A piece of metal with a density of 4.69g/cm^3 and a mass of 1500 grams, is submerged in a container of oil, with a density of .75 g/cm^3. What volume of oil does the metal displace?
Work:
4.69g/cm^3->4690kg/m^3
1500g->1.5kg
.75g/cm^3->750kg/m^3
I'm not sure what equations to use? I know p=m/v and B=pvg.
The volume of the fluid displaced equals the volume of the piece of metal. That volume is mass/density = ??
Check my thinking.
which density do I use?
Use the metal's density, because you want the volume that the metal occupies or "displaces". You don't need the density of oil to answer the question.
To find the volume of oil displaced by the metal, you can use the equation B = pvg, where B is the buoyant force, p is the density of the fluid (oil), v is the volume of the fluid displaced, and g is the acceleration due to gravity.
First, convert the mass of the metal to kilograms:
Mass of metal = 1500 g = 1.5 kg
Next, calculate the buoyant force using the density of the metal, the density of the oil, and the volume of the fluid displaced:
Buoyant force (B) = Density of oil (p) × Density of metal (p) × Volume of oil displaced (v) × g
Since the buoyant force is equal to the weight of the displaced fluid, you can equate it to the weight of the metal:
B = Weight of metal = Mass of metal × g = 1.5 kg × 9.8 m/s^2
Now, you can rearrange the equation to solve for the volume of oil displaced (v):
v = B / (Density of oil × Density of metal × g)
Substitute the given values into the equation:
v = (1.5 kg × 9.8 m/s^2) / (750 kg/m^3 × 4690 kg/m^3 × 9.8 m/s^2)
Simplify the equation:
v = 0.000412 m^3
Therefore, the metal displaces approximately 0.000412 cubic meters (or 0.412 liters) of oil.