A 79.3 kg person puts on a life jacket, jumps into the water, and floats. The jacket has a volume of 2.92 x10-2 m3 and is completely submerged under the water. The volume of the person's body that is underwater is 6.62x10-2 m3. a) what is the total volume of water displaced? b) What is the mass of the jacket? c) What is the density of the life jacket?
The volume of water displaced by the person’s body = V =The
volume of the person’s body that is underwater = 6.62 x 10^-2
m^3.
The volume of water displaced by the person’s body = V =6.62 x
10^-2 m^3.
Mass of displaced water = volume*density
Mass of displaced water = 6.62 x 10^-2*1000 = 66.2 kg
Volume of water displaced by jacket = 2.92 x 10^-2 m^3
b)
Weight of water displaced by jacket = [2.92x10^-2]1000 = 29.2
kg
Weight of water displaced by jacket = 29.2 kg
Weight of total water displaced =66.2 + 29.2 =95.4 kg
Weight of total water displaced = weight of person+weight of
jacket
weight of jacket =weight of total water displaced - weight of
person
weight of jacket =95.4 - 79.3 = 16.1 kg
Mass of jacket = 16.1 kg
c)
Density of jacket = mass / volume
Density of jacket = 16.1 / 2.92 x 10^-2 = 551.36 kg/m^3
The density of the life jacket is = 551.36 kg/m^3
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