Chapter 6 Flashcards
What are compressive and tensile forces
Compressive forces are any pair of forces that shorten the length if an object
Tensile firces are any pair that extend them
Explain the graph of forces against extension for tensile forces (or compressive) acting ina spring
1) for a while, the force is proportional to the extension, under hooked law. This is until the PORPEOTIONAILKTY LINKT
2) past the properijanlity limit, the extension is no longer proportional. However until it reached the ELASTIC LIMIT, if the firces is removed, the spring will still deform elasticsllt and return back to Orginal length
3) once it reaches elastic limit and goes past this, any energy transferred here will be used to permantley alter arrangement of atoms and thus PLASTICALLG DEFORM the spring , energy is not retuned. Plastic deformation
Hooked law thus only applies to the propetijality limit
Hooked law
Here force is directly proportional to the extension, thus f= is, where k is the constant in the equation
K is known as the SPRING CONSTANT or stiffness in Nm-1
Where is K on force ere soon graoh and what does till you
Basics,ky force / ex = k so the GRADIENT is the spring vinstant in the proportional region
Springs with higher spring constant are more stiff, and thus need more force for same extension = this would look like a higher gradient on the graph !
What is proper word definition fir k
Why does this not hold forever and why can’t we jus say you need this much force extaclt to stretch it by like 10p0,
Spring constant is a measure of how much firce is needed ti extenedthe object by 1 m
In reality This doesn’t hold (as we see past proprtnisly limit), the l changes making it harder to stretch.
What happens to spring constant calculations with multiple springs in
- series
- parallel
1) in series
- in series it is EASIER TO PULL FOR THE SAME DISTANCE . This is because they are connected, so the same force is transmitted across BOTH springs, so basically they both extend a bit, making extension big
So the formula similar to resitsntce
1/ktot = 1/k1 + 1/k2
2) parallel
This is harder!
Makes sense, to pull one by 1m , gonna be harder to pull two by one meter , instead you’re gonna pull both by half if you apply the same force as before
Same as resistance in series, the total Ktot = k1 + k2
How to investigate spring constant in PAG
So abdiall Lamp everything does took cg
1) set up a clamp stand and a clamp , set with a SET SQUARE to ensure this is perpendicular
- ALSO SECURE TO BENCH USING CLAMPS for safety, and clamp a METER RULER TOO to measure
2) then attach a spring , and measure
3) now can add mass and record extension
Make sure you record at eye level to reduce systematic error
Repeat
Yh again when using hooked law what ssumptuon yiu make
Thst the object HASNT REVAHED THE PRORPTINALUTH LIMIT YET, FIR WHICH THE FORMUSLR STOPS WORKIGN SS SPRING FISNTSJT DHANGED
How is accuracy imorived in this experiment?
Using a set square and measuring t from eye level
What to remember for all this about compression too
That it follows all the same rule, elastic limits eberhtijfn
What happens to energy when extending snd when is it recovered or lsot
When you extend something until elastic linit, the energy is stired in the object, which can be returned when force is removed
However when you extended something past, not all energy can be received as some was used ti structurak,y alter the object in plastic deformation
Work done by spire gmoving?
This is known as elastic port is energy
And for this energy fan be reviverer
Work done = f x X
So area
Area = 1/2 fx
F=kx
So area = 1/2kx2
So what is wrong with the spring constants and why is there a better thing out there
Spring constant can be dependent on
- length, the longer it is, the easier it is to pull, so K is lower with length longer
- cross sectional area, if you make this bigger, then harder to pull, k is bigger for higher area
Basically k is clearly DHALE DEPENDENT, but you don’t want that, want something like rrsitivity which is independent ofmshape and size
What is tensile stress
Stress = the force / cross sectional area
So Nm-1
What is tensile strain
Strains = a ratio of new length to original length, extend / length
Has no units, is just a quantity
Extension is actual extension not new Lenten gtw
So what is young modulus and why is it good
Young modulus e= stress/ strain = FL/AX
What you’ve done here is basically if are and length is 1, then they have no effect and you still have a value for property of materials, different material still hold one
The units are NM-2,mor pa(?)
Bridge question for tensile bs compressive
Again the top of bridge is hsoterning si co prestige, bottom stretching so tensile
Explain stress strain graph for an alloy, and what is an alloy
An alloy is a material made from a combimantionif metals for benifits which can be different sized atoms ,
All we’ve done with graph is applied some constant and rescaled growth nothing changed
1) similar to first graph, stress is proportional to strain until proportionality limit= this means object obeys hooked law until here
2) from here to elastic limit, object still deforms elasticallg
3) past here it will deform plasticsllt = energy not recoverable
-so from here itsplasticsllt deforming whilst extending until it reaches a point , this is the first yield point Y1
- at this point, the atoms in the alloy (due to being different sizes) UNLOCK, and rapid acceleration is caused,
Thin about it, if accelerates quickly (like untiring a knot), then less force is needed to extend it, thus it DIPS in the force whilst extension still increases.
