A solid has a mass of 200g in air and when partly immersed in a certain liquid it has a mass of 160g. Given that the relative density of the liquid is 0.80, calculate the volume of the solid immersed in the liquid.
dude u waited 1 minute
Archimedes says volume of fluid displaced times its density = kilograms of buoyancy
0.200 - 0.1600 = .8 (1000 kg/m^3 ) (volume in m^3)
or in your units density water = 1 g / cm^3
200 - 160 = .8 V in cm^3
and please forward emergency funds for emergency response by dumb old retired engineer volunteer.
To calculate the volume of the solid immersed in the liquid, we need to use the concept of relative density and the Archimedes' principle. Here's how to solve the problem step-by-step:
Step 1: Understand the concept of relative density. Relative density, also known as specific gravity, is the ratio of the density of a substance to the density of a reference substance (usually water). In this case, the relative density of the liquid is given as 0.80.
Step 2: Determine the density of the liquid. Since the relative density is the ratio of the density of the liquid to the density of water, we can calculate the density of the liquid by multiplying 0.80 with the density of water. The density of water is approximately 1000 kg/m^3, but we need to convert it to g/cm^3 to match the given mass units. Therefore, the density of water is 1 g/cm^3.
Density of liquid = Relative density x Density of water
= 0.80 x 1 g/cm^3
= 0.80 g/cm^3
Step 3: Apply Archimedes' principle. According to Archimedes' principle, the buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid displaced by the object. In other words, the buoyant force is equal to the weight of the liquid pushed out of the way by the immersed solid.
The weight of the liquid displaced = Mass of the liquid displaced x Acceleration due to gravity
Step 4: Calculate the weight of the liquid displaced. Since the solid has a mass of 200g in air and 160g when partly immersed in the liquid, the weight of the liquid displaced is the difference in the weights.
Weight of the liquid displaced = Weight in air - Weight in liquid
= 200g - 160g
= 40g
Step 5: Convert the weight of the liquid displaced into mass, as the density of the liquid is given in grams per cubic centimeter (g/cm^3). Since the acceleration due to gravity is approximately 9.8 m/s^2, we can use the equation:
Weight = Mass x Acceleration due to gravity
40g = Mass x 9.8 m/s^2
Solving for mass:
Mass = 40g / 9.8 m/s^2
= 4.08g
Step 6: Calculate the volume of the solid immersed in the liquid. Using the formula for density:
Density = Mass / Volume
Volume = Mass / Density
Given that the mass of the solid is 4.08g and the density of the liquid is 0.80 g/cm^3, we can now calculate the volume:
Volume = Mass / Density
= 4.08g / 0.80 g/cm^3
= 5.1 cm^3
Therefore, the volume of the solid immersed in the liquid is 5.1 cm^3.