The greatest height h of the sand pile that can be erected without spilling the sand onto the surrounding circular area of radius R (if is the coefficient of friction between sand particles) is
Answers
Given:
Radius of the circular area = R
Height of the sand pile = h
Coefficient of friction = u
To find:
The height of the sandpile that can be erected without spilling the sand onto the surrounding circular area.
Solution:
F = mg = p × v. where p is the density of sand volume
Greatest height of sandpile that can be created = μsR.
tanθ = μs = hR
Area of cone = 1/3πR²h
Work needed = 1/3πR²hpg × h/4
= π/12 u²R`4.
Answer: The height of the sandpile π/12 u²R`4.
Given:
Radius of the circular area = R
Height of the sand pile = h
Coefficient of friction = u
To find:
The height of the sandpile that can be erected without spilling the sand onto the surrounding circular area.
Solution:
F = mg = p × v. where p is the density of sand volume
Greatest height of sandpile that can be created = μsR.
tanθ = μs = hR
Area of cone = 1/3πR²h
Work needed = 1/3πR²hpg × h/4
= π/12 u²R`4.
Answer: The height of the sandpile π/12 u²R`4.