A density bottle weighs 0.25N when empty and 0.75 when filled with water and 0.65N when filled with alcohol.Calculate
i)volume of the bottle
Ii)the density of alcohol
Density of water =1000kg/m³
Acceleration due to gravity=10m/s²
To find the volume of the bottle, we need to determine the difference in weight when it is filled with water and when it is empty.
Weight when filled with water = 0.75N
Weight when empty = 0.25N
Weight of water = Weight when filled with water - Weight when empty
Weight of water = 0.75N - 0.25N
Weight of water = 0.5N
We know that weight = mass × acceleration due to gravity.
Weight of water = mass of water × acceleration due to gravity
Mass of water = Weight of water / acceleration due to gravity
Mass of water = 0.5N / 10m/s²
Mass of water = 0.05 kg
The density of water is given as 1000 kg/m³.
Density of water = Mass of water / Volume of water
Volume of water = Mass of water / Density of water
Volume of water = 0.05 kg / 1000 kg/m³
Volume of water = 5 × 10^(-5) m³
Therefore, the volume of the bottle is 5 × 10^(-5) m³.
To find the density of alcohol, we need to determine the difference in weight when the bottle is filled with alcohol and when it is empty.
Weight when filled with alcohol = 0.65N
Weight when empty = 0.25N
Weight of alcohol = Weight when filled with alcohol - Weight when empty
Weight of alcohol = 0.65N - 0.25N
Weight of alcohol = 0.4N
We know that weight = mass × acceleration due to gravity.
Weight of alcohol = mass of alcohol × acceleration due to gravity
Mass of alcohol = Weight of alcohol / acceleration due to gravity
Mass of alcohol = 0.4N / 10m/s²
Mass of alcohol = 0.04 kg
We can use the formula density = mass / volume to find the density of alcohol.
Density of alcohol = Mass of alcohol / Volume of alcohol
Density of alcohol = 0.04 kg / Volume of alcohol
Since the volume of the bottle is the same when it is filled with water or alcohol (the volume of the bottle remains constant), we can use the previously calculated volume of the bottle to find the density of the alcohol.
Density of alcohol = 0.04 kg / (5 × 10^(-5) m³)
Density of alcohol = 800 kg/m³
Therefore, the density of alcohol is 800 kg/m³.
To calculate the volume of the bottle, we need to use the principle of buoyancy and Archimedes' principle:
i) Volume of the bottle:
The difference between the weight of the empty bottle and the weight of the bottle when filled with water gives us the weight of the water displaced. Similarly, the difference between the weight of the empty bottle and the weight of the bottle when filled with alcohol gives us the weight of the alcohol displaced.
Let's calculate the volume of the bottle step by step.
1. Calculate the weight of water displaced:
Weight of water displaced = Weight of filled bottle - Weight of empty bottle
Weight of water displaced = 0.75 N - 0.25 N
Weight of water displaced = 0.5 N
2. Calculate the volume of water displaced:
Density of water = 1000 kg/m³
Weight of water displaced = Density of water × Volume of water displaced × acceleration due to gravity
0.5 N = 1000 kg/m³ × Volume of water displaced × 10 m/s²
Volume of water displaced = 0.5 N / (1000 kg/m³ × 10 m/s²)
Volume of water displaced = 0.05 m³
3. Calculate the volume of the bottle:
The volume of the bottle is equal to the volume of the water displaced because when the bottle is completely filled, it displaces an equal volume of liquid.
Therefore, the volume of the bottle is 0.05 m³.
ii) Density of alcohol:
To calculate the density of alcohol, we need the mass of alcohol and the volume of the bottle.
1. Calculate the weight of alcohol displaced:
Weight of alcohol displaced = Weight of filled bottle - Weight of empty bottle
Weight of alcohol displaced = 0.65 N - 0.25 N
Weight of alcohol displaced = 0.4 N
2. Calculate the mass of alcohol displaced:
Weight of alcohol displaced = mass of alcohol displaced × acceleration due to gravity
0.4 N = mass of alcohol displaced × 10 m/s²
mass of alcohol displaced = 0.4 N / (10 m/s²)
mass of alcohol displaced = 0.04 kg
3. Calculate the density of alcohol:
Density of alcohol = mass of alcohol displaced / Volume of the bottle
Density of alcohol = 0.04 kg / 0.05 m³
Density of alcohol = 0.8 kg/m³
Therefore,
i) The volume of the bottle is 0.05 m³.
ii) The density of alcohol is 0.8 kg/m³.