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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 1/3πμr 3


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            

 



 


 






 




 

 


 






 


 





 












 



















 

















 















 













 











 









 







 





 



 


 

Grade:10

2 Answers

Aman Bansal
592 Points
10 years ago

 

 

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 :

 

 

 

 

 

 

 

μ=tan theta = h/r = rμ

Vcone = A*h /3 = piμs r3/3

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AMAN BANSAL

AKASH GOYAL AskiitiansExpert-IITD
419 Points
10 years ago

Dear Kaushik

See the pic for the solution

All the best.                                                           

AKASH GOYAL

AskiitiansExpert-IITD

 

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