A block of wood of density 0.6g/cm, weighing 3.0N in air, floats freely in a liquid of density 0.8g/cm. Calculate the volume of the portion immersed (g=10ms)
To calculate the volume of the portion of the block immersed in the liquid, we need to use 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.
First, let's find the weight of the block of wood in air. We are given that it weighs 3.0N.
Next, let's find the weight of the block of wood in the liquid. The weight of the block in the liquid is equal to the buoyant force acting on it. The buoyant force is given by the equation:
Buoyant force = Weight of the liquid displaced
The weight of the liquid displaced is equal to the weight of the portion of the block immersed in the liquid. Let's denote the volume of the portion immersed as V.
The weight of the liquid displaced can be calculated as follows:
Weight of the liquid displaced = Density of the liquid * Volume of the liquid displaced * acceleration due to gravity
The density of the liquid is given as 0.8g/cm³, and the acceleration due to gravity is approximately 10 m/s².
Since the block of wood weighs 3.0N in air and the weight of the liquid displaced is equal to the weight of the portion of the block immersed, we can set up the following equation:
3.0N = 0.8g/cm³ * V * 10m/s²
Now we need to convert the density from g/cm³ to kg/m³ to make sure the units are consistent.
0.8g/cm³ = 800 kg/m³ (since 1 g/cm³ = 1000 kg/m³)
Therefore, we have:
3.0N = 800 kg/m³ * V * 10m/s²
Simplifying the equation further, we have:
3 = 800 * V * 10
Dividing both sides by 800 * 10, we get:
V = 3 / (800 * 10)
V ≈ 0.000375 m³
So the volume of the portion immersed is approximately 0.000375 cubic meters.