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A worker wishes to pile a cone of sand on to a circular area in his yard. The radius of the circle is r; no sand is to spill on to the surrounding area. If μ is the static coefficient of friction between each layer of sand, show that the greatest volume of sand that can be stored in this manner is 1/3πμr3
N =Fgy = mgcosθ
f = Fgx = mg sinθ < fs max = µN= µmgcos theta--> μ > tan theta
The surface of the cone has the greatest slope and the height of the cone is maximum if :
The surface of the cone has the greatest slope and the height of the cone is
maximum if :
μ=tan theta = h/r = rμ
Vcone = A*h /3 = piμs r3/3
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Dear Kaushik
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AKASH GOYAL
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