Specific gravity is defined as the density of a substance divided by the density

Question

Specific gravity is defined as the density of a substance divided by the density of water. (Therefore the specific gravity of water is 1). A 500 kg block of wood is floating in a pool of water. The block of wood is 3/4 submerged.

a. What is the specific gravity of the block of wood?

b. A mass of iron is suspended below the block of wood to submerge the block of wood. The density of iron is 8920 kg/m3. What volume of iron is required to keep the block of wood submerged? (i.e. not sinking, not floating, but in equilibrium)

c. What is the mass of the iron in part b?

Explanation / Answer

a)
Let V is the volume of the wodden block.

In the equilibrium, buoynat force on wooden block = weight of wooden block

B = weight of wooden block

weight of dispalced water = m*g

rho_water*(3*V/4)*g = rho_wood*V*g

rho_wood/rho_water = 3/4

specific gravity of wooden block = 0.75 <<<<<----Answer

b) Let V_Iron is the volue of Iron required.

let T is the tension in the rope.

in the equilibrum

B = m*g + T

rho_water*V*g = 500*9.8 + T

1000*(500/750)*9.8 = 500*9.8 + T

==> T = 1000*(500/750)*9.8 - 500*9.8

= 1633.3 N

now, T + B = m*g

T = m*g - B

T = rho_iron*V_iron*g - rho_water*V_iron*g

V_iron = T/(rho_iron*g - rho_water*g)

= 1633.3/(8920*9.8 - 1000*9.8)

= 0.002104 m^3

c) mass of iron = density*volume

= 8920*0.02104

= 187.7 kg

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