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

[chawki]

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

W_{water displaced} = 1240*0.12*9.81 = 1459.728 N and that's the buoyancy force ''buoyant force'' Fb

Fb=W_mattress+W_load
W_load=Fb-W_mattress
m_load*g=Fb-m_mattress*g
m_load=(Fb-m_mattress*g)/g
m_load=(1459.728-6*9.81)/9.81
m_load=142.8 Kg

 

[SammyS]

It looks good.

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