Find the displacement in cubic meters of a boat weighing 4710 N.
To find the displacement of a boat, we can use Archimedes' principle, which states that an object submerged in a fluid experiences a buoyant force equal to the weight of the fluid it displaces.
The buoyant force (FB) acting on the boat is equal to the weight of the fluid displaced by the boat, which is also equal to the weight of the boat itself.
Given:
Weight of the boat (W) = 4710 N
Now, to find the displacement (V) in cubic meters, we need to calculate the volume of the fluid displaced by the boat.
Step 1: Convert the weight from Newtons to kilograms (kg):
1 N is equal to 1 kg*m/s^2
So, 4710 N = 4710 kg*m/s^2
Step 2: Calculate the displacement (V) using the formula:
V = W / ρ * g
where ρ is the density of the fluid and g is the acceleration due to gravity (approximately 9.8 m/s^2 on Earth).
Step 3: Determine the density of the fluid.
To calculate the displacement accurately, we need to know the density of the fluid in which the boat is floating. This could be fresh water, saltwater, or any other fluid.
Let's assume the boat is floating in fresh water, which has a density of approximately 1000 kg/m^3.
Substituting the values into the formula, we get:
V = 4710 kg*m/s^2 / 1000 kg/m^3 * 9.8 m/s^2
Step 4: Calculate the displacement:
V = (4710 / 1000) * (9.8) m^3
V ≈ 4.82 m^3
Therefore, the displacement of the boat is approximately 4.82 cubic meters.