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.
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
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.
where did you got the buoyant force in water?
I'm confused about the "1 g gravitational field". What's the 1 g referring to and why is it 1 g?
It's well known it doesn't need to be given (like the gravitational force)
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.
To find the density of the unknown liquid, we need to use Archimedes' principle, which states that the buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.
Let's break down the problem step-by-step:
1. Calculate the weight of the metal when submerged in water:
Weight in water = Weight in air - Buoyant force in water
Weight in water = 50.0 N - 36.0 N
Weight in water = 14.0 N
2. Calculate the volume of water displaced by the metal:
According to Archimedes' principle, the volume of water displaced is equal to the volume of the metal. Therefore, to calculate the volume of water displaced, we need to know the density of the metal.
3. Calculate the weight of the metal when submerged in the unknown liquid:
Weight in unknown liquid = Weight in air - Buoyant force in unknown liquid
Weight in unknown liquid = 50.0 N - 41.0 N
Weight in unknown liquid = 9.0 N
4. Calculate the volume of the unknown liquid displaced by the metal:
According to Archimedes' principle, the volume of the unknown liquid displaced is equal to the volume of the metal. Therefore, to calculate the volume of the unknown liquid displaced, we again need to know the density of the metal.
5. Finally, calculate the density of the unknown liquid:
Density of the unknown liquid = Weight in unknown liquid / Volume of unknown liquid displaced
Since we don't have information about the density or volume of the metal, we cannot directly determine the density of the unknown liquid using the provided information. Additional information is needed to solve this problem.