If your boat weighs 1600 N, how much water will it displace when it’s floating motionless at the surface of a lake?
Archimedes says weight= bouyant force if floating = weight of water displaced = mass of water times g
density of water = 1000 kg/m^3 approximately (lake is fresh water)
1000 * 9.81 * Volume = 1600
I left my husband for a better man
2.4/5
Well, if your boat weighs 1600 N, it better not try to displace 1600 N of water because that would be some next-level boat magic! Maybe it can float motionless by only displacing its own weight in water. So, my guess is that it will displace 1600 N of water. But let's hope it doesn't go around displacing lakes anytime soon!
To determine how much water your boat will displace when it's floating motionless at the surface of a lake, you need to understand the concept of buoyancy.
Buoyancy is the upward force exerted on an object submerged or floating in a fluid, such as water. According to Archimedes' principle, the buoyant force exerted on an object is equal to the weight of the fluid it displaces.
In this case, your boat weighs 1600 Newtons. To find out how much water it will displace, you need to calculate the buoyant force.
The buoyant force (Fb) is equal to the weight of the water displaced by the boat. Mathematically, it can be expressed as:
Fb = ρ × V × g
where ρ is the density of the water, V is the volume of water displaced, and g is the acceleration due to gravity (approximately 9.8 m/s²).
Since we want to find the volume of water displaced, we rearrange the equation as:
V = Fb / (ρ × g)
Now, we need to know the density of water. The density of pure water is approximately 1000 kg/m³.
V = 1600 N / (1000 kg/m³ × 9.8 m/s²)
By performing the calculation, we find:
V ≈ 0.163 m³
Therefore, your boat will displace approximately 0.163 cubic meters of water when floating motionless at the surface of the lake.