Part 2!!!!
An object weighing 305 N in air is immersed
in water after being tied to a string connected
to a balance. The scale now reads 270 N .
Immersed in oil, the object appears to weigh
279 N .
Find the density of the object.
Answer in units of kg/m3
To find the density of the object, we can use the concept of buoyancy and Archimedes' principle.
Step 1: Find the buoyant force in water:
The difference between the weight of the object in air and its weight in water is equal to the buoyant force acting on it when submerged in water.
Buoyant force = Weight in air - Weight in water
Buoyant force in water = 305 N - 270 N = 35 N
Step 2: Find the buoyant force in oil:
Similarly, the difference between the weight of the object in air and its weight in oil is equal to the buoyant force acting on it when submerged in oil.
Buoyant force in oil = Weight in air - Weight in oil
Buoyant force in oil = 305 N - 279 N = 26 N
Step 3: Find the volume of the object:
The volume of the object can be calculated using the formula:
Volume = Buoyant force / Density of the fluid
We need to find the volumes for both water and oil.
Volume in water = Buoyant force in water / Density of water
Volume in oil = Buoyant force in oil / Density of oil
Step 4: Find the densities:
Using the formula for density:
Density = Mass / Volume
We can rearrange the formula to solve for mass.
Mass = Density * Volume
Substituting the values we have:
Mass in water = Density of water * Volume in water
Mass in oil = Density of oil * Volume in oil
Step 5: Equate the masses and volumes:
Since the object has the same mass in both water and oil, we can equate the two mass expressions.
Density of water * Volume in water = Density of oil * Volume in oil
Step 6: Solve for the density of the object:
Density of the object = Mass / Volume, which is equal to the density of water or oil.
Therefore, the density of the object is equal to the density of water, which is approximately 1000 kg/m^3 (or 1 g/cm^3).