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slega [8]
3 years ago
14

You are trying to determine the specific gravity of a solid object that floats in water. If m is the mass of your object, mS is

the apparent mass of the combination of 2 masses with one (the sinker) submerged, and mOS is the apparent mass of the combination of 2 masses with both submerged, what is the formula for specific gravity
Physics
1 answer:
Alisiya [41]3 years ago
8 0

Answer:

Specific Gravity = m/[m(s)-m(os)]

Explanation:

Specific gravity, also called relative density, is the ratio of the density of a substance to the density of a reference substance. By this definition we need to find out the ratio of density of the object of mass m to the density of the surrounding liquid.

m = mass of the object

<u>Weight in air</u>

W (air) = mg, where g is the gravitational acceleration

<u>Weight with submerged with only one mass</u>

m(s)g + Fb = mg + m(b)g, <em>consider this to be equation 1</em>

where Fb is the buoyancy force

Weight with submerged with both masses

m(os)g + Fb’ = mg + m(b)g, <em>consider this to be equation 2</em>

<u>equation 1 – equation 2 would give us</u>

m(s)g – m(os)g = Fb’ – Fb

where Fb = D x V x g, where D is the density of the liquid the object is submerged in, g is the force of gravity and V is the submerged volume of the object

m(s)g – m(os)g = D(l) x V x g

m(s) – m(os) = D(l) x V

we know that Mass = Density x V, which in our case would be, D(b) x V, which also means

V = Mass/D(b), where D(b) is the density of the mass

<u>Substituting V into the above equation we get</u>

m(s) – m(os) = [D(l) x m)/ D(b)]

Rearranging to get the ratio of density of object to the density of liquid

D(b)/D(l) = m/[m(s)-m(os)], where D(b)/D(l) denotes the specific gravity

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