Brain cells needed - 1955 test

found this test lurking in the filing cabinet at work, some of the questions might need a bit more context.
https://drive.google.com/file/d/0B_U7i5Hd7WKpbVBuTFU2bnN1c0U/view?usp=sharing
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I like that...bit like O level Physics .....or applied mechanics
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On Thu, 25 May 2017 11:16:16 -0700 (PDT), misterroy

Would I be disqualified for putting a mark on the line provided, rather than crossing out the letter corresponding to the correct answer as instructed?
--

Graham.
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Graham. wrote:

You do not need to you can see where the mark is rubbed out.
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wrote:

I hadn't noticed that. Still, it's a strange implementation of "crossing out"
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On Fri, 26 May 2017 22:19:58 +1000, FMurtz wrote:

usp=sharing

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
G
M assuming diameters of tops of the LH ones = widths of the RH square and equilateral triangular cross sectioned tanks
Q
All equal
A
O
Move 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 fuck 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)
N
Fall
V (looks closest to the optimal 45 degree angle ignoring air resistance)
A
H
R
V
C
All equal (assuming we ignore friction effects as Galileo was able to)
N
Fall
Rise and then fall
H
L
R
W
D (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?)
S
X (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. :-)
H
One
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.
--
Johnny B Good

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On 28/05/2017 03:38, Johnny B Good wrote:

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.
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On Sun, 28 May 2017 11:07:10 +0100, dennis@home wrote:

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. :-)
--
Johnny B Good

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On 25/05/2017 19:16, misterroy wrote:

Is the gate question a trick? H has the brace the wrong way round.
Bill
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On 25/05/17 21:27, Bill Wright wrote:

tesnd to work either way.
There were more than one question however where there seemed to be insufficient information.
The car skid for example.
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On 25/05/2017 21:34, The Natural Philosopher wrote:

The butchers hook one as well... depending what you want to achieve - least load on the supports, then in the middle. Least bending of the rail, then right at the end.
--
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On 25/05/2017 23:52, John Rumm wrote:

Also the capstan.

Least distance to carry the bloody thing :)
--
Robin
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On 26/05/2017 08:55, Robin wrote:

The one with the weight hanging off rope at the top of the well? There's enough information there.
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Here are my answers with reasoning:
1. C 2. G    goes deepest into ground while being angled towards the pulling force (at 45 degrees) 3. M    area is s^2 rather than pi (s/2)^2    (where s is the length of the side or diameter) 4. Q    closest to the pivot: need greatest ratio of length of handle side to length of twig side (lever - maginfication of force inversely proportional to distance from pivot) 5. All equal (not entirely confident on this one) 6. A    smallest radius 7. H    cross-brace, even if it *is* in tension rather than compression! 8. O    greatest number of pulleys 9. move to and fro 10. V    if the objective is to prevent the hanging rail bending/breaking 11. B    smallest surface area of liquid and smallest area of cup 12. F and G (H turns in opposite direction) 13. N    at pivot, with greatest distance and therefore greatest turning moment from children on either end) 14. Fall radius of "fall" side of rope is greater than radius of "rise" side 15. X    45 degrees 16. D    longest length of strut from its pivot 17. H    load is carried closest to the pivot/wheel, with longest distance from load to handle 18. L    narrowest arch relative to height 19. S    goodness knows - hard to estimate how the curved line continues 20. V    longest anchor line so greatest component of force sideways compared with vertically 21. C    if same amount of energy (mgh1-mgh2) = (mgh2-mgh3) is lost on each bounce 22. J    smallest surface area so smallest air resistance 23. N    roughly in same direction as line through centres of white and black balls 24. fall    balls fly outwards, causing collar to rise and hence pointer to fall - a governor 25. W    guessing - not sure 26. rise and then fall: pipe that fills X is bigger than one that drains it so inflow is greater than outflow 27. H    furthest away from either end (eg F) where it will stop and reverse 28. O    greatest turning moment furthest from pivot 29. R    others will roll freely only until off-centre bar is at bottom and will experience retarding force after that 30. W    greatest mass concentrated furthest from centre 31. D    because he's having to bank over furthest to compensate for (mv^2)/r centripetal force 32. move in circle (both small cogs are same radius and will turn in same direction, so no jam) 33. S    closest to centre so he's exerting least turning moment to overcome whatever the capstan is turning 34. X    resultant force is midway between directions of pushing forces 35. smallest radius of curvature so greatest (mv^2)/r centripetal force (assuming all cars doing same linear speed) 36. H 37. one ball hits the group of four so one ball leaves group (as for Newton's Cradle) 38. all equal 39. opposite, unevenly (won't jam because ends of rod are 180 deg out of phase so no vertical component to motion)
I'm open to argument/correction on some of them!
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snip

33 He is doing the same amount of work (force X distance moved) wherever on the capstan he pushes. If they meant force they should have said so.
--

Roger Hayter

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On 26/05/2017 12:35, Clive George wrote:

I had in mind the nautical capstan with 4 men and "Which man would have to work hardest to turn the capstan alone?" ISTM "hardest" is ambiguous between (a) the force exerted (highest for shortest lever), (b) the energy required per unit time (ditto if they walk at the same speed - linear not angular - when walking alone), and (c) the energy required per revolution (same for all).
--
Robin
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On 26/05/2017 13:40, Robin wrote:

Ah, right, fair enough.
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Yes, that’s the obvious answer.

That’s not working harder.

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If you assume the capstan has to be pushed with a constant rotational speed then c) is right. If the man has a constant force available he is doing more work the faster he walks so the furthest out one is the answer. But unless the capstan has to be pushed at a constant speed it is a bit hard to see any sensible answer for work done.
--

Roger Hayter

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They arent normally, so that cant be assumed and that would have been stated if it was a requirement.

a) is the obvious answer, because with the longer arm, you have more leverage and so don’t have to work so hard. That’s the whole point of the arms.
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