A 0.52 kg piece of wood floats in water but is found to sink in alcohol (specific gravity = 0.79) in which it has an apparent mass of 0.040 kg. What is the SG of the wood?
The specific gravity must be between 1.00 and 0.79 if it sinks in water but not in alcohol.
The apparent mass in alcohol is
V*(wood density) - V*(alcohol density) = 0.040 kg ..after subtracting the bouyant force.
Wood density = alcohol density + 0.040 kg/V = 790 kg/m^3 + 0.040 kg/V
Wood density = 0.52 kg/V
0.48 kg/V = 790 kg/m^3
V = .000608 m^3 = .608 liters
S.G = 0.52 kg/.608 l = 0.855
Well, it seems like the wood is playing hide and seek with its true identity! We have to delve into a little math to find its specific gravity.
In water, the wood floats, which means it displaces an amount of water equal to its own weight. So, the weight of the water displaced is 0.52 kg.
In alcohol, the wood sinks, so it displaces an amount of alcohol equal to its own weight. The apparent mass of the wood is 0.040 kg. Since the specific gravity of alcohol is 0.79, the weight of the alcohol displaced is 0.040 kg * 0.79.
Now, comparing the two displacements, we can set up an equation:
Weight of Water Displaced = Weight of Alcohol Displaced
0.52 kg = 0.040 kg * 0.79
By doing some fancy math gymnastics, we can solve for the specific gravity of the wood:
Specific Gravity = Weight of Wood / Weight of Water Displaced
Specific Gravity = 0.52 kg / (0.040 kg * 0.79)
Specific Gravity ≈ 16.45
So, this elusive piece of wood has a specific gravity of approximately 16.45. It's a little heavier than we originally thought!
To find the specific gravity (SG) of the wood, we need to compare its density to the density of water.
First, let's find the density of water:
Density of water = mass of water / volume of water
Since the wood floats in water, it displaces an amount of water equal to its own weight. Therefore, the volume of water displaced by the wood is the same as the volume of the wood.
We can calculate the volume of water displaced by the wood using its apparent mass and the density of alcohol.
Volume of water displaced = apparent mass of wood / density of water
Next, let's find the density of the wood:
Density of wood = mass of wood / volume of wood
Now, let's calculate the specific gravity of the wood:
SG of wood = density of wood / density of water
Let's plug in the given values for the calculations:
Mass of wood = 0.52 kg
Apparent mass of wood = 0.040 kg
Density of water = 1 kg/L
Density of alcohol = 0.79 * density of water
Calculating step-by-step:
Step 1: Calculate the volume of water displaced by the wood.
Volume of water displaced = apparent mass of wood / density of water
Volume of water displaced = 0.040 kg / 1 kg/L
Volume of water displaced = 0.040 L
Step 2: Calculate the density of the wood.
Density of wood = mass of wood / volume of wood
Density of wood = 0.52 kg / 0.040 L
Density of wood = 13 kg/L
Step 3: Calculate the specific gravity of the wood.
SG of wood = density of wood / density of water
SG of wood = 13 kg/L / 1 kg/L
SG of wood = 13
The specific gravity of the wood is 13.
To find the specific gravity (SG) of the wood, we need to compare its density to the density of water, which has a specific gravity of 1.
First, let's find the density of the wood using the information given. We know the mass of the wood is 0.52 kg. Since the wood floats in water, it is less dense than water. Therefore, we can assume that its density is less than 1000 kg/m^3 (the density of water).
Next, let's find the volume of the wood. We can use the formula:
Density = Mass / Volume
Rearranging the formula, we get:
Volume = Mass / Density
Given that the mass of the wood is 0.52 kg, we need to find the volume of the wood. We divide the mass by the density.
Now, let's find the density of alcohol. The specific gravity of alcohol is given as 0.79. Specific gravity is the ratio of the density of a substance to the density of water. Therefore, the density of alcohol is 0.79 * 1000 kg/m^3.
Next, let's find the mass of the displaced alcohol when the wood is submerged in alcohol. The apparent mass of the wood in alcohol is given as 0.040 kg.
Now, let's find the volume of the displaced alcohol using the formula:
Volume = Mass / Density
Given that the mass of the displaced alcohol is 0.040 kg and the density of alcohol is 0.79 * 1000 kg/m^3, we divide the mass by the density to find the volume.
Finally, let's find the volume of the wood to calculate its density:
Volume of wood = Volume of displaced alcohol
Since the wood displaces an equal volume of alcohol, the volume of the wood is the same as the volume of the displaced alcohol.
Now, we have the mass and volume of the wood. To find the density of the wood, we divide the mass by the volume.
Density of the wood = Mass of the wood / Volume of the wood
Now, the specific gravity of the wood can be calculated by comparing its density to the density of water.
SG of the wood = Density of the wood / Density of water (which is 1000 kg/m^3)
By substituting the calculated density of the wood and the known density of water into the formula, we can find the specific gravity of the wood.