materials Flashcards
What is the equation for density?
density = mass / volume
What is “Hooke’s Law”?
Hooke’s law states: the force required to stretch a material is directly proportional to the extension, up to the limit of proportionality
This means that below the limit of proportionality we have
𝐹=𝑘∆𝐿
where 𝑘 is the stiffness, measured in N m^(−1)
What is meant by the “elastic limit” (in the context of springs)?
The maximum extension caused by a force where the spring will return to its orginal length when the force is removed - Largest extension in which deformation is still elastic
Elastic Deformation
material returns to its original shape when force is removed
Plastic Deformation
material does not return to its original shape when force removed
Limit of proportionality
Largest extension at which Hooke’s law applies
Permanent deformation:
change in shape that remains after force removed
How do you calculate the elastic strain energy of a spring? When can you not use these equations?
The work done when stretching a material is given by the area under its force-extension graph
If the deformation is elastic, this work is stored as elastic potential energy
If the material follows Hooke’s law the area is a triangle, and we have
Why is the initial energy stored in the spring greater than 2.2 J?
As work is also done against friction in moving the block
Describe the energy changes that occur as the bungee jumper fall to the lowest point.
The bungee cord has an unstretched length of 25m.
Point Q represents the point where the forces are in equilibrium
Assume there is no air resistance
The gravitational store of energy decreases
The elastic store of energy remains zero until point P and then increases between P and R
The kinetic store of energy increases from zero to a maximum at point Q and then decreases to zero at R
At which point will the bungee jumper be travelling fastest? Why?
P is the point at which the bungee begins to extend
Q is where the bungee jumper ultimately comes to rest
R is the lowest point the bungee jumper reaches
They are fastest at point Q
The resultant force on the jumper always acts downward until point Q so they accelerating downward until that point. Beyond point Q the resultant force acts upwards causing the speed of the bungee jumper to reduce.
A student thinks that the bungee jumper first comes to a stop when the tension in the bungee cord is equal to their weight. Explain why they are wrong.
When the tension in the cord becomes equal to the weight of the bungee jumper they are still moving down and so the tension continues to increase.
As the tension is now greater than the weight the resultant force on the bungee jumper now acts upwards causing the speed of the bungee jumper to decrease as they continue to fall.
The bungee jumper will first come to a stop when the tension is greater than their weight.
The graph below shows the extension of a rubber band as it is loaded and unloaded. What does it tell you about the work done done by the load when the rubber band extends compared to the work done by the rubber band as it returns to its orginal length?
More word is done by the load to extend the rubber band than is done by the rubber band as it returns to its original length. This is because some of the work done by the load increases the internal store of energy of the rubber band (as well as the elastic store of energy)
Springs in series
Springs in series have the same force and their extensions add together
1/𝑘_𝑇 = 1/𝑘_1 + 1/𝑘_2
Springs in parallel
Springs in parallel have the same extension and their forces add together
𝑘_𝑇 = 𝑘_1 + 𝑘_2
What is meant by “tensile stress”?
Tensile stress = tensile force (tension) / cross-sectional area
stress=𝜎=𝐹/𝐴
What is meant by “tensile strain”?
Extension / original length
strain = 𝜖 = ∆𝐿 / 𝐿
What is meant by “breaking stress”?
The maximum stress (force per unit area) a material can stand before it fractures
What is meant by brittle behaviour?
A material that breaks without exhibiting plastic behaviour (or exhibiting very little)
What is meant by plastic behaviour?
Permanent deformation/ extension (i.e. does not return to original length when the load is removed)
Stress-Strain Graphs: Linear Region
The gradient of the linear portion of a stress-strain graph is the measures the stiffness of the material
The area under the stress strain curve is the work done per unit volume, for the linear section:
