A worker wishes to pile a cone of sand onto a circular area inhis yard. The radi

Question

A worker wishes to pile a cone of sand onto a circular area inhis yard. The radius of the circle is R = 1.2 m, and nosand is to spill onto the surrounding area (Fig. 6-62). Ifs = 0.55 is the static coefficient offriction between each layer of sand along the slope and the sandbeneath it (along which it might slip), find the greatest volume ofsand (in m^3) that can be stored in this manner. (The volume of acone is Ah/3, where A is the base area andh is the cone's height.) A worker wishes to pile a cone of sand onto a circular area inhis yard. The radius of the circle is R = 1.2 m, and nosand is to spill onto the surrounding area (Fig. 6-62). Ifs = 0.55 is the static coefficient offriction between each layer of sand along the slope and the sandbeneath it (along which it might slip), find the greatest volume ofsand (in m^3) that can be stored in this manner. (The volume of acone is Ah/3, where A is the base area andh is the cone's height.)

Explanation / Answer

R = 1.2 m, s = 0.55 height h = R*tan friction f = smgcos mgsin = smgcos tan = s volume = R2*R*s/3= sR3/3 = 0.995m3

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