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I have a problem: A typical compartment domestic refrigerator with freezer can be represented by 3 temperature reservoirs connected to the cyclic device which absorbs W' of work. - cool box at Tc = +279K from which Q'c heat is extracted - freezer at Tf = -269k from which a further Q'f...

Ah yes i think I have a solution to this problem now using the general formula for plane stresses. There is a second part to the question where it now asks to find the angle which the maximum stresses make with the direction sigma(x)? Does this involve the 2D Mohr Circle?

Principal stresses help please? I am looking through past paper examinations and have come a across a question: At a certain critical point in a stressed component, calculations show that the stresses are sigma(x) = 220MPa sigma(y) = -95MPa and shear = 60MPa Find the maximum and minimum...

Current against slip relationship of induction machine?? Please could someone explain to me the relationship between the current and the slip value of an induction machine. I have plotted a graph and I am wondering how to interpret this? Thankyou.

Im just looking through examples of finding the Fourier coefficients. in one particular example bn is found to be = (-1/npi) (cosnpi - cos 0) then it says this is 0 when n is even and 2/npi when n is odd are we just substituting values of n e.g. 1,2,3... to find this result? i...

The function f(x) 1, -pi < x < 0 0, 0 < x < pi now after sketching the function i believe i am correct in saying it is neither symmetrical about the x-axis or the origin and therefore is neither odd nor even? It is a square wave? Am...

to find the sum of a Fourier series...? My problem is: I must find the sum of ((-1)^(n+1))/2n-1 between infinity and n=1. I have looked in all my available textbooks for a clear example but I am still unsure as to how i should approach the problem? Help with this would be much...

I have to differentiate (e^-x) ((1-x)^1/2) twice: The first time i differentiate i get (-e^-x) ((1-x)^1/2) + (e^-x) ((1-x)^-1/2) (-1/2) then differentiating this i get [(e^-x) ((1-x)^1/2)] - [(e^-x) ((1-x)^-1/2) (-1/2)] + [(-1/2e^-x) (1/2(1-x)^3/2) + ((1-x)^-1/2) (1/2e^-x)] are...

I have to differentiate (e^-x) ((1-x)^1/2) my answer is: (-e^-x) ((1-x)^1/2) + (e^-x)/((-1/2 + 1/2x)^-1/2)) is this correct? thankyou

table leg design... Suppose i want to make 4 table legs from aluminium square tube...how should I go about designing the dimensions of the square tube? The table itself needs to support a load of 90kg through the four legs. Help on this would be very much appreciated. Cabellos

aluminium framework... I am designing an aluminium frame bed. I have desided to use aluminium extrusion either square or rectangular shape to form the main 4 bars at the base supported by 4 legs. I will use panels of plywood at the centre holding the mattress. My question is...suppose the...

Ok thanks. Could you offer me some advise on how i might go about analysing the bending stress of the material for a certain size?

Would this work...? Im designing a folding bunk bed and was wondering whether to keep the weight down I could use a metal wire mesh material as the top bunk fixed to aluminium square tube? Also would it be possible to attach this to the tube main frame fairly easily and how much does the...

Stress analysis of bed design... I have a bed design and i need to do a stress analysis of the top bunk under a 90kg load. I will be designing it from 20mm thick plywood but i need to work out whether this is thick enough to support the load and also determine the width of the leg supports...

Designing folding legs for a bunk bed... Im having trouble finding a suitable hinge mechanism which would allow 2 legs under a bed to be locked and pulling them down into a vertical position they would lock. Does anyone have any ideas or links to a suitable hinge design. Thanks

how about -3?

ok sorry. i think iv got the answer now. -1 ?

the gradient i found was -2z/(2x+y)^2 i + -z/(2x+y)^2 j + 2x+y/(2x+y)^2 k i thought the directional derivative was then s.grad what should the answer be?

