Question

An object is solid throughout. When the object is completely submerged in ethyl alcohol, its apparent weight is 17.0 N. When completely submerged in water, its apparent weight is 13.7 N. What is the volume of the object?

Answer 1

The Archimedes Principle which governs buoyancy says that the upward force which keeps things afloat is equal to the weight of the fluid which is displaced by the object.

We can use this to set up two free-body equations, both along the same lines:

Net force (N) = Weight (W) of the object - Buoyant (upward) force (B) on the object

N = W - B

B = Density*Volume*(gravitational acceleration, g)

Ethyl alcohol has a specific gravity of 0.789, which means that it is 78.9% as dense as water: 789 kg/m^3

So, for ethyl alcohol,

17.0 N = W - (789 kg/m^3)*(9.8 m/s^2)*V

For water,

13.7 N = W - (1000 kg/m^3)*(9.8 m/s^2)*V

Subtract the second equation from the first equation to get

3.3 N = V*(9.8 m/s^2)*(-789kg/m^3 + 1000 kg/m^3)

V = 3.3/(9.8*211) m^3

V = 0.001595899 m^3 = 1595.899 cm^3