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An object has a volume of 4.0 m^3 and weighs 40,000 N. What will its apparent weight be in water of density 1000 kg/m^3
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Added Mon, 03 Aug '15
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W: actual weight, weight when measured in a vacuum (air is good enough)
B: buoyancy (upward)
N: Normal force from the tub floor (upward)

If the object is negatively buoyant (i.e. sinks), the following force balance holds true
Force balance:
B + N = W

Solve for N:
N = (W - B)

Origin of buoyancy force:
B = rho_water*V*g

Thus:
N = W - rho_water*V*g

Plug in data and check whether or not this comes out to a positive number:
W:=40000 N; rho_water:=1000 kg/m^3; V:=4.0 m^3; g:=9.8 N/kg;

If it comes out negative, it implies that the object will float on the water surface.

Result:
N = 800 Newtons
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