However like a knot in string, it LOCKS AGAIN , and at this point it is the second yield point y2
Note that this is tyOical for alloymliek steel bpmaybe nti be in Akku alloys
- from yield 2man increase in force is required to extend and plasticsllt keep on deforming . Normal and curved because not proportional
- this keeps happening until it reaches the UTS , ultimate tensile strength . This is a point where the material can take MAXIMUM FIRCE AND STRESS before it breaks
Thus a higher UTS means a stricter material
Past the UTS the process of breaking happens , here it may extend a bit more with less force in a process called necking (simialr ti like stretching blu tack it stretches a lot and thins for a bit), until you reach the BREAKING POINT, past this the Karteikarten break
Summary again and UTS ?
Ultimate tensile force, higher value for this means a material is more stronger
So does First Part the same, prosperously, elastic limit and then plasticsllt deforms
L- reaches a point where atoms unlock= y1, then rapid acceleration occurs making it easier to extend with less force, so it dips to y2, where atoms lock again
Then plastic continues, extension increases with FIRCE but curved because not proeptijal
Happens u til you reach UTS which si amd stress it can take befire breaking
Past this it may neck, where the thing thins and less force required for a bit more extension so dip
However finally itnrevshed breskig. Lost snd obkct snaps I half
How to calculate hound modulus from a stress strain graph
Again the gradient until proportionality limit
Why do we compare materials young modulus
A material with higher young modulus is stiffer than a lower one , which is dependent solely on material and not like thin or bit p
So thin copper and thick will have same young modulus! Useful in cimrdtructuon
How to calculate young modulus PAG
How to make it better
1) clamp a section if copper wire across a table stretching with two clamps on either side
2) run a control copper wire or to use to measure extension
3) make sure copper wire OBER PULLEY which minimises friction when extending
4) set up a berneirnfalliper here to measure small changes in extension
5) add masses of known and then measure extension
6) can then after REPEATS olotnforce /x , and manipulate egrsdient for E
Here measure dismayed using micrometer average and length with masre stick too!
Make it better
Ensure use pulley, vernier and micrometer
Tröste
Now what would stress strain graph look like for pure metal
What properere does this give a metal
Metal would be jus withiut any yield point s(because Atom size the same) and go to Usus and then thin and then breaks
This means a metal fan be MALLEABLE AND DUCTILE TOO
Loading vs u loading
Adding FIRCE = loading , removing force = unloading
These habe different curved !
As area in f x graph is energy, then area between them represents ENEERGY LOST DUE TO DEFORMATION , this is why both loading and unloading happen on same graoh
Loading unloading curve for a wire?
Remember it’s elastic limit not proportionality!
A wire loads and unloads the same for until the proprtinslith limit
But passed to ELASTIC limit the unloading is parallel to the loading but not the same
The final destination is also not at 0, the extension is oermeantlh deformed to new place
And the area in between= energy needed to deform object by the extension amount !
Rubber
What happens
Does it obey hooked law?
Does it plasticsllt deform?
What does area duow
For rubber it dint fillownhooked law
Loading and unloading follow a hysteresis loop
Essentially more work is done when deforming the loop then work when released
The difference ein area is nti deformation, it is the THERMAL ENERGY that it released
Rubber kinds remembers some energy when work is done to it, and releases it when force is removed as thermal
Deforms elasticallg but special
This to do with polymer property
As a result what will happen to the rubber
The rubber will be hot at the end due to thermal energy ti gave out
Polythene like shopping bags?
Not obey hooked law
Suffers plastic deformation, very easily o, very little energy is retuned, a lot of energy is used to deform, thus are a large and so is ectneison
Is plastic deformation always bad?
No m for example you want your car bumbers to plasticsllt deform instantly tonsbdibe impsctmsnd make it longer so change in momentum happens slower and less force felt , otherwise if it elasticallg drforme,d all the force would be felt by you snd bones broken lmaom
Stress train for brittle objects? Like glsss etc
They prorptinsly elssticlay extend until elastic limit, then they break,m and the amount fi extnsion very little (glsss
What is ENERGY TRANSFERRED IN A STRESS STRAIN GRAPH AND WHAT IS ENERGY DENSITY?
