The EMF induced in the secondary is just the ratio of the number of turns so it's 400*1000/50 = 8000V. And you can calculate the flux using either the primary or secondary voltage since it will come out the same. We'll use the primary.
Assuming that 400V is the RMS voltage the voltage will be $V(t) = 400\sqrt{2} \sin( 100\pi t)$
If you have some object under tension then the tension is the same everywhere in the object, and the stress is the tension divided by the cross sectional area. So the stress would be lower in the large cylinder because it has a higher area.
@Aladdin but I don't get why the force at the end of the large cylinder is 54kN and the force at the end of the small cylinder is 45kN.
Does that mean the total force on the large cylinder is 54 + 45kN?
For the large cylinder AB there is a force of 45 kN because the force is transmitted through the small cylinder to the large cylinder. But there is an extra force being applied to the end of the large cylinder of 54 kN. So the total force on the large cylinder is 54 + 45 = 99 kN. Yes?
At a high enough stress these dislocations start to move through the metal and the metal starts to deform plastically. The stress at which the dislocations start to move is called the yield stress.
For steel the stress-strain curve actually shows a dip when the dislocations start to move, while the aluminium rod just shows a change of gradient. I'm not sure how significant this difference is.
Anyhow, as the dislocations move they start to tangle up with each other and get to the point where they can't move any more. As this happens the metal actually gets stronger. This process is known as work hardening. Here they've called it strain hardening but it's the same thing.
The final fall is when the metal starts to form a neck. What happens is the neck reduces the cross section area so once the neck forms the metal deforms plastically and snaps.
I don't know why steel shows an initial fall after the yield stress while aluminium doesn't.
I suspect that the vertical axis is actually recording force not stress.
The way you do these measurements is you put the rod into a machine that applies a strain increasing linearly with time and the machine measures the force. Then the force is converted to a stress by dividing it by the original cross sectional area of he rod.
But as the neck forms it reduces the cross sectional area of the rod and the calculation of the stress doesn't take this into account because it just divides the measured force by what is assumed to be a constant area.
I think the extensometer is a very sensitive length measurement and they use it in the early stages because up to the yield stress the length changes are very small. Once the metal has started yielding the length changes are a lot bigger and you no longer need a very accurate measurement.
And I guess the extensometer could get damaged when the rod breaks.
@JohnRennie what's difference between elastic limit and yield point
Elastic Limit: The maximum stress or force per unit area within a solid material that can arise before the onset of permanent deformation. In this diagram, 2nd point gives the elastic limit.
Yield Stress: A yield strength or yield point of a material is defned as the stress at which a material begins to deform plastically. Prior to the yield point the material will deform elastically and returns to its original shape when stress is removed
The elastic limit is the strain at which permanent deformation occurs i.e. up to the elastic limit if you remove the stress the metal will return to its original length.
Elastic Limit - the point upto which the wire reatins its original length after the force is withdrawn.
Yield Point - The point where there is a large permanent change in length with no extra load force.
These are how these two are defined in my A Level book and also stated by my teacher.
In W...
I think the way you analyse these diagrams is to start at the right end. The force at the right end is 120kN so the force on the right cylinder is 120 kN.
So we can calculate the extension of the right cylinder $\delta\ell = \sigma\ell/E$. The force is 120 kN so we divide by the area to get the stress then multiply by $\ell/E$ to give the extension.
Then we have to calculate $\delta\ell$ for the middle cylinder.
Now, the middle cylinder has the rightmost force of 120 kN acting on it, but there is an extra force of -180 kN i.e. a 180 kN force to the left. So the total force acting on the middle cylinder is a compressive force of -60 kN. Yes?
So again we calculate $\delta\ell = \sigma\ell/E$ with $\sigma = -60/A$ where $A$ is the area of the middle cylinder. This extension comes out negative because it's actually a compression. Add this to the extension we calculated for the right cylinder and we get the total extension of the two cylinders.
Finally for the left cylinder (AB) we have the -60 kN sum of the two right forces plus the extra +300 kN force exerted at B so the total force is +240 kN. Yes?
And you use this 240 kN force to calculate the extension of the AB cylinder. Add this to the two extensions we already calculated and you get the final result.
I'd have to go through the calculation to see if they have lost a factor of $10^3$ somewhere, but I feel little excitement at the thought of doing that.
I think what they are saying is that both metals have to extend by the same amount because they are fused into a single cylinder so $\delta_{cu} = \delta_{al} = \delta$
Elastic Limit - the point upto which the wire reatins its original length after the force is withdrawn.
Yield Point - The point where there is a large permanent change in length with no extra load force.
These are how these two are defined in my A Level book and also stated by my teacher.
In W...
