An object has a weight of 265 N and the apparent weight of the water at 20 °C is 186.5. Calculate the Archimedes force and the volume of the object Formula = Fa=Fz=m×g=rou×V×g What we know is the Archimedes force 265N-186.5N=78.5N Now I’m stuck? I’ve tried reshaping the formulas to achieve the volume and I always come up with something big.

## Answer

Dear Dynamo,

Indeed the Archimedean force will be equal to the difference between the weight (m*g=265N) and the apparent weight (m*g – Fa = Fapparent –> 265N – Fa = 186.5N –> Fa = 78.5N).

What else do we know? We know that the Archimedean force = Rho*g*V. But what do those symbols represent? Well, Rho is the density, but not the density of the object, but the density of the gas or liquid in which the object is located. g is the acceleration of gravity (9.81m/s²). And V is the volume of gas/liquid that is displaced by the object. (This is not necessarily the same as the volume of the object, for example think of an ice floe that is still part above the water, or a boat that has not sunk .)

We now know that 78.5N=Rho_{water} *g*v_{waterway printed} .

The density of water is not constant (Unless this is given in a physics problem, it is assumed to be 1000kg/m³…but since we know the temperature here, we know that the density of water at 20° = 998.2071 kg/m³ )

Entering and calculating yields the following result:

v_{waterway printed} = 78.5N / (998.2071 kg/m³ * 9.81m/s²) = 0.008016m³ = 8.016 dm³ = 8.016 liters.

I hope this helps you forward.

Danny

## Answered by

#### Dr. Danny Vanpoucke

Computational materials research

Agoralaan University Campus Building D BE-3590 Diepenbeek

http://www.uhasselt.be/

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