Indeed. On that type of construction, it is the "right" way. For the type pictured in the mechanics paper, it does not matter.
Indeed. On that type of construction, it is the "right" way. For the type pictured in the mechanics paper, it does not matter.
If it were steel, then it would be better in tension - steel is stronger that way, and not going to buckle.
And translates any tendency to sag into a tension force on the top ledge.
Depends on whether its an open frame rather than skinned and on how thick te steel is.
Of course steel buckles all the time.
The failure mode of most trusses is in fact buckling.
I think you are misreading what I typed.
Which is why I was saying you can use a much thinner brace if it is in tension. In tension you don't need to worry about it buckling. In compression it could, and so you would need a stiffer brace to start with.
Only in about half the cases. I looked at every "Question" with a view to answering each one and noticed that some had been marked incorrectly, others correctly and some, seemingly not at all.
Starting with the boxes one (which is hardest to turn over?) my answers are as follows:
C GM assuming diameters of tops of the LH ones = widths of the RH square and equilateral triangular cross sectioned tanks
QAll equal
A OMove to and fro
It wasn't clear what this butcher's weight question was about. I can see three possible 'correct' answers to this one, each depending on how you interpret what the real question is.
The previous student's rubbed out answer (V) suggests it was interpreted as a requirement to minimise bending stress on the hanging beam. Another interpretation of the problem is to minimise pull out forces on the beam's anchor rods, suggesting Y as the answer. However, mention of the
*heaviest* weight strongly suggests both those answers are wrong due to the use of "Trickery" involving common sense and observational skills in the real world.We know that such butchers' meathook rails are amply over-engineered for the butcher's normal every day usage so we can exclude 'structural integrity' issues from our deliberations (plus, any fatigue induced failure here can be remedied without expensive and painful medical procedures being invoked).
This just leaves us with the question of, "If I were that butcher, carrying the heaviest lump of meat from the direction implied by that sketch, where would I want to place it to minimise musculoskeletal wear and tear?" The answer, quite obviously, becomes "The nearest to hand, stupid!", in this case, Z. :-)
The only fly in the ointment with this last option is WTF didn't the daft butcher slide all the hooks to the right hand end of the bar beforehand? That way, he could have reduced the strain and effort on his musculoskeletal system even further by arranging for hook V to be nearer again, allowing him to slide the 'heaviest weight' to the far end of the bar with even less strain and effort, leaving the remaining hooks close to hand and available for more '(but slightly less) heavy weights'.
I may be wrong in interpreting this question as one of 'ergonomics' but f*ck it all, that's the only way to make any sense of this one.
Moving onto the cups question which seems to be a question of which of the four cups encloses a presumed identical volume of liquid with the least amount of surface area, I'm rather drawn to B despite answers C and D looking like they could be equally as good a choice (the 'All equal' option is rather spoilt by A being quite obviously the one destined to cool the fastest).
All of them (cogs question)
NFall
V (looks closest to the optimal 45 degree angle ignoring air resistance)
A H R V CAll equal (assuming we ignore friction effects as Galileo was able to)
NFall
Rise and then fall
H L R WD (as the previous student indicated, assuming a sweeping bend rather than a tight hairpin bend where the right answer could easily be "All equal"). Again, yet another question where I can't decide whether I'm facing a cunningly disguised question concerned with the dangers of making unwarranted assumptions or just very shoddy question setting.
Move in a circle
N assuming disks with holes punched in them (in which case, WTF is causing M to remain poised in its depicted position?)
SX (assuming equal effort on the part of the 'pushers')
Wow! Yet another imponderable question (about skiddiest car). Yet again, we are left to make several assumptions from the very poor quality 'evidence of our eyes' but I'll give it a go.
I'm led to assume we are looking at a piss poor sketch of a snapshot overhead view of a sharp bend or corner on a race track and further obliged to assume a dry equally grippy road surface with no adverse camber or rubber crum to penalise any of the cars which I'm further obliged to assume all have equally grippy tyres and are all travelling at the same speed in some sort of race event.
Having been forced to make all these assumptions just to drill down to what I *think* is the core of the problem, I can only conclude that car C is most likely to skid due to its higher rate of change of velocity needed to negotiate the bend on a tighter radius than the other three cars which results in higher side forces being applied to the tyres from the resultant centripetal force.
In real life, there are many reasons why answer C will be most emphatically wrong but, what the hey, this is just a question on a 1950's mechanics exam paper. :-)
HOne
All equal
The mechanism will jam (I'm only 99% sure but if I'm wrong then opposite direction unevenly becomes the only viable alternative)
I would hope that such shoddy exam question setting as exhibited by JR Morrisby's efforts would be rejected today. However, I believe (rightly or wrongly) that such shoddiness in examination question standards still abounds to this day.
