Consider three wooden blocks floating in fresh water. They all have a volume of 1.0 m3. How do you calculate the buoyant forces acting on each block using:
• by applying the condition for static equilibrium: 𝛴𝐹𝑦 = 0
• by the Archimedes’ principle
To calculate the buoyant force acting on each wooden block, you can use either the condition for static equilibrium or Archimedes' principle. Here's how you can apply each method:
1. By applying the condition for static equilibrium: ΣFy = 0
The condition for static equilibrium states that the sum of all forces acting on an object must be zero. In this case, the buoyant force is the only vertical force acting on the block, so we can write the equation as:
ΣFy = F_submerged - F_gravity = 0
To calculate the buoyant force, we need to calculate the weight of water displaced by the block, which is equal to the weight of the block itself. The weight of the block can be calculated using the formula: F_gravity = m x g, where m is the mass of the block and g is the acceleration due to gravity.
Since the volume of the block is given as 1.0 m^3 and the density of fresh water is approximately 1000 kg/m^3, we can determine the mass using the formula: m = density x volume.
Substituting the values, we have:
m = 1000 kg/m^3 x 1.0 m^3 = 1000 kg
Therefore, F_gravity = 1000 kg x 9.8 m/s^2 (assuming g = 9.8 m/s^2) = 9800 N.
Since the buoyant force is equal to the weight of the water displaced, the buoyant force acting on the block is also 9800 N.
2. By using Archimedes' principle:
Archimedes' principle states that the buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.
The volume of the block is given as 1.0 m^3, so the water displaced by the block is also 1.0 m^3.
Using the density of water (1000 kg/m^3) and the formula F_buoyant = density x volume x g, we can calculate the buoyant force:
F_buoyant = 1000 kg/m^3 x 1.0 m^3 x 9.8 m/s^2 = 9800 N.
Hence, according to Archimedes' principle, the buoyant force acting on each block is 9800 N.
Both methods will give you the same result because they are based on the same principles of fluid mechanics.