A 1.2 kg rectangular air mattress is 2.1 m
long, 0.46 m wide, and 0.09 m thick.
If it has a mass of 1.2 kg , what additional
mass can it support in water?
Buoyancy Force equals
Fb=(pObject-pFluid)*Volume*Gravity
p=density=m/v
density of mattress equals
pObject=1.2/(2.1*0.46*0.09)=13.8026225 kg/m^3
(13.8026225-1000(density of water))*0.8694*9.8
Take absolute value and the answer is
11.76
To find the additional mass that the air mattress can support in water, we need to calculate the buoyant force acting on the air mattress in water and then convert it to additional mass.
The buoyant force is equal to the weight of the water displaced by the object. The weight of the water displaced is given by the formula:
Weight of water displaced = density of water * volume of water displaced * acceleration due to gravity
The density of water is approximately 1000 kg/m^3, and the volume of water displaced is equal to the volume of the air mattress. The volume of the air mattress is given by:
Volume = length * width * thickness
Substituting the given values:
Volume = 2.1 m * 0.46 m * 0.09 m
Once we have calculated the volume of water displaced, we can calculate the weight of water displaced using the density of water.
Finally, we can calculate the additional mass that the air mattress can support by converting the weight of water displaced to mass using the equation:
Additional mass = Weight of water displaced / acceleration due to gravity
The acceleration due to gravity is approximately 9.8 m/s^2.
By following these steps and performing the necessary calculations, we can find the additional mass that the air mattress can support in water.