Energy transferred is the same for f x graph, you need to work out f and x and do 1/2 fx
But for energy density, this the area
Which represents 1/2 Fx/LA
= energy / volume
So it’s the amount of energy per metre cubed if materiaknsotred
Again need to see how to calculate energynins trees trains
Apparently justn@/2 fx again!
What changes velocity
A resultant force , as object remains at rest or constant until acted on by this
This can change
By speed.
or direction
Also for Newton’s third law what is important about the type of forces
The pair of forces will ALWAYS BE THE SAME TYPE
So gravity pulls us, we pull earth up by gravity
Normal with contact force etc
So firces can never act in the SAME OBJECT !!
What firces are there
Gravity electrostatic nuclear weka and strong
Every touch is exactly an electrostatic one
Why can’t we always use f=ma for like describing cars etc
Because the MASS IS IFTEN CHANGING WITH FUEL
Thus need to use f = change in momentum/time jbstead
Equation form momentum
Mass x velocity
Vectorm
Principle of conversation for momentum
ACRUAL DEFO
Total momentum is conserved, momentum at the start = momentum at the end
Sum of momentum = 0
For a susyemmofmimterwfrimf objects, the total momentum in a specific direction remains constant, so long as no additional force is acted upon them
So for closed system kn a direction momentum is constant
Gun bulkier make rum conserved?
At the start =0
When momentum changed, it still should end up 0
Bullet goes forward and so fun hsd ti recoil backwards to
How to invetsigatenmonetum in the lab, whatsbest equipment
Linear air tracks because this reduces resistive firces
Preferably use lighthwtesetc to capture accurately too
What makes a collision elastic vs inellastic
L
An e,as tic Cillia sn is one where the KE is 100% conserved .
- no KE is transferred to any other form other than the Ke of the object it’s colliding with
Here energy is still conserved
An inelasric collison is when not all of the KE is transferred to the object
- some is transferred to other stores like sound, doing work against resistance, thermal
- in reality this happens all the time
IN BOTH FASES HOWEVER ENERGY IS CONSERVED, KTS JUST KE IS NOT
Under what circumstance is A COLLISON ELASTIC, what must be constant
The MASSES must be the same bith time, or else there is no way the KE will be conserved after ,onetuj bevause of 1/mv2, the square causes problems
How can elastic collisions look like
Elastic vs inealsric
If you hit a ball, yiu stop moving and other starts moving
- if they hit each other and both STOP then always INELASRIC!!
- if they hit Esch other snd bounce back I guess elastic
What’s conserved in each situation
Momentum , total energy
Ke for elastic
Not for inelasrjc
Secondary law
Use good one from now on
Thrnrueirsjrnfirfrnof s Body is drei toy propetinslntonthe rwte of changes of momentum
Again why do we use this equation instead of f=ma
This accounts for changes in amss such as when going at the speed of light or when fuel depletes top
So what is the whole theory behind air bags and crash zones etc, what’s going on
When you crash yiu experience a crazy change of momentum in a short amount of time, so resultsnt force you wilk edpeifmcd is crazy and will break all your bones
So as a result , the crash bumbers and air bags are designed to INCREASE THE TIME it takes for you to chanhe your momentum
Thus leadimg to a lower resultant force
And so less damage hopefully
- examples include
- nswagbelt deforming
- bumpers
- airbag
- crash sines
When can you use f=ma
When constant force allows constant velocity
Whey is momentum always conserved !
Because whenever two bodies interest they extend = but oppsite firced
On the system net FIRCE is always 0, so that the change in momentum must be 0
This coming um always conserved due to Newton’s laws, good for uni me can’t lie
Hat is change in momentum if something REBOUNDS OFF A WALL
If it rebounds, then it comes back at negative velocity, thus it is -2inital !
- x -x =-2x
What is imoulse ?
What’s the idea behind this
Impulse is the product of FIRCE on an object multiplied by the time it spend extending kn ibject
Impulse is the same as rate of change if monetise
F= m/t
Ft= change momentum= impulse
2) idea is that in reality the FIRCE extered in sn object changed as itd extering on it, and this csn be any lauded using s FIRCE time graoh.
Here the are is = to its impulse and change in monentum
How to solve MOMENTUM IN TWO PLAMES CALCUALTIONS
What importsnt feature about momentum being conserved!
MOMENTUM IS CINSERVED IN ALL PLANES
So that means momentum before in x plane same as after
Momentum before in y olane = same as after
So if momentum in y was 0, then after it Idm
0!!
Is impulse conserved too!
YES!
Impulse is just Firce x time
So Newton third law say if I hit you I feel hit, force conserved
Time acting upon Esch other same
So if Impulse that , Impulse this way too!
And if momentum acts 90 to Esch other, what is final momentum?
As with vectors, Pythagorean!