Im doing the following question: calculate the directional derivative of the function f(x,y,z) = z/(2x + y) at the point (0,1,1) in the direction d = 2i - 2j - k could someone please check my answer is correct as i calculated -3i -6k Also how do i find the unit vector in the direction...

differentiating with respect to... I have a question on differentiating the function z/(2x + y) with respect to x. Is the answer -2z/(2x + y)^2 ? Thanks:smile:

i need some sleep! Yeah i meant y^3 lol !

ooops I am getting myself all confused now. I know how to do partial differentiation after all. I was reading the wrong solution as the question was z = x^2 y^2 and ofcourse dz/dy would = 3x^2 y^2 !

Iv forgotten the basics of this. How do we go about differentiating 3x^2 y^2 w.r.t y? I know the answer is 3x^2 y^2 but could someone explain this for me please?

inverse laplace method for equation ... Just doing some revision but I am a little stuck on how to find the inverse laplace of 1/s(s-2)

i meant multiplication

yes i did know that but i didnt think it was as simple as that. From reading the certain rules we can apply to problems e.g the shift rule to solve L(sin2t * e^3t) do we HAVE to use the shift rule or can we separate each part and solve then multiply them together?

how do i go about solving the laplace transform of sint * cost ? i know the answer becomes 1/(s^2 + 4) but what is the method? thanks.

How do you go about differentiating rcos$ with respect to time...? In the book I am studying from it says d$/dt d/d$ (rcos$) is the process to find the answer... but what does this mean...?

ok....is it -cos(xy) / y

I just need a check on when integrating sin(xy) with respect to x? Does this become -cos(xy) or -cos(x) thanks

I think iv got my head round it now. If someone has a spair few minutes could they check my answer of -8xy +8zy -12xz

material derivative? I have to find the material derivative of the density P for the following steady state flow: P = -1-2xy-3z^3 and u = (3x-z, y+3z, x-y) I have looked at previous examples but I am not sure what i have to do with the density -1-2xy-3z^3 ... ? please help.

I did apply it...this is how i calculated that result: d/dz In(3y-2z) y=In u therefore dy/du = 1/u u=3y-2z therefore du/dz = -2 dy/du x du/dz = -2/(3y-2z) where am i going wrong?

ok so is it -2/3y + z

I should know this, but i just wanted to check...differentiating ln(3y-2z) with respect to z...does this = -1/2z ?

725 flights in total? as my sum was 1.379x10^-3....

ok...im working it out now

Please could you tell me what answer you get for the total number of flights so I can check?

Ok i took the simple case and my answer was approimately 9600 flight cycles. Do I just do the same for the next 2 and add them together?

Im having a problem with the following question and my understanding of it... An aluminium alloy obeys the fatigue law S = 895N^-0.12, where S is the stress amplitude and N is the number of cycles. An airdraft componentfabricated from this alloy, undergoes the following stress amplitude...

Spring hinges..? I need a spring type hing to do a particular job. From a closed position when in use it can be pulled open to 90 degrees and locks in position. Then can be released to spring back to closed position? Also could one open to 180 degrees?...is this possible? thanks

hi, oops I am not awake :zzz: ...i used s-2 as the denominator for both A and B. Thanks :rofl:

inverse laplace question help please... i am trying find the inverse laplace transfor of s+1/s^2 -4s +4 using partial fractions and solving my answer is e^2t + 3e^2t however checking this in an online fourier-laplace calculator it comes up with e^2t + 3te^2t who is correct? could you...

how does that change anything...still can't solve A and B??

thanks for the tips, can u find the LT of 2sinh2t and the tsinh2t and add them together which gives 4/(s^2 - 4) + 4s/(s^2 + 4) ^2 is this correct?

How do i find the inverse laplace transform of s/(s-2)^2

i can see the first relationship with 2.10 but what do i need to do to s/(s-2)^2 ? use partial fractions? Thats what i tried at the start but how do i find A and B if s = A(s-2) + B(s-2) ?

ok thanks - does this mean i find the inverse laplace transform of 1/(s-2)^2 and add this to the inverse LT of s/(s-2)^2 ? I can do the first that would be te^2t wouldn't it? Not sure about the second part? :cry:

i haven't made a mistake i have to find the inverse laplace transform of s+1/(s^2 - 4s + 4) and I am using partial fractions to do this...but I am stuck now...:cry:

But say I use 2 as my x value, it removes both A and B in this equation...