If your boat weighs 1400 N, how much water will it displace when it’s floating motionless at the surface of a lake?
To calculate the amount of water displaced by the boat, we can use Archimedes' principle. This principle states that the buoyant force acting on a submerged object is equal to the weight of the water displaced by the object.
The formula to calculate the volume of water displaced is: V = W / ρg
Where:
V = Volume of water displaced (in cubic meters)
W = Weight of the boat (in Newtons)
ρ = Density of water (approximately 1000 kg/m^3)
g = Acceleration due to gravity (approximately 9.8 m/s^2)
Given:
Weight of the boat (W) = 1400 N
By substituting these values into the formula, we can calculate the volume of water displaced:
V = 1400 N / (1000 kg/m^3 * 9.8 m/s^2)
V ≈ 0.143 m^3
Therefore, the boat will displace approximately 0.143 cubic meters of water when it's floating motionless at the surface of a lake.
To find out how much water the boat will displace when it's floating motionless at the surface of a lake, we need to understand the concept of buoyancy.
Buoyancy is the upward force exerted by a fluid on an object immersed in it. According to Archimedes' principle, the buoyant force is equal to the weight of the fluid displaced by the object.
In this case, the boat weighs 1400 N. The weight of the water displaced will be equal to the buoyant force, which is also 1400 N.
Now, to calculate the volume of water displaced, we can use the formula:
Volume = Weight of the water displaced / Density of water
The density of water is approximately 1000 kg/m^3.
Converting the weight in newtons to kilograms:
Weight in kg = Weight in N / 9.8 (acceleration due to gravity)
Weight in kg = 1400 N / 9.8 ≈ 142.86 kg
Now, we can calculate the volume of water displaced:
Volume = 142.86 kg / 1000 kg/m^3 ≈ 0.14286 m^3
Therefore, the boat will displace approximately 0.14286 cubic meters (or 142.86 liters) of water when it's floating motionless at the surface of the lake.