A nylon 6 fiber has a diameter of 20 mu m. The volumetric density of nylon 6 is 1.14 g/cm^3. \ 1. Calculate the linear density of the nylon 6 fiber in denier? 2. Is the nylon fiber described a micro fiber?

1. The linear density of the nylon 6 fiber can be calculated as follows: First, we need to convert the diameter from micrometers to centimeters: 20 ?m = 0.002 cm The cross-sectional area of the fiber can be found using the formula for the area of a circle: A = ?r^2 where r is the radius of the fiber, which is half the diameter: r = 0.001 cm A = ?(0.001 cm)^2 A = 0.00000314 cm^2 The mass of the fiber can be calculated using the volumetric density and the volume of the fiber: V = AL where L is the length of the fiber, which we don't know yet. However, we can assume a unit length of 1 meter for the purpose of calculating linear density: V = 0.00000314 cm^2/m ? 1 m = 0.00000314 cm^3 m = ?V m = 1.14 g/cm^3 ? 0.00000314 cm^3 = 0.0000035856 g The linear density, or fineness, of the fiber is simply the mass per unit length: FD = m/L Since we assumed a unit length of 1 meter, FD = m. Finally, we need to convert the linear density from grams per meter to denier, which is a common unit of measure for the fineness of fibers: 1 denier = 0.1111 tex where tex is another unit of measure for fiber fineness, equal to the mass of 1 kilometer of fiber. Denier = FD ? 9.00024 Denier = 0.0000035856 ? 9.00024 Denier ? 0.0323 Therefore, the linear density of the nylon 6 fiber is \approx imately 0.0323 denier. 2. Whether the nylon fiber is considered a micro fiber or not depends on the definition being used. Some sources define a