[Given]
Fiber Linear Density = 1 denier = 1 g/9000m
Fiber Density = 1.14 g/cm^3
[Find..]
Fiber surface area in cm^2/g
Assume that the fiber strand is a uniform cylinder
[Answer]
Surface area = 3,150 cm^2/g
....... how do i get to the answer? my professor gives us these notes:
Pi*D*L
Pi*D is the diameter of the top of the cylinder when it is cut vertically in half. and L is the height.
((Pi*D^2)/(4)) * L = volume of the cylinder
((Pi*D^2)/(4)) * L * Density = weight
..please help!
If it is a cylinder of length L
volume= PI r^2 *L
Surface area= PI*2(r)L
mass=masslineardensiy*L
density= mass/volume=1.14g/cm^3
fiberarea/g= fiberarea/mass=
PI*2*r*L/massdensity*V=
PI*2r*L/(1.14g/cm^2 * PI*r^2*L)
2cm^2/(1.14g*r)= 2/1.14r g/cm^2
Now, r
linear density=1g/9000m
= mass/L= volumedensity*volume/L
1g/9000m=1.14g/cm^3*PIr^2/L
r^2=1cm^3/(1.14*9000m*PI)
=1/(1.14*900000*PI) cm^2
t hen find the sqrt root of that.
final answer= 2/(1.14r) and it will give you your answer.
how to do surface area
To find the surface area of the fiber in cm^2/g, you can follow these steps:
1. Determine the diameter of the fiber strand:
Given that the linear density of the fiber is 1 denier or 1 g/9000m, we know that 1 g of fiber occupies 9000 meters. The linear density is essentially the mass per unit length of the fiber.
Therefore, the mass of 1 meter of fiber can be calculated as 1 g / 9000m.
2. Convert the fiber density to grams per meter cubed:
The given fiber density is 1.14 g/cm^3, which means that 1cm^3 of fiber weighs 1.14 grams.
3. Calculate the volume of the fiber cylinder:
Using the formula for the volume of a cylinder: volume = (Pi * D^2 / 4) * L, where D is the diameter and L is the length (height). Since we want to find the surface area in cm^2/g, the length can be considered as 1 (1 meter of fiber).
4. Calculate the weight of the fiber:
Multiply the volume of the cylinder by the density of the fiber to obtain the weight of the fiber in grams.
5. Calculate the surface area:
To find the surface area, we need to calculate the circumference of the circular cross-section of the cylinder.
The formula for the circumference of a circle is C = Pi * D.
Since we want to find the surface area per gram, divide the circumference by the weight of the fiber.
Ultimately, the equation for the surface area in cm^2/g can be written as:
Surface Area = (Pi * D) / (Weight)
where D is the diameter of the fiber strand.
By substituting the values for diameter and weight, you can find the surface area in cm^2/g.