A block of mass 200g and density 0.8g/cm3 is submerged in a liquid of density 0.2g/cm3. find minimum force required to keep the block floating.
If the density of an object is 8 g/m3, and the mass is 200 g.
what is the volume of the object?
To find the minimum force required to keep the block floating, we need to consider the forces acting on the block and apply Archimedes' principle.
Archimedes' principle states that an object partially or fully submerged in a fluid experiences an upward buoyant force equal to the weight of the fluid displaced by the object.
First, calculate the volume of the block:
Volume of the block = mass / density
Volume of the block = 200g / 0.8g/cm³ = 250 cm³
Now, let's calculate the weight of the block:
Weight of the block = mass × acceleration due to gravity
Weight of the block = 200g × 9.8 m/s² = 1960 N
Since the block is floating, it displaces an amount of liquid with the same weight as the block. We can calculate the volume of liquid displaced using the density of the liquid:
Volume of the liquid displaced = weight of the block / density of the liquid
Volume of the liquid displaced = 1960 N / 0.2 g/cm³ = 9800 cm³
So, the minimum force required to keep the block floating is equal to the weight of the liquid displaced:
Force required = weight of the liquid displaced
Force required = density of the liquid × volume of the liquid displaced × acceleration due to gravity
Force required = 0.2 g/cm³ × 9800 cm³ × 9.8 m/s²
Now, let's convert the units to get the final answer:
Force required = 0.2 g/cm³ × 9800 cm³ × 9.8 m/s²
Force required = 0.2 kg/m³ × 0.0098 m³ × 9.8 m/s²
Force required ≈ 0.0392 N
Therefore, the minimum force required to keep the block floating is approximately 0.0392 Newtons.
The volume of the mass is
V = 200/0.8 = 250 cm^3 = 250*10^-6 m^3 and the buoyancy force (up) is
Fb = V*200 kg/m^2*g = 0.49 N.
The weight force (down) is 0.2 kg*g = 1.96 N.
To keep it floating, an upward force of at least 1.96 - 0.49 N = 1.47 N is needed