Suppose you are drifting on a lake in a boat that measures 1 m high, 1 m wide, and 3 m long. The water level reaches halfway up the boat.
1. What is the volume of water that is displaced by the boat? (density of water = 1000 kg/m^3 or 1.00 g/cm^3).
2. What is the mass of the water displaced?
3. If the liquid were different than water, would your answers change? If so, which ones and how? What information would you need to know about the fluid?
Wouldn't this just be yes because the density of the liquid would be different from water? Oil would be an example, which is less dense than water?
Use Archemides' Principle to answer this problem
Yes, the answers will be different if the density of the liquid changes.
Apparently, I can't use Archemides' Principle because we have not covered it in class.
The buoyancy force equals the weight of the fluid displaced. That is what the principle says.
To find the answers to these questions, we need to understand the concept of displacement and how it relates to volume and mass.
1. Volume of water displaced:
The volume of water displaced by an object submerged in it is equal to the volume of the object itself. In this case, the boat measures 1 m high, 1 m wide, and 3 m long. So, the volume of water displaced by the boat is:
Volume = Length x Width x Height = 3 m x 1 m x 0.5 m (since the water level reaches halfway up the boat) = 1.5 cubic meters.
2. Mass of the water displaced:
To calculate the mass of the water displaced, we need to use the density of water. Given that the density of water is 1000 kg/m^3, we can use the formula:
Mass = Density x Volume = 1000 kg/m^3 x 1.5 m^3 = 1500 kilograms.
Therefore, the mass of the water displaced is 1500 kilograms.
3. Effect of a different liquid:
If the liquid were different from water, the answers would change since different liquids have different densities. The volume of liquid displaced would remain the same since it depends on the physical dimensions of the boat. However, the mass of the liquid displaced would differ according to the density of that particular liquid.
For example, if the liquid were oil, which has a lower density than water, the mass of the displaced liquid would be lower compared to water. To determine the new mass, you would need to know the density of the specific liquid in question.
So, to find the mass of the liquid displaced, you would need to know the density of the liquid and apply the formula: Mass = Density x Volume, where the volume remains the same regardless of the type of liquid.