A cube of copper, each edge of which is 3.50 cm is floating ina container full o

Question

A cube of copper, each edge of which is 3.50 cm is floating ina container full of mercury. Both are initially attemperature of 20.0 o C density of copper = 8.9 x 10 3 kg/m3 density of mercury = 13.6 x 10 3 kg/m3 What is the mass of the cube of copper? What percentage of the copper block is submerged below thesurface of the mercury? Both copper and mercury heated to temperature of 110oC b= 5.6 x 10 -5/oC for copper b= 1.8 x 10 -4/oC for mercury. What percentage of copper is now submerged below surface ofmercury? A cube of copper, each edge of which is 3.50 cm is floating ina container full of mercury. Both are initially attemperature of 20.0 o C density of copper = 8.9 x 10 3 kg/m3 density of mercury = 13.6 x 10 3 kg/m3 What is the mass of the cube of copper? What percentage of the copper block is submerged below thesurface of the mercury? Both copper and mercury heated to temperature of 110oC b= 5.6 x 10 -5/oC for copper b= 1.8 x 10 -4/oC for mercury. What percentage of copper is now submerged below surface ofmercury? density of mercury = 13.6 x 10 3 kg/m3 What is the mass of the cube of copper? What percentage of the copper block is submerged below thesurface of the mercury? Both copper and mercury heated to temperature of 110oC b= 5.6 x 10 -5/oC for copper b= 1.8 x 10 -4/oC for mercury. What percentage of copper is now submerged below surface ofmercury?

Explanation / Answer

A cube of copper, each edge of which is 3.50 cm is floating ina container full of mercury. Both are initially attemperature of 20.0 o C. density of copper = 8.9 x 103 kg/m3 .density of mercury = 13.6 x 103 kg/m3
What is the mass of the cube of copper?
m = V = (.035)^3 * 8900 = .382 m^3

What percentage of the copper block is submerged below the surfaceof the mercury?
If fraction f is below the surface,
displaced Hg = fV
weight of displaced Hg = fV'g = weight of cube = Vg
f = /' = 8.9/13.6 = .6544 = 65.44%
Both copper and mercury heated to temperature of 110oC b= 5.6 x 10 -5/oC for copper b= 1.8 x 10 -4/oC for mercury. What percentage of copper is now submerged below surface ofmercury?
The volume of the cube is larger, say, V1, but density is lower,say 1. Mass remains same, so
mass of cube = V = V1 1
If fraction f1 is below the surface,
displaced Hg = f1V1
weight of displaced Hg = f1V1''g = weight of cube =Vg         ('' = new density of Hg)
f1 = (V)/(V1'')
V1 = V(1+.000056*90)
'' = '/(1+.00018*90)
f1 = (V)(1+.00018*90)/[V(1+.000056*90)'] =(8.9)(1+.00018*90)/[(1+.000056*90)(13.6)]
= .6617 = 66.17%

What is the mass of the cube of copper?
m = V = (.035)^3 * 8900 = .382 m^3

What percentage of the copper block is submerged below the surfaceof the mercury?
If fraction f is below the surface,
displaced Hg = fV
weight of displaced Hg = fV'g = weight of cube = Vg
f = /' = 8.9/13.6 = .6544 = 65.44%
Both copper and mercury heated to temperature of 110oC b= 5.6 x 10 -5/oC for copper b= 1.8 x 10 -4/oC for mercury. What percentage of copper is now submerged below surface ofmercury?
The volume of the cube is larger, say, V1, but density is lower,say 1. Mass remains same, so
mass of cube = V = V1 1
If fraction f1 is below the surface,
displaced Hg = f1V1
weight of displaced Hg = f1V1''g = weight of cube =Vg         ('' = new density of Hg)
f1 = (V)/(V1'')
V1 = V(1+.000056*90)
'' = '/(1+.00018*90)
f1 = (V)(1+.00018*90)/[V(1+.000056*90)'] =(8.9)(1+.00018*90)/[(1+.000056*90)(13.6)]
= .6617 = 66.17%

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