Compute Density & Buoyancy: Metal & Plastic

[JJBrian]

Homework Statement

apparent mass of the metal weight in air = 100g
apparent mass of the metal weight in water = 75g

a)Compute the buoyancy force. From this, compute the volume of the metal. Compute the density of the metal. The density of aluminum is 2.7 g/cm3, of iron is 7.9 g/cm3, and of gold is 19.3g/cm3. Is your metal mostly aluminum, iron, or gold?
b)The mass of a plastic sphere is 110g. Calculate the buoyancy force and use it as above to compute the
density.

The Attempt at a Solution

F bouyancy = density water * vmetal*g
Fbouyancy = Mdw*g

Fbouyancy = (Mmetal in air - Mmetal in water)
Fbouyancy =( 100-75)(9.8) = 245g*m/s^2
F bouyancy = density water * vmetal*g
245g*m/s^2 = 1g/cm^3 *Vmteal*9.8m/s^2
Vmetal = 25cm^3
p = m/v
p = (100g/25cm^3)
p=4g/cm^3
I not too sure if this is correct...
I don't know how to do part b)

 

[ehild]

Your result is correct.

ehild

 

[kerimek]

a) The buoyancy force can be calculated using the formula Fb = ρVg, where ρ is the density of water (1 g/cm^3), V is the volume of the metal, and g is the acceleration due to gravity (9.8 m/s^2). Rearranging the equation to solve for V, we get V = Fb / (ρg). Plugging in the values from the problem, we get V = 245 g*m/s^2 / (1 g/cm^3 * 9.8 m/s^2) = 25 cm^3.

To determine the density of the metal, we can use the formula ρ = m/V, where m is the mass of the metal (100 g) and V is the volume we calculated earlier (25 cm^3). This gives us a density of 4 g/cm^3. Comparing this to the given densities of aluminum, iron, and gold, we can see that the metal is most likely iron, as its density is closest to the calculated value.

b) The buoyancy force for the plastic sphere can be calculated in the same way as in part a), using the density of water (1 g/cm^3) and the mass of the sphere (110 g). This gives us a buoyancy force of 110 g*m/s^2. To find the volume of the sphere, we can use the formula V = Fb / (ρg), where ρ is the density of water (1 g/cm^3) and g is the acceleration due to gravity (9.8 m/s^2). Plugging in the values, we get V = 110 g*m/s^2 / (1 g/cm^3 * 9.8 m/s^2) = 11.2 cm^3.

To determine the density of the plastic, we can use the formula ρ = m/V, where m is the mass of the sphere (110 g) and V is the volume we calculated earlier (11.2 cm^3). This gives us a density of 9.8 g/cm^3. Comparing this to the given densities of aluminum, iron, and gold, we can see that the metal is most likely gold, as its density is closest to the calculated value.