Respuesta :
First off, we have to assume that the 2.8 kg mass of the air matress includes both the material that the matress is constructed from and the air that is contained within.
The mattress can support a total weight that is equal to the weight of water that the air matress displaces.
The volume of the air mattress is:
V(mattress) = (2 m)(0.5 m)(0.1 m) = 0.1 m³
This volume is equal to the maximum amount of water that the matress can displace in the water before it begins sinking.
The density of water is 1000 kg / m²
The weight of the maximum amount of displaced water is:
V(matress) * (density of water) * (g) = (0.1 m³) * (1000 kg / m³) * (9.81 m / s²) = 981 N.
Let m represent the mass that the matress is supporting.
The total weight of the matress and the supported mass is:
(2.8 + m) * 9.81
Setting this weight equal to the weight of the water displaced gives:
(2.8 + m) * 9.81 = 981
2.8 + m = 100
m = 100 - 2.8
m = 97.2 kg
The mattress can support a total weight that is equal to the weight of water that the air matress displaces.
The volume of the air mattress is:
V(mattress) = (2 m)(0.5 m)(0.1 m) = 0.1 m³
This volume is equal to the maximum amount of water that the matress can displace in the water before it begins sinking.
The density of water is 1000 kg / m²
The weight of the maximum amount of displaced water is:
V(matress) * (density of water) * (g) = (0.1 m³) * (1000 kg / m³) * (9.81 m / s²) = 981 N.
Let m represent the mass that the matress is supporting.
The total weight of the matress and the supported mass is:
(2.8 + m) * 9.81
Setting this weight equal to the weight of the water displaced gives:
(2.8 + m) * 9.81 = 981
2.8 + m = 100
m = 100 - 2.8
m = 97.2 kg
Mass the air mattress support before sinking will be M = 97.2 kg
What will be the mass mattress will support?
Given that
mass of mattress m=2.8 kg
Length = 2.00 m
width =0.5 m
The mattress can support a total weight that is equal to the weight of water that the air mattress displaces.
The volume of the air mattress will be equal to
[tex]V= (2\times 0.5\times 0.1)[/tex]
[tex]V= 0.1 m^{3}[/tex]
This volume is equal to the maximum amount of water that the mattress can displace in the water before it begins sinking.
We know the density of water is 1000 kg / m²
We can calculate the weight of the maximum amount of water that mattress will displace
[tex]V\times density of water\times g=0.1\times 1000\times 9.81=981N[/tex]
Let M represent the mass that the mattress is supporting.
The total weight of the mattress and the supported mass is:
[tex](2.8+M)\times9.81[/tex]
Setting this weight equal to the weight of the water displaced gives:
[tex](2.8+M)\times9.81=981[/tex]
[tex]2.8+M=100[/tex]
m = 97.2 kg
Hence Mass the air mattress support before sinking will be M = 97.2 kg
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