking several diameter readings and finding an average
- Using a thin marker on the wire
- Looking directly at the marker and ruler when measuring extension
On a stress-strain graph, what does the area under the straight part of the line represent?
- The strain energy stored per unit volume.
* i.e. The energy stored per 1m³ of wire
Describe a typical stress-strain graph for a DUCTILE material being stretched, with all the important points.
- Straight line up until the limit of proportionality.
- Curves towards the x-axis slightly until the elastic limit
- Curves more towards the x-axis until the yield point
- After yield point, the line goes down slightly
- There may be a second peak before the breaking stress
- The UTS is the highest stress reached, usually on the second peak
On a force-extension and stress-strain graph, what do the gradient and area under the line give?
FORCE-EXTENSION:
* Gradient = Spring constant (k)
* Area under line = Work done (or elastic energy stored)
STRESS-STRAIN:
* Gradient = Young modulus
* Area under line = Elastic energy stored per unit volume
What are the units for elastic strain energy stored per unit volume?
J/m³
What is the yield point on a stress-strain graph? (2)
- The point beyond which the material starts to stretch without any extra load.
- It is the stress at which a large amount of plastic deformation occurs with constant or reduced load
Will a material return to it’s original size and shape if it goes past it’s limit of proportionality?
Yes
Will a material return to it’s original size and shape after it goes past it’s elastic limit?
no
Give the equation for the Young modulus.
E = Stress / Strain
E = (F x L) / (A x ΔL)
Where:
F = Force (N)
A = Cross-sectional area (m²)
L = Original length (m)
ΔL = Extension (m)
