A sample of an unknown material appears to weigh 270 N in air and 165 N when immersed in alcohol of specific gravity 0.700.
(a) What is the volume of the material?
(b) What is the density of the material?
YOu know immersed, its bouyancy force is equal to the weight of the displaced medium; Archimedes discovered that. change specific gravity to density.
270-165=densityalcohol*volumedisplaced*g
solve for volume displaced, duh, double duh, that is the volume
density= mass/volume= 270/g * 1/volume in kg/m^3
To find the volume and density of the unknown material, we can use Archimedes' principle, which 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.
Let's break down the problem into two parts:
(a) Finding the volume of the material:
To find the volume of the material, we need to determine the volume of alcohol displaced by the material.
Given:
Weight of the material in air = 270 N
Weight of the material in alcohol = 165 N
The buoyant force acting on the material in alcohol can be calculated as the difference in weight in air and weight in alcohol:
Buoyant force = Weight in air - Weight in alcohol
Buoyant force = 270 N - 165 N
Buoyant force = 105 N
We can now calculate the weight of the alcohol displaced by the material using the specific gravity of alcohol.
Specific gravity is defined as the ratio of the density of a substance to the density of a reference substance, in this case, water.
Given:
Specific gravity of alcohol = 0.700
We know that the density of water is 1000 kg/m³.
Density of alcohol = Specific gravity × Density of water
Density of alcohol = 0.700 × 1000 kg/m³
Density of alcohol = 700 kg/m³
The weight of the alcohol displaced can be calculated using the formula Weight = Density × Volume × gravitational acceleration (W = ρVg), where ρ is density, V is volume, and g is the acceleration due to gravity.
Thus, we have:
Buoyant force = Weight of the alcohol displaced
105 N = (700 kg/m³) × V × (9.8 m/s²)
Rearranging the equation to solve for V:
V = Buoyant force / (Density × gravitational acceleration)
V = 105 N / (700 kg/m³ × 9.8 m/s²)
V ≈ 0.015 m³
Therefore, the volume of the material is approximately 0.015 cubic meters.
(b) Finding the density of the material:
The density of the material can be calculated using the formula Density = Mass / Volume.
Since we already have the volume of the material, we need to find the mass.
Given:
Weight of the material in air = 270 N
Weight is equal to Mass × gravitational acceleration
270 N = Mass × 9.8 m/s²
Solving for Mass:
Mass = 270 N / 9.8 m/s² ≈ 27.55 kg
Now we can calculate the density using the formula Density = Mass / Volume:
Density = 27.55 kg / 0.015 m³
Density of the material ≈ 1836.67 kg/m³
Therefore, the density of the unknown material is approximately 1836.67 kg/m³.