Chapter 6 Springs Flashcards
Compressive and tensile forces?
Compressive forces give rise to compression , tensile to extension
Describe the force / extension graph for a spring
When elastic or plastic ?
1) initially a straight line THROUGH ORIGIN to a point called proportionality limit
2) now I’d you extend beyond this to elastic limit , it won’t extend proportionally, but if you let go, it hasnt deformed yet - STILL ELASTIC DEFORMATION and will go back to 0
3) past the elastic limit, it will deform AND PLASTIC DEFORMATION
So hookes law applies only to the proportionality limit
What is hookes law and derrive equation
What is k? How find on graph
Force is directly proportional to extension until the proportional limit
so with a constant this becomes
F= KX
2) k is the gradient
Where k is the spring constant or force constant or stiffness
What is elastic deformation and plastic
Elastic = return to original length when force removed Plastic = permanent structural changed to the spring and does not return to original lemtbh
What is a definition for K
The amount of force needed to stretch by 1 meter
What happens to the spring constant with multiple springs in
- Parallele
- series
Importsnt
1) you add all the spring constants together = harder to pull
2) it is actually easier to extend if you have in series as Both springs experience the SAME FORCE so it is shared and essentially 1/2 needed
= so like resistance in Parallel, 1/ ktot = 1/ k1 + 1/k2 etc
How to investigate spring constsnts in pag and how to make experiment better
- attach spring to clamp boss clamp stand and secure to bench , and also clamp a meter ruler next to.
- add masses and see change of length
2) - use a set square to make COMPLETELY VERTICAL
- eye level reduce systematic parallax error
- repeats
What assumptions do you make when calculating potential forced
Thst the ELASTIC LIMIT , PROPORTIONALITY LIMIT NOT REACHED
Why is in series force constant halved and in parallel doubled?
Importsnt for series
In Series, the same force is Applied across BOTH SPRINGS , so both springs will extend each and total extension will be addition of both and that’s just double . Here, force is transmitted across both
- both springs extend each
2) in parallel the force is split equally amongst the springs. That’s why half the force given to each and they will both half extend , giving half extension
What happens to energy and extending , when can it be recovered and when lost
Energy can be recovered provided it doesn’t go past the elastic limit, if it does, then energy when let go won’t all be recovered as some was used to deform It as moving atoms into permanent new position
What about work done by a force to a extend something by a certain distance
Derrive all equations then for work done by spring / elastic potential energy
Just like before, work done = force x distance = force x extension
This is given by the area of the graph
WD= Area = 1/2 F X x
Now f = KX
So WD= 1/2 KX2 by substituting
What is tensile strain
Strain defined by the force applied per unit cross sectional area
= F/ m2 = Nm-2 or pa
What is tensile stress
This is a ratio between the new extension and the original length
X/L and has no units —> could be a percentage fraction etc
So what is Young’s modulus? Why do we need another property- can’t we use spring constant? (Essentially what’s wrong with spring constant (2))
Spring constant is dependent on two things
- increase length = reduce spring constant
- increase area = increase spring constant
= thus spring constant deadened on size but young modulus is not, it is a property Independenzen
What is Young’s modulus then actually
Equation
Units
A ratio between stress and strain Stress / strain Sigma / epision = FL/AX flax In Nm-2 or Pam
How young modulus Independent of area and length
If strain , x / l are both 1 then they are removed and you just have a property different for different materials
Need to clarify what are tensile forces and what are compressive
Tensile anything that causes to stretch (such as underside of bridge)
Compress is anything that causes to shorten (such as top of bridge ) question
Explain the whole stress strain graph from the first plastic limit , why do they dip rise etc
Think about a wire stretching and properties of an alloy
What is Uts
An alloy is a combination of metals of different sized atoms
- when increasing force from the elastic limit, the material plastically deforms but extends
- comes to a point where after enough force, the locking aspect of the alloy atoms UNLOCKS. DUE TO THIS UNLOCK, THE ATOMS accelerate as they slip past each other = Y1
- think about it, if they accelerate, it requires less force to cause that extension. They accelerate for a bit until they lock again . = Y2
- from Y2 they plastically deform like normal, increase f increase x but at a curved rate as not proportional . This happens until UTS
- UTS is the point where a material takes maximum stress before it starts to break, thus a material with higher UTS = stronger material
- past the UTS it starts to dip again, this is called necking and basically wire just extending easily and becoming thinner (think of play doh when strech, it thins fro a bit before snapping)
As a result the force applied to cause extension decreases, so that’s by there is a dip
Finally you reach breaking point, here the object will snap….
