a 1.6kg block of wood is floating in water. what is the magnitude of the buoyant force the block?
To find the magnitude of the buoyant force on the block of wood, we need to use Archimedes' principle. The buoyant force is equal to the weight of the water displaced by the object.
To determine the weight of the water displaced, we can use the formula:
Weight of water displaced = Density of water × Volume of water displaced × Acceleration due to gravity
The density of water is approximately 1000 kg/m³, and the acceleration due to gravity is 9.8 m/s². The volume of water displaced is equal to the volume of the block of wood, as long as the wood is fully submerged.
Now, let's find the volume of the wood block:
Density = Mass / Volume
We know the mass of the wood block is 1.6 kg, and since the density of wood can vary depending on the type, let's assume a typical value of around 700 kg/m³ for wood.
700 kg/m³ = 1.6 kg / Volume
Volume = 1.6 kg / 700 kg/m³
Volume ≈ 0.0023 m³
Therefore, the volume of water displaced by the block of wood is 0.0023 m³.
Now, we can calculate the magnitude of the buoyant force:
Buoyant force = Density of water × Volume of displaced water × Acceleration due to gravity
Buoyant force = 1000 kg/m³ × 0.0023 m³ × 9.8 m/s²
Buoyant force ≈ 22.54 N
So, the magnitude of the buoyant force acting on the block of wood is approximately 22.54 Newtons.