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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

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

Added Mon, 03 Aug '15

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