Volume of Submerged Solid: Solve Given Densities

[stratomire]

Homework Statement

Problem : An object is solid throughout. When the object is completely submerged in ethyl alcohol, its apparent weight is 15.2N. When completely immersed in water, its apparent weight is 13.7 N. What is the volume of the object? (The density of ethyl alcohol is 806 kg/m3 )

Homework Equations

SG = (W_A - W_L) / (W_A - W_W)

SG = ρL/ρW

ρ = m/v

W_A = mg

The Attempt at a Solution

I tried answering the problem by using the equation for specific gravity of a liquid lighter than water, which is:

SG = (W_A - W_L) / (W_A - W_W)

I know that SG can also be expressed as ρL/ρW, and from that I tried solving for V and got this equation:

V = (ρ_L W_A - ρ_W W_L) / [(ρ_L ρ_W) (g) (ρ)] ; g is 9.8 m/s2.

From this point on I was stuck.

I know the densities of water and ethyl alcohol because it was given but I don't know the density of the object so I just can't directly substitute the values. Because of this I am in great need of help, I can't think of another way to solve for the object's volume. Can you guys help me a little?

Thank you to those who'll be reading this and to those who'll try to help.

 

[alphysicist]

Hi stratomire,

Homework Statement

Problem : An object is solid throughout. When the object is completely submerged in ethyl alcohol, its apparent weight is 15.2N. When completely immersed in water, its apparent weight is 13.7 N. What is the volume of the object? (The density of ethyl alcohol is 806 kg/m3 )

Homework Equations

SG = (W_A - W_L) / (W_A - W_W)

I don't recognize this equation in the context of this problem. Isn't this related to the s.g. of a mixture?

Anyways, I don't think the specific gravity is the way to think approach this. Instead, when the problem says that the apparent weight in alcohol is 15.2N, how are the buoyant force and gravitational force related? What equation can you get from that?

Do the same for the apparent weight in water, and you should find two equations with two unknowns.