It is delicious to have my masters level in Mechanical Engineering put to apply in resolving historic period old technology problems .
One can never have a go at it the exact human body or size of it of the slippers that Cinderella wore , but one can venture a guess that they must have looked something like :
Now , rent ’s babble out about unsuccessful person . No , not about Cinderella ’s failure to keep her shoes on her base , but about mechanical failure . Whenever we design something that needs to bear forcefulness , we test for various possible modes of nonstarter and endeavor to ensure that our object is strong against all of them .
Now , one possible agency the skidder could bust is by generate to the compressive stress come up due to Cinderella ’s weight . But will that encounter ?
We can safely assume that Cindy did n’t weigh more than than 50 kilogram . I mean , her cousins were fat and ugly , so we have to leave them some way on the top , correct ? Let ’s assume this weight to be utilize uniformly across the shoe . Note that , asYehong Zhupointed out in a gossip , the toe part of a heeled brake shoe bears almost thrice as much force as the bounder region , but it wo n’t count for our intent .
Using a rough estimate of her invertebrate foot sizing , her foot area come out to be about
If 50 kgs of weight unit were to be apply uniformly across this orbit , the compressive stress develop in the textile would be :
The Yield effectiveness of ordinary glassful for compressive stress is some 50 MPa , which is 3 order of order of magnitude more than what Cinderella ’s weight unit can produce , so we can safely conclude that any regular trash can support it . Since the tension is so low , we do n’t even need to worry about the uneven shipment on the shoe .
So , is she safe now ? Can she safely dance at the ball without fright of tiny shards of glass cut her skin and ruin her dress ?
Not so presently , buddy !
There ’s another way her shoe could intermit , and this is due to the compressive stress due to the bend moment applied to her heel every prison term she walks .
Now , I do n’t want to be here all day , and I do n’t desire to mold her brake shoe in ANSYS , so I will make a few simplifying assumptions . allow her heel have a diameter 2 centimetre . and have a duration of 6 centimeters from the tip to the point where it joins the rest of the brake shoe . The heel can now be pose as a simple cantilever beam of orbitual interbreeding section .
I ’m in a bite of a haste and I have to get back to readingThe Casual Vacancy ( 2012 book ) , so I will defer tothisfor the actual calculation of the maximum flex stress . I will assume her step angle to be about 30 ° , which means that only half of her free weight ( 500sin 30 ) would do in the normal focusing to the heel ( do the deflexion ) . Plugging 250N as the flex power and the rest of the figures in place , we get the maximum bending stress in the blackguard to be 19 MPa . mark that this is hazardously near to our critical stress of . Even if we make a few more allowance by making the heel thicker or the stepping slant smaller , we can not let our little princess veer so dangerously close to catastrophe .
In order for her to be safe enough , we would take a safety factor of at least 2 , and also presume that the bending stress can go as eminent as 75 MPa . This stand for that her shoe need to be made of glass that has a yield strength of at least 150 MPa .
Safety ice ( thermal toughened glass ) seems to be a skillful bet . It has a issue strength of about 200 MPa and a higherYoung ’s Modulustoo , so I imagine Cinderella can utilize it safely without fear of it founder just when she is shaking a leg with our awesome prince . Ideally , we would also want it mixed with something to make it less brittle , but I do n’t want to make it too unlike from trash or the answer becomes nonmeaningful .
Steve Davispoints out an interesting issue — what happens when she starts running out of the castle at midnight approaches ?
When Cinderella run , I expect the encroachment power to be 3 - 5 fourth dimension that of the even walk force ( this is reasonably affirm by the paper “ Ground reaction forces at different speed of human walk and running “ ) . The shoes should be secure for these value .
We must also take into consideration the fact that Cinderella ’s frock would probably not allow her take long stride . This would mean that her stepping angle would rest within safe limit , further ensure that her shoes do n’t give .
Most importantly , she would be well - advised to develop a toe - first base smasher , which would completely lick the problem . This can not be maintained for enceinte distances , but would certainly take Cinderella out of the danger zone .
Bharat Jakatipoints out another caveat . What if the friction between her shoe and the priming coat / story is so small that she slips ? Well , we can assume that the floor is either made of stone or is carpetted . The coefficient of friction for Glass on Stone is about 0.42 , which is not very eminent , but is high enough for her to not fall away . I could n’t get a note value for the coefficient for chalk on carpeting , but I imagine it to be similar .
And yes , I am well aware that Cinderella ’s shoes were most in all likelihood made of pelt and that the glass in the story is mostly a result of mistranslation . But what ’s the sport in that ?
Image : Shutterstock / MR Shining
What character would the drinking glass in Cinderella ’s slippers need to have in order for her to take the air and dance well ( and obtain her weight)?originally appeared onQuora . you may follow Quora onTwitter , Facebook , andGoogle+ .
This result has been lightly edited for grammar and lucidity .
CinderellaPhysicsQUORAScience
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