Answer:
78kg
Explanation:
Let water density [tex]\rho = 1000 kg/m^3[/tex]. We can calculate the buoyant force generated by water displaced by the air mattress from the volume of the mattress:
[tex]V = l*w*t = 2*0.5*0.08 = 0.08 m^3[/tex]
where l, w, t are the length, width and thickness of the mattress, respectively.
Let g = 10 m/s2. The buoyant force is then:
[tex]F_b = g*V\rho = 0.08 * 1000 * 10 = 800N[/tex]
Let g = 10 m/s2. The gravity force acting on the mattress is
[tex]F_g = mg = 2*10 = 20 N[/tex]
So the mattress can still support an additional gravity of 800 - 20 = 780N or 78kg
The additional mass the rectangular mattress can support in water is 78 kg.
The given parameters;
The volume of the rectangular mattress is calculated as follows;
[tex]V = lwh\\\\V = 2 \times 0.5 \times 0.08\\\\V = 0.08 \ m^3[/tex]
The buoyance force on the rectangular mattress in water is calculated as follows;
[tex]F_b = \rho V g\\\\F_b = 1000 \times 0.08 \times 9.8\\\\F_b = 784 \ N[/tex]
The weight of the mattress is calculated as;
W = mg
W = 2 x 9.8
W = 19.6 N
The additional weight the rectangular mattress can support in water is calculated as follows;
[tex]F = 784 \ N \ - \ 19.6\ N \\\\F= 764.4 \ N[/tex]
The additional mass the rectangular mattress can support in water is calculated as follows;
[tex]m = \frac{F}{g} \\\\m = \frac{764.4}{9.8} \\\\m = 78 \ kg[/tex]
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