An object hanging on a scale reads 24.0g when submerged in water, but 48.0g when submerged in oil (specific gravity 0.80) Find the density of the object.
assume Mass M for the object.
in water, 24=M-densitywater*volume
in oil, 48=M- densityoil*volume
subtract top equation from bottom.
24=densitywater*volume-densitoil*volume
volume=24/(1-.8) cm^3
volume= 120cm^3
Now, solve for M.
24=M-1*120
M=144grams
density=144/120 g/cm^3
To find the density of the object, we need to use the concept of specific gravity.
The specific gravity of a substance is the ratio of its density to the density of a reference substance, usually water. In this case, the reference substance is water.
Given that the object reads 24.0g when submerged in water, we can use this information to determine the density of the object.
First, we need to find the volume of the object submerged in water. We can use the formula:
Density = Mass / Volume
Rearranging the formula, we have:
Volume = Mass / Density
Substituting the given values, we get:
Volume = 24.0g / Density of water
Next, we need to find the volume of the object submerged in oil. Since the specific gravity of oil is given as 0.80, we know that the density of oil is 0.80 times the density of water.
Therefore, the volume of the object submerged in oil is:
Volume = Mass / (0.80 * Density of water)
Given that the mass of the object submerged in oil is 48.0g, we can plug in the values:
48.0g = Mass / (0.80 * Density of water)
Now, we have two equations:
Volume = 24.0g / Density of water
48.0g = Mass / (0.80 * Density of water)
Since both volumes are the same (the object doesn't change), we can equate the two equations:
24.0g / Density of water = Mass / (0.80 * Density of water)
We can cancel out the densities of water on both sides, resulting in:
24.0g = Mass / 0.80
To find the mass, we multiply both sides by 0.80:
Mass = 24.0g * 0.80 = 19.2g
Now we can plug the mass back into the equation:
19.2g = Mass / Density of water
Rearranging the equation, we have:
Density of water = Mass / 19.2g
Plugging in the mass, we get:
Density of water = 19.2g / 19.2g = 1g/cm^3
So, the density of the object is 1g/cm^3.