A flat slab of styrofoam, with a density of 32kgm3 , floats on a lake. What minimum volume must the slab have so that a 33kg boy can sit on the slab without it sinking?

Question

A flat slab of styrofoam, with a density of 32kgm3 , floats on a lake.  What minimum volume must the slab have so that a 33kg boy can sit on the slab without it sinking?

Durst37 · Accepted Answer

let the volume be V ;  submerged volume = V ;  volume of water displaced = V ;  buoyant force =ρωVg; ....1  downward force =33⋅g+ρs⋅V⋅g.....2  but since body is in equilbrium , so eqn 1 = eqn 2 ,  ρωVg=33g+ρω⋅V⋅g  ρωV=33+ρω⋅V  or V ( 1000 - 32 ) = 33;  or V=0.034090m3   (ans)

Philip Williams · Accepted Answer

Step 1  In order for the slab and the boy to stay floating on the water buoyancy force must be equal to the sum of the weights. That is,  FB=Gboy+Gslab  ρwaterVg=mg+Mg  ρwaterVg=mg+Vρslabg  V(ρwater−ρslab)=m  V=mρwater−ρslab  Step 2  Substituting the givens,  V=33kg1000kg⋅m−3−32kg⋅m−3  =0.034m3  Therefore, the minimum volume is 0.034m3.

A flat slab of styrofoam, with a density of 32kg/m^{3}

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