6. If your boat weighs 1200 N, how much water will it displace when it’s floating motionless at the surface of the lake?
To determine how much water a boat will displace when it is floating motionless at the surface of a lake, you need to understand the concept of buoyancy. According to Archimedes' principle, an object immersed in a fluid experiences an upward force equal to the weight of the fluid it displaces. This upward force is called buoyant force.
In this case, the weight of the boat, which is 1200 N, is equal to the buoyant force. This means that the boat displaces an amount of water that generates a buoyant force of 1200 N.
Now, let's calculate the volume of water displaced by the boat using the formula:
Buoyant force = Weight of displaced water
We know the density of water (ρ) is approximately 1000 kg/m³ and the acceleration due to gravity (g) is approximately 9.8 m/s². The formula for calculating buoyant force is:
Buoyant force = (density of water) × (volume of water displaced) × (acceleration due to gravity)
Since we want to find the volume of water displaced by the boat, we rearrange the formula:
Volume of water displaced = Buoyant force / (density of water) / (acceleration due to gravity)
Substituting the given values:
Volume of water displaced = 1200 N / (1000 kg/m³) / (9.8 m/s²)
Calculating this equation will give us the volume of water displaced by the boat when it is floating motionless at the surface of the lake.
To determine the amount of water displaced by the boat when it is floating motionless at the surface of the lake, we need to use Archimedes' principle. According to Archimedes' principle, the buoyant force experienced by an object submerged in a fluid is equal to the weight of the fluid displaced by the object.
Step 1: Write down the given information:
- Boat weight = 1200 N
Step 2: Calculate the amount of water displaced:
The weight of the water displaced is equal to the weight of the boat. Therefore, the boat will displace 1200 N of water.
Step 3: Write down the final answer:
The boat will displace 1200 N of water when it is floating motionless at the surface of the lake.