Posted by Phillip on Tuesday, December 16, 2008 at 12:15am.
A piece of metal weighs 50.0 N in air, 36.0 N in water, an 41.0 N in an unknown liquid. Find the density of the unknown liquid.

Physics  Buoyant Force  Damon, Tuesday, December 16, 2008 at 3:25am
find volume of metal first
Buoyant force in water = 14 N = weight of water displaced in 1 g gravitational field
mass of water displaced = 14 N/9.8 m/s^2 = 1.43 kg of water displaced
the density of water = 1,000 kg/m^3
so
volume of metal = 1.43*10^3 m^3
Buoyant force in unknown = 50  41 = 9 N
so mass of unknown displace = 9/9.8 = .918 kg
so the density of unknown = .918kg/1.43*10^3 = 642 kg/m^3
or 64.2% of the water density 
Physics  Buoyant Force  Phillip, Tuesday, December 16, 2008 at 8:59am
I'm confused about the "1 g gravitational field". What's the 1 g referring to and why is it 1 g?

Physics  Buoyant Force  Damon, Tuesday, December 16, 2008 at 10:43am
g is the acceleration of gravity which is about 9.8 m/s^2 on the surface of earth.
Since the weights were given in Newtons, a unit of force, not mass, I used weight in Newtons = mass in kilograms * acceleration in meters / second squared to find the mass in kilograms. 
Physics  Buoyant Force  kriz, Wednesday, September 30, 2009 at 12:50pm
where did you got the buoyant force in water?

Physics  Buoyant Force  Mohammed, Wednesday, February 4, 2015 at 5:45pm
It's well known it doesn't need to be given (like the gravitational force)

Physics  Buoyant Force  Thabo, Sunday, May 31, 2015 at 7:52pm
Take the actual weight (in air) of the object and subtract the weight(apparent) the objects seems to have in the unknown fluid ie take 50N and subtract 36N to get 14N which is the buoyant force/upthrust.