Max Load for Beach Mattress on Dead Sea Surface: 142.8 kg

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The maximum load a beach mattress can carry on the surface of the Dead Sea is calculated to be 142.8 kg. This is based on the mattress's volume of 120 L and its mass of 6.0 kg, with the saline water's density at 1240 kg/m3. The buoyant force, determined by the weight of the water displaced, is 1459.728 N. The load capacity is derived by subtracting the weight of the mattress from the buoyant force. The calculations confirm that the mattress can support this maximum load without sinking.
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Homework Statement


A beach mattress filled with air has a volume of 120 L and a mass of 6.0 kg. The saline
water of the Dead Sea has a density of 1240 kg/m3. Assume that the mattress retains its
shape and volume regardless of load.

Homework Equations


What is the maximum load the mattress can carry on the surface of the Dead Sea?

The Attempt at a Solution


Wwater displaced = 1240*0.12*9.81 = 1459.728 N and that's the buoyancy force ''buoyant force'' Fb

Fb=Wmattress+Wload
Wload=Fb-Wmattress
mload*g=Fb-mmattress*g
mload=(Fb-mmattress*g)/g
mload=(1459.728-6*9.81)/9.81
mload=142.8 Kg
 
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It looks good.

Note: mload = (1459.728-6*9.81)/9.81 = (1240*0.120*9.81-6*9.81)/9.81 = (1240*0.120-6) = 142.8 kg
 
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