Water ice has a density of 0.91 g/cm2, so it will float in liquid water. Imagine you have a cube of ice, 10 cm on a side. a. What is the cube's weight? b. What volume of liquid water must be displaced in order to support the floating cube? c. How much of the cube is under the surface of the water

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aristocles aristocles · Answer 1 · 2019-07-07T06:02:28+02:00

Answer:

(i) W = 8.918 N

(ii) [tex]V = 9.1 \times 10^{-4} m^3[/tex]

(iii) d = 9.1 cm

Explanation:

Part a)

As we know that weight of cube is given as

[tex]W = mg[/tex]

[tex]W = \rho V g[/tex]

here we know that

[tex]\rho = 0.91 g/cm^3[/tex]

[tex]Volume = L^3[/tex]

[tex]Volume = 10^3 = 1000 cm^3[/tex]

now the mass of the ice cube is given as

[tex]m = 0.91 \times 1000 = 910 g[/tex]

now weight is given as

[tex]W = 0.910 \times 9.8 = 8.918 N[/tex]

Part b)

Weight of the liquid displaced must be equal to weight of the ice cube

Because as we know that force of buoyancy = weight of the of the liquid displaced

[tex]W_{displaced} = 8.918 N[/tex]

So here volume displaced is given as

[tex]\rho_{water}Vg = 8.918[/tex]

[tex]1000(V)9.8 = 8.918[/tex]

[tex]V = 9.1 \times 10^{-4} m^3[/tex]

Part c)

Let the cube is submerged by distance "d" inside water

So here displaced water weight is given as

[tex]W = \rho_{water} (L^2 d) g[/tex]

[tex]8.918 = 1000(0.10^2 \times d) 9.8[/tex]

[tex]d = 0.091 m[/tex]

so it is submerged by d = 9.1 cm inside water