Again what is UTS and what makes a material stronger than another
UTS is the maximum stress a material can take before it starts to break.
As a result a more strong material has higher UTS
Summary graph very brief
- stress strain Hooke law proportional to proportionality limit
- then elastic deform still not proportionally to elastic limit
- now plastically deforms until Y1
- but then drops due to unlocking acceleration to y2
- then locks again y2 so past this plastically deform again until UTS
- after UTS necking, reach breaking point and snap
How to calculate young modulus from a graph of stress vs strain
Stress proportional to strain until proportionality limit , here stress / strain = gradient = young modulus .
What do you get by comparing young modulus of other materials
Why do we use young modulus to do this- what special about it
The more young modulus, the more stiffer it is. Here we just using advanced form of spring constant that does NOT BE AFFECTED BY AREA OR LENGTH, just a property
Therefore a thin or thick copper wire will have the same young modulus !
How to calculate young modulus of a wire in a lab (PAG)
How to make pag better
- set up two wire to be stretched over a table using clamps at both sides . Here run it over A PULLEY TO MINIMISE THE FRICTION
- then set up a vernier calliper to measure the slight extension on the other side
- add Mass known quantity and measure extension,
- now plot graph f against x and find gradient
- if you know Orginal length and used micrometer to find diameter average , then can manipulate gradient to find E
2) use repeats and pulley
What is stress strain graph for just pure metal
Same as alloy without dip
What is loading and unloading?
Then what are loading and unloading curves and why are they plotted on same graph
Adding force and removing force
2) this is just the graph to show extension when loading snd unloading, they plotted because they might not be the same each time …
How does loading unloading look like for a wire
This is after elastic limit the loading returns and wire is left slightly extended
Unloading is parallel but thus not same, with area in middle the energy needed to plastically extend it
Loading unloading for rubber?
What’s going on? How are lines still different but return to same ?
- what is area
What is this graph called
Doesnt follow hookes law, yet when you release force, it returns back to its Orginal length = ELASTIC DEFORMATION
- but loading and unloading are still different, more work is done by force to extend it then when it de extends ?
- basically thermal energy is released when the Material is loaded and then unloaded. It kind of stored energy until unloading , does it right at the end.
- this energy released is shown by the area
- to do with polymer propertied
This is a hysteresis loop
Polystyrene load unload?
It takes little force to stretch and they suffer plastic deformation straight away, and so final return is further than initial = shows plastic deformation
Is plastic deformation always a bad thing?
No for example steel being shaped in car needs to retain its plastic deformed shape so we can use it etc
What about the stress strain for brittle materials like glass and cast iron?
These show proportional elastic extension until its breaking point - they never plastically deform, elastic and then snap
Final summary on all materials in chapter
- ductile metal, pure metal
- metal wire load vs unload
- polymers : rubber load vs unload , polythene
- brittle materials stress vs strain
- ductile dips when unlock and dips after UTS due to neck and the. Breaks
- pure metal does same thing except first dip
- metal wire unloads parallel but shows the permanent extension plastic
- rubber takes more work to extends vs when under ending, this let out as thermal (stores energy)
- polythene just deforms hella fast , shown by final extension different to initial
- brittle materials will extend elasticsllt snd break = never plastic
IMPORTANT WHAT IS STRAIN DENSITY AND HOW TO FIND ENERGY OF STRESS STRAIN
Energy =1/2 fx
Area = strain density which is amount of energy per m-3
Why in a wire when deform is grsdient still the same ?
Because of extension the force before are still identical between the binds
