(a) Derive the equations used in this problem based on forces and the experiment

Question

(a) Derive the equations used in this problem based on forces and the experiment on specific gravity. A wooden block with dimensions 10.0cm x 20.0cm x 10.0cm has a density of 0.600g/cm3. (a) An iron block is placed on top of the wooden block so that the wooden block is level with the water around it and the iron is not submerged. The theoretical force or weight of the displaced water equals?(write formula) (b) using part (a), what mass of iron (iron = 7.86 gcm3) is requried? (c) If iron were attached to the bottom of the instead, deterimine the volume of the mass of the iron it would take to bring the top of the wooden block down just below the level of the water. (d) if aluminum (AL= 2.70g/cm3) was used instead and attached to the bottom, determine the volume and mass of aluminum it would take to bring the top of the wooden block down to just below the level of the water.

Explanation / Answer

a) weight of displaced water=water*V*g=1000*(0.10*0.20*0.10)*9.81=19.62 N

here water is taken to be= 1000 kg/m^3

b)weight of water displaced= weight of iron placed+wt of block

19.62=600*(.1*.2*.1)m^3 *9.81+m *9.81

m=0.8 kg ans

c)1000*(0.10*0.20*0.10)*9.81+1000*(v iron)*9.81=600*(.1*.2*.1)m^3 *9.81+7860*viron *9.81

2+1000v=1.2+7860v

0.8=6860v

v=0.000116180 m^3=1116.18 cm^3 ans

d)

1000*(0.10*0.20*0.10)*9.81+1000*(v allu)*9.81=600*(.1*.2*.1)m^3 *9.81+2700*v allu *9.81

2+1000Val=1.2+2700 val

0.8=1700 Val

val=0.000470588 m^3=470.588 cm^3 ans

m al=2700*0.000470588

=1.270 kg ans

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