A block of wood has a mass m and a density of ?. It is to be loaded with lead (d

Question

A block of wood has a mass m and a density of ?. It is to be loaded with lead (density ?Pb) so that it will float in water with some fraction f of its volume submerged. What mass of lead is needed if the lead is attached to (a) the top of the wood and (b) the bottom of the wood? State your answers in terms of the given variables, using ?w (the density of water) when necessary. A block of wood has a mass m and a density of ?. It is to be loaded with lead (density ?Pb) so that it will float in water with some fraction f of its volume submerged. What mass of lead is needed if the lead is attached to (a) the top of the wood and (b) the bottom of the wood? State your answers in terms of the given variables, using ?w (the density of water) when necessary.

Explanation / Answer

(a) mass of lead needed if the leads is on top..

ml=mass of lead ?

for this part the amount immersed is wood

Fb=?Vg

the force displaced is equal to the weight

Fb=Fg

?wVg(mw/?wood)=(mw+ml)g,gravity cancels out and solve for ml

ml=?wV(mw/?wood)-mw= plug and solve

(b)this time the lead and block are immersed, the block holdsthe lead.

?wVg(mw/?wood)+(?w/?l)mlg=(mw+ml)g, gravity cancels out, and solve for ml

ml=?wV(mw/?wood)+(?w/?l)ml-mw

ml=pwv(mw/?wood)-mw= plug and solve

           (?w/?l)

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