Materials and Density Flashcards
What is Hookes Law?
Extension is directly proportional to force until the limit of proportionality
What happens to the spring constant for two Identical springs in series
The spring constant would halve to allow for the extension to double as both springs would feel a force of mg pulling on the bottom of them, and the bottom spring would pull on the top spring
Describe the graph of a spring obeying hookes law until it’s breaking point
Force would be directly proportional to its extension up until the limit of proportionality, this is called the hookes law region, after this as the curve flattens the elastic limit is reached where the object will no longer form back to its original shape meaning it now behaves plastically and everything under this was behaving elastically. At the end there is the breaking point where the object will simply break due to the forces
What does it mean for an object to behave plastically?
After the point of the elastic limit where the spring will no longer go back to its start state, and so is permanently deformed
What does it mean for a material to behave elastically?
When the spring is able to return back to its original length, ie hasn’t gone past the elastic limit
What is the elastic limit?
The point at which beyond the spring will not follow the path back to its original length and so the rest length is > 0
What happens to two identical springs in parallel?
The extension would be halved as both springs have the spring constant of k so essentially the spring constant of the whole system is 2k and for F=ke to balance we need F=2k x e/2 so the half and two cancel
What does it mean for a material to be brittle?
It will have no plastic deformation and only a small plastic region before it breaks or shatters, meaning no flat region on the graph
What does it mean for a material to be ductile?
It will have a large plastic region before it breaks, meaning a large flat region on the graph
What does it mean for a material to be stiff?
It has a small extension when a load is put on it, meaning a very steep gradient on an F on x graph
What does it mean for a material to be strong?
It has a high ultimate stress meaning a lot of force is needed for extension to happen
What is the area under a force-extension graph?
The work done stretching the object
What is the definition of youngs modulus?
Ey = stress/strain where stress if force per unit cross-sectional area and strain is the ratio of extension to the original length
What effect does having a smaller cross-sectional area have on the stress of a material?
As stress = F/Ac meaning stress ∝ 1/Area, a smaller area would mean a higher stress
Why is the gradient of loading the same as the gradient of unloading on a force-extension graph
This is because youngs modulus is a constant value for any given material and the bonds between the atoms have not changed meaning the material still has the same stress/strain value
