more%20structures%20class%2019[1]

more%20structures%20class%2019[1] - inclined axes, limits...

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α 30o M cans, each of weight W Determine the maximum number of cans that can be stacked on the smooth surfaces shown as a function of the angle α of the left hand surface before the stack loses equilibrium and the lowest can is kicked out. Let α range from 0o to 55o 1 2 M 3 inclined axes, limits on equilibrium
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30 α M 1 2 M-1 cans W W W F x 30o N1 60 - α F 30o W N2 y α ( 29 ( 29 0 1 sin 30 0 1 / 2 x o F F M W F M W = - - = = - ( 29 ( 29 ( 29 2 2 0 cos 60 sin 30 1 / 2 2cos 60 x o F N W F M W MW N α = - - = = - = - ( 29 ( 29 1 2 1 0 cos30 sin 60 0 3 tan 60 2 y o F N W N W N M = - + - = = - -
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function M =cans(a) arg = (60- a)*pi/180; M = floor(sqrt(3)./tan(arg)); N1 = 0 when M must be an integer so need to round values down to nearest integer we can evaluate and plot this easily in MATLAB. First we define and save a function called cans: ( 29 3 tan 60 M α = - ( 29 1 3 tan 60 2 W N M = - -
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>> a =linspace(0, 55, 1000); % the angle alpha in degrees >> m=cans(a); >> plot(a, m) 0 10 20 30 40 50 60 0 2 4 6 8 10 12 14 16 18 20 α M then we plot the number of cans versus angle
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F B C A 3' 2' 1' 3' 9' x y z A plate, whose weight can be neglected, is supported by a single smooth
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more%20structures%20class%2019[1] - inclined axes, limits...

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