Plastic and Elastic Behaviour
A material can be stretched elastically or plastically.
ELASTIC DEFORMATION is when a material returns to it's original shape once the forces are removed.
- When the material is put under tension, the atoms are pulled apart from one another
- Atoms can move small distances relative to their equilibrium positions, without actually moving positions in the material.
- Once the force is removed, the atoms return to their equilibrium distance apart.
A metal obeying Hooke's law will stretch elastically.
PLASTIC DEFORMATION is when a material remains permanently stretched, even when the force is removed.
- Some atoms in the material move position relative to each other
- The atoms don't return to their original position when the force has been removed.
Stretching a metal past it's elastic limit will make it show plastic deformation.
Hooke's Law states that Extension (or change in length) is proportioanal to force.If a metal sire is supported at the top, and then a mass attached the the bottom, the mass pulls down with a force F, producing an equal and opposite force at the support. The extension of the wire is directly proportional to the load:
F=kΔx where k is a constant. k is called the stiffness constant.
Hooke's law also applies to springs. However, in any material Hooke's law only applies up to a certain point, called the limit of proportionality. After such limit, it stops being proportional. A little after the limit of proportionality is the elastic limit. After this point, the material will no longer exhibit elastic behaviour, and will start behaving plastically.
Calculating Stress and Strain
TENSILE STRESS = force / cross sectional area >>>> Stress = F/A It's measured in Nm-2 or Pascals (Pa)
TENSILE STRAIN = change in length / original length >>>> Strain = e/l Strain has no units - because it's meters / meters which gives 0. Its just a number.
Key features of a stress-strain graph are shown here. The only thing important that's not shown is Ultimate Tensile Stress. This is the maximum stress a material can withstand. Also note that after the Yield point the material begins to stretch without any extra load. (x axis = strain)
Elastic Strain Energy
When a material is stretched, work is done in stretching the material. This is called Elastic potential energy, or elastic strain energy. This is the energy stored in a stretched material. On a force extension graph, this is given as the area under the graph:
Work Done = F x s - but the force isn't constant, so we need an average - so 1/2 it >>>>E = 1/2Fe - because Hooke's Law is being obeyed, F = ke >>> E = 1/2ke2
The Young Modulus
Below the limit of proportionality, Stress divided by strain is a constant. this constant is called the YOUNG MODULUS, E. It can be found using the following equation:
E = Stress / Strain = (F/A)/(e/l) = (Fl) / (eA) The units are Pa, as for stress, as strain has no units.
You can also use a Stress-Strain graph to find E:
Gradient = Stress/Strain = E___Area under graph = Elastic Strain Energy per unit volume
Stress and Strain Experiment
Use a thin, long wire. The longer and thinner the wire, the more it extends to the same force. Start with the smallest mass necessary to straighten the wire
Measure the distance between the fixed end of the wire and the marker. This is the un-stretched length.
Increasing the mass causes the wire to stretch and the marker to move.
Terms to Describe the Behaviour of Solids
- BRITTLE materials break suddenly without deforming plastically
- DUCTILE materials can be deformed plastically using tensile forces without losing their strength, allowing them to be drawn into wires.
- MALLEABLE materials can be deformed plastically using compressive forces, allowing them to be hammered into shape.
- HARD materials are very resistant to cutting, indentation and abrasion.
- STIFF materials are very resistant to bending and stretching. Stiffness is measured in the Young Modulus; the higher the value, the stiffer it is. It can also be found in Hooke's Law F=ke, where k is the stiffness constant.
- TOUGH materials are very difficult to break. This is because they can absorb a lot of energy from an impact before breaking.
Fluids are made up of 'fluid elements' - groups of particles all moving in the same direction with the same speed. The path that a fluid element takes is called a flowline. When all elements on a flowline follow the same path, it is said to be stable.A stable flowline is called a stream line. There are two types of fluid flow:
- In LAMINAR FLOW the streamlines are parallel. This means that the velocity at any one point within the fluid remains constant. This type of flow normally occurs at slower speeds.
- In TURBULENT FLOW the flow lines are unstable. This means the velocity at any one point within the fluid varies. The fluid will often move around in mini whirlpools - or eddy currents, and this type of flow normally occurs at higher speeds.
The force of friction produced by a flowing fluid is called VISCOUS DRAG - the friction between the different layers and an object. Viscous drag is larger in turbulent flow. In a pipe, water towards the centre will be faster, because there is less friction from the sides.
Viscosity and Upthrust
Flow rate depends on VISCOSITY of the fluid. A more viscous fluid will have a slower flow rate, because the liquid is thicker.
Viscosity of the fluid depends on the temperature of the fluid. The viscosity of most fluids decreases as the temperature increases.
As we have seen viscous drag acts on objects moving through fluids; it doesn't just act between the streamlines. The force due to viscous drag on a spherical object can be found using stokes law:
F = 6πηrv where F = force, 6 = a number, π = 3.14, η = coefficient of viscosity, r = radius and v = velocity
Fluids exert UPTHRUST on immersed objects. This is caused by fluid pressure. The size of this force is equal to the weight of the the fluid displaced by the object. Also, by using what we know about density, we can say that the mass of the fluid displaced is equal to the volume of the object multiplied by the density of the fluid. By combining these 2 factors, we can find an equation for Upthrust....
(1) W = mg and (2) m = ρv >>> substitute (2) into (1) >>> W = Vρg