a solid weighs 0.040N in air and 0.025N when fully immersed in a liquid of density 800kg/mcube calculate the volume of the solid
the solid displaces 0.015N of the liquid
convert from weight (N) to mass (kg)
use the density of the liquid to find the volume of liquid displaced
To calculate the volume of the solid, we can use Archimedes' principle. Archimedes' principle states that the buoyant force acting on a submerged object is equal to the weight of the fluid displaced by the object.
Given:
Weight of the solid in air = 0.040 N
Weight of the solid when fully immersed = 0.025 N
Density of the liquid = 800 kg/m^3
Step 1: Calculate the buoyant force
The buoyant force can be calculated as the difference between the weight of the solid in air and the weight of the solid when fully immersed in the liquid:
Buoyant force = Weight in air - Weight when fully immersed
Buoyant force = 0.040 N - 0.025 N
Buoyant force = 0.015 N
Step 2: Calculate the weight of the fluid displaced
The weight of the fluid displaced is equal to the buoyant force, which is 0.015 N.
Step 3: Calculate the volume of the solid
To find the volume of the solid, we can use the equation:
Buoyant force = Density of liquid × Volume of solid × g
0.015 N = 800 kg/m^3 × Volume × 9.8 m/s^2
Rearranging the equation to find Volume:
Volume = Buoyant force / (Density of liquid × g)
Volume = 0.015 N / (800 kg/m^3 × 9.8 m/s^2)
Volume ≈ 1.53 × 10^(-6) m^3
Therefore, the volume of the solid is approximately 1.53 × 10^(-6) cubic meters.