Or, as I was forced to conclude, a question of ergonomics relating to reduction of fatigue induced stress on that classic and timeless mechanical system, the musculoskeletal system of the butcher himself! :-)
Nothing else made any sense due to lack of information in regard of the rail and its supports. One was left to make far too many completely unwarranted assumptions about the non biological content leaving only the biomechanical and mindset assumptions of the butcher himself as the least contentious of all the possible assumptions that could be made from the cunningly disguised content of that question.
If you analyse that question very closely and carefully, you'll realise it was actually a cunningly disguised question of an ergonomically driven common sense based solution to a problem faced by the butcher rather than anything to do with what was least stressful to the hook rail and its supports. Even so, it did beg the question as to why the butcher wasn't clever enough to slide all the hooks to the right hand end of the rail beforehand to ease the load even further but I guess this may have made the required answer all too obvious for the examiner's liking. :-)
No trick. The brace works in both compression and tension and adds the additional stiffness against sag all the other examples were all completely lacking.
Oh yes indeedy! That one needed a ton of (unwarranted in real life) assumptions to be made just to drill down to the core of the question (an issue of which vehicle was being subjected to the highest sideways forces on that part of the corner).
The capstan one was a straight forward "Lever Question". Nothing complicated or tricky about it at all.
Again, far too many unknowns to decide whether R would land up working the hardest due to an extremely light load which would make S the more energy efficient option or whether, as was implied, that R would have to work the hardest by virtue of greater effort to move a heavier load.
To attempt to answer on the basis of effective energy input by one person alone at each indicated position in turn requires addressing the issue of 'matching impedances' between the generator and the load. Whilst it's true that the energy input by R trotting around the capstan at half the effort is the same as T walking at half the speed but full effort, the energy expended by R and T is unlikely to be the same.
If this question is merely a trick question where the correct answer is deemed to be "All equal", then it falls far short of the quality of 'trick question' demonstrated by the Butcher's hook question.
Is the *right* answer! :-) (a cleverly disguised question of ergonomics and perhaps a reminder that the human skeleton and musculature is constrained by the same laws of 'mechanics' as apply to 'engineered' mechanical systems.
What's the difference?
Bill
Alternatively, the answer could be "none of the above" as the meat clearly already has a hook attached and he can hang it on the rail anywhere he likes.
Tim
He doesn't need to he has a hook in the meat already and would just hook it on the rail nearest him.
truss answer missing here.
If the truss has been dimensioned correctly they will all have the same strain but they may well have different loads causing that strain.
doesn't that depend on the taps being identical? if the flow rate is slow the fall will be impossible to see even if you know it is there.
Its the inside one assuming they depict someone going around the same bend as you have to lean more the faster you go around the bends which is why motorcylists scrape their knees and then fall off.
The examiners hand.
It depends how you define work. S would have to push hardest but travel less distance. In reality he wouldn't be able to shift the thing as you wouldn't have four operating positions if you only needed one man to do the job.
Looking at it C can't be turning yet or the rear wheels will hit the curb.
B is going to have to turn sharpest or he will hit A.
I would say B because he is going to have to hit the brakes to avoid A.
doesn't the sliding pivot stop it from jamming?
Well done. have a gold star.
Nicely spotted! :-)
If this was a question of observational skills and 'common sense' (as it seems since it's the only way to make any sense of it), then I'm afraid I've only got half marks (and the question setter zero marks for failing to provide any means for the student to demonstrate the 'best answer').
Oops! 'My Bad'. :-( I'm afraid I was so hung up on trying to work out an answer to this one, I decided to 'deal with it later' and moved onto the rest of the questions, forgetting to return to it before posting my follow up.
I got as far as seeing this as a "vectors" calculation, depending on (yet more) assumptions that the strains due to the mass of the bridge components themselves would be insignificant enough compared to the "1 ton load" and largely balance themselves out of the equation for the purpose of this question anyway as well assuming the structure is made up entirely from right angled isosceles triangles.
With all those assumptions in place (all pigs prepped up and ready to fly, so to speak), I can see that members V and X are in tension to the tune of 0.707 tons with W and Y each carrying a 1 ton force in compression.
It is impossible to correctly answer this question when complying with the instruction to select "The one and only correct option" from the list supplied since I'd want to select the *two* correct options, V and X. If I ignore my understanding of the examiner's definition of the word 'strain' to decide the most likely singularly correct option, I'd be forced by such logic to select 'All equal' and hope I'd correctly 'second guessed' the examiner's definition of a 'correct answer'.
OTOH, it may simply show my ignorance of the mechanics of bridge construction and the definition of 'strain'. :-)
No, it depends on the taps *not* being identical; in this case the LHS tap of tank X being a much larger bore, matching the fatter pipework allowing a faster fill rate than the smaller tap and pipework linking to the tank on the RHS of tank X will allow it to drain away.
Rise and then fall describes exactly what will happen to the water level in tank X during the early part of the process. Eventually, the water levels in all three tanks will level off. The level in the LHS tank will only fall whilst that in the RHS tank will only rise. Tank X is the only one of the three that will exhibit this 'interesting behaviour' in the scenario depicted.
