If a force of 10 N is required to keep a piece of wood 1m under water (density=1g/cm3
), the force needed to
keep it at 2 m under water is:
To determine the force needed to keep the wood at 2m under water, we need to understand the concept of buoyancy and the principle of Archimedes.
The buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid displaced by the object. According to Archimedes' principle, an object submerged in a fluid experiences an upward buoyant force equal to the weight of the fluid it displaces.
Since the wood is submerged in water, it displaces an amount of water equal to its volume. The volume of the wood can be calculated using its density and the given mass.
Given that the density of water is 1 g/cm³ and we know the density of the wood is also 1 g/cm³, we can assume that the wood is neutrally buoyant, meaning it neither sinks nor floats. This means that the weight of the submerged wood is equal to the buoyant force acting on it.
Now, we can calculate the force required to keep the wood at 2m under water.
The force required to keep an object submerged is equal to the weight of the object.
To determine the weight, we can use the formula:
Weight = Mass x Acceleration due to gravity
The density of water is 1 g/cm³, which means 1 cm³ of water has a mass of 1 gram. We assume the wood has the same density as water, so its mass is also 1 gram.
We need to convert the mass to kg since the SI unit of force is Newtons (N), and the SI unit of mass is kilograms (kg). 1 gram is equal to 0.001 kilograms.
Weight = 0.001 kg x 9.8 m/s² (acceleration due to gravity)
Therefore, the weight of the submerged wood is 0.0098 N.
So, the force needed to keep the wood at 2m under water is also 0.0098 N.