A sample of an unknown material appears to weigh 285 N in air and 165 N when immersed in alcohol of specific gravity 0.700.
(a) What is the volume of the material?
Answer is in m3
(b) What is the density of the material?
Answer is in kg/m3
To find the volume and density of the unknown material, we need to use the information given about its weight in air and when immersed in alcohol.
(a) Volume of the material:
To find the volume, we need to determine the buoyant force acting on the material when immersed in alcohol.
Buoyant force (Fb) = weight in air - weight in liquid
Given:
Weight in air = 285 N
Weight in alcohol = 165 N
Specific gravity (SG) of alcohol = 0.700
Weight in alcohol = Buoyant force = Fb = ρfluid * g * V
Here, ρfluid is the density of the alcohol, g is gravitational acceleration (approximately 9.8 m/s^2), and V is the volume of the material.
We need to rearrange the equation to solve for the volume (V):
V = Fb / (ρfluid * g)
Substituting the given values, we have:
V = (285 N - 165 N) / ((0.700) * (9.8 m/s^2))
Simplifying the expression, we get:
V = 12.06 m^3 (rounded to two decimal places)
Therefore, the volume of the material is approximately 12.06 m^3.
(b) Density of the material:
To find the density of the material, we can use the formula:
Density (ρ) = Mass (m) / Volume (V)
Since we are not given the mass directly, we need to find it using the weight (W) and the acceleration due to gravity (g).
Given:
Weight in air = 285 N
Weight (W) = m * g
m = W / g
Substituting the given values, we have:
m = 285 N / 9.8 m/s^2
m ≈ 29.08 kg (rounded to two decimal places)
Now, we can calculate the density:
Density (ρ) = 29.08 kg / 12.06 m^3
Density (ρ) ≈ 2.41 kg/m^3 (rounded to two decimal places)
Therefore, the density of the material is approximately 2.41 kg/m^3.
To solve this problem, we can use the concept of buoyancy and apply Archimedes' principle.
(a) In order to find the volume of the material, we need to calculate the apparent weight loss when it is immersed in alcohol.
The apparent weight loss can be calculated using the formula:
Apparent weight loss = Weight in air - Weight in fluid
Weight in air = 285 N
Weight in fluid = Weight in air - Buoyant force
The buoyant force can be calculated using the formula:
Buoyant force = Weight of the fluid displaced
The weight of the fluid displaced can be calculated using the formula:
Weight of the fluid displaced = Density of the fluid * Volume of the fluid displaced * g
where g is the acceleration due to gravity.
Given:
Specific gravity of alcohol = 0.700
Density of alcohol = Specific gravity * Density of water
Density of water = 1000 kg/m^3 (approximately)
g = 9.8 m/s^2 (approximately)
Density of alcohol = 0.700 * 1000 kg/m^3 = 700 kg/m^3
Weight in fluid = 165 N (given)
Buoyant force = Weight in air - Weight in fluid
= 285 N - 165 N
= 120 N
Weight of the fluid displaced = Buoyant force
= 120 N
Now, we can calculate the volume of the material using the formula:
Volume of the fluid displaced = Weight of the fluid displaced / (Density of the fluid * g)
Volume of the fluid displaced = 120 N / (700 kg/m^3 * 9.8 m/s^2)
= 0.017 m^3
Therefore, the volume of the material is 0.017 m^3.
(b) To find the density of the material, we can use the formula:
Density = Mass / Volume
Since we have the weight of the material in air, we can calculate the mass using the formula:
Mass = Weight in air / g
Mass = 285 N / 9.8 m/s^2
≈ 29.08 kg
Density = Mass / Volume
= 29.08 kg / 0.017 m^3
≈ 1709.41 kg/m^3
Therefore, the density of the material is approximately 1709.41 kg/m^3.