The question is about what happens to the water level in tank X regardless of whether or not it can be observed. The sketch shows three, apparently transparent tanks, along with quite obviously different sized 'taps' (valves) and plumbing to save the student from thinking up ways to impose difficulties in arriving at a correct answer. :-)
No, the ambiguity lies in the fact that the amount of lean to balance centripetal force depends not on the speed alone but that of the velocity change (in this case a change of velocity due to a change in direction rather than speed).
This sketch could be a snapshot of a group of riders negotiating a hairpin bend on a wide road where the innermost rider, D, is in fact moving at the slowest speed but requiring the most lean to balance the higher change of velocity due to the much tighter turn being made on the inside of the bend. Indeed, it's just as possible to have this set up so that all riders are travelling at the same scalar speed and show the same succession of increasing lean angles.
This yet another badly set question wherein the only way the examiner could have saved himself from total and utter disgrace would be by replacing the "All equal" option with "Totally impossible to discern from the given sketch".
That lacked a smiley imho. :-)
I think the sliding pivot is most likely the reason it *will* jam up imo (varying ratio of the linking bar as a lever). Now that I've had a break from pondering this question, it seems to me to be a question of can such a linkage without the extreme and unusual wear on the centre pin bearing of the linkage bar even work?
Consider this; shrink the slot in the linkage bar down to a round hole for the pivot pin bearing and you'll see straight away that such a linkage cannot allow movement (you land up with two triangles which cannot be contorted without bending or altering at least one of the connecting lines. You might think turning the bearing hole in the middle of the linkage bar into an elongated slot will help but the problem there is that the varying lever ratios will still result in a jammed machine.
I may not have been entirely sure of my initial answer last night but, having taken another look at the problem in the bright light of day, I'm now convinced that the mechanism *will* jam. :-)
Thank you very much! You're so kind. :-)
An excellent point! Sadly, the rules of the game, as set by the examiner, rather precludes such an accurate answer. Indeed, this has meant that quite a few of the other questions have also been blighted by this same limitation. :-(
And yet another potentially correct answer... "It doesn't matter where he hangs it if the bar and supports have been adequately engineered". If it hasn't been, then it all depends on which bit of the system hasn't been adequately engineered, the bar or the bar supports.
Tim
That's exactly the problem, Ambiguity! (and in spades!).
In fact there's so many of these ambiguously posed questions sprinkled around where the only way the student can provide the (or most) correct answer is by 'breaking the rules' in regard of indicating which of five possible answers is the correct *one* that it makes me wonder whether this (contrary to most examination papers) was designed specifically to identify budding geniuses (or troublemakers) prepared to stand up and be counted.
It's almost as if this was some sort of inverse precursor to "The Milgram Experiment"[1] which was carried out in 1961 at Yale University to examine the issue of "Obedience" which had been raised at the Nazi war criminal trials by the defendants' claims that "They were just following orders."
I guess it's the common factor of the deceitful nature of that sprinkling of "Trick Questions" embedded in the exam paper that's made me think of the Milgram Experiment which had relied entirely upon deception to gain insight into the nature of obedience to authority figures.
In the case of this exam paper, one would prefer to think of it as a way to identify free thinking geniuses as candidates for further educational advancement but it could just as easily be a way to deal with potential trouble makers by denying them access to further education. How the test results are interpreted depends on the aims of the sponsor who may not necessarily have taken the question setter entirely into his confidence [2].
[1]
In a framed construction, the brace is inline with the other timbers. This means that its not easy to make a joint at the brace ends that would work well in tension unless you are going to opt for more difficult to construct angled M&T joints. So the expedient option is to ensure this brace is oriented that it acts in compression like a gallows bracket, since this puts little stress on the fixing points of the brace.
With a picket style construction like that shown in the paper, all the joints are simply planted on top of each other and fixed with a bolt through the faces (rather like you were bolting together three lengths of Meccano). Unlike M&T joinery, there is no inherent ability of the joints themselves to resist racking, everything comes down to shear loads on the bolts caused by the triangulation. Some will be in compression and some in tension.
You can argue in the latter case that the brace used in the "wrong" orientation will have a failure mode with the fixing tearing out of the end of the brace (or the bolt shearing - depending on whether the bolt or gate material is stronger). This would be true, but in the circumstance with the "right" orientation, you simply get the same failure at the end of the top cross member instead. The engineering approach will often opt for the tension brace in circumstances like this since it can be much thinner and needs no inherent stiffness. (as someone else mentioned, even a cable would function here). The result being a lighter (so less self loading in the first place) and cheaper to construct gate.
I think one has to read the hook in the meat as being the "real" hook, and those depicted on the rail simply being virtual hooks indication possible positions where the real hook may be placed. Kind of like quantum hooks, you have a hook superposition, and its only when you collapse the wave function you get to work out where it is! ;-)
Brilliant! Perhaps this examination paper has been designed to spot not only budding geniuses but geniuses with the potential to make budding geniuses look like a bunch of cretins. Genius! :-)
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