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Old Apr 15th 2018, 12:02 PM   #1
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Mechanics

Four same homogenious bricks are stacked on top of each other as illustrated below. They all have the horisontal sidelength of a. The bricks are not rotated in comparison to each other. What is the maximum value of the distance d that possibly can be achieved?

A illustrative picture of the system: https://i.imgur.com/ITYlGhE.jpg

I am aware that the question obviously has to do with balancing the forces. The best answer of mine is d=15*a/16. The correct answer is d=11*a/12. I need help with deriving the correct answer.
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Old Apr 15th 2018, 01:55 PM   #2
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You must begin from the top down. Putting the maximum overhang at the top is the best way to optimize this scenario. Every time you go down a level you must make sure that the load is balanced, i.e. half the load sits on the left hand side of the fulcrum (corner of the brick) and the other half must sit on the right hand side.

Therefor the first overhang distance will be 1/2 of A.
The distance or overhang to get the top two bricks balanced on the third brick is 1/4.
Finally the distance or overhang to get the top three bricks balanced on the fourth brick is 2/12.

Adding up the successive overhangs gets you to 11/12 of A.
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Old Apr 15th 2018, 02:55 PM   #3
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Thanks dor your reply. I got that the second brick should be layed at the firat ones fulcrum, although not the reasoning behind the third one, and therefore, also fourth. What is the precise reasoning that it is 1/4 and not 1/2? I would love to see how you reason, step by step.
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Old Apr 15th 2018, 03:23 PM   #4
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W is the weight of one brick. On the top level you need to balance 0.5W followed by 1W on the second level and on the third level 1.5W. It is 1/4 because the height above the 1/4 increment is two bricks so the weight is doubled. On the third level it becomes 1/6 (2/12) because there are three bricks above.

'````````````````````````````````````````````````` ``` -------------------------------
'````````````````````````````````````````````````` ``` |******************************|
'````````````````````````````````````````````````` ``` |******************************|
'````````````````````````````````````````````````` ````-------------------------------
'````````````````````````````````````````````````` ```<-0.5W----><----0.5W-->
'````````````````````````````````````````1/2``````````````````1/2
'````````````````````````````````-------------------------------
'````````````````````````````````|**************** **************|
'````````````````````````````````|**************** **************|
'```````````````````````````````-------------------------------
'``````````````````````````````<--------------------> <-------------------->
'``````````````````````````````````````````W`````` `````````<---->`````W
'````````````````````````````````````````````````` `````````````1/4
'```````````````````````-------------------------------
'```````````````````````|************************* *****|
'```````````````````````|************************* *****|
'```````````````````````-------------------------------
'```````````````````````<----------------------> <------------------------>
'````````````````````````````````````1.5W `````````````````````1.5W
'````````````````````````````````````````````````` ````<2/12>
'```````````````-------------------------------
'```````````````|******************************|
'```````````````|******************************|
'```````````````-------------------------------

Last edited by YellowPeril; Apr 15th 2018 at 03:37 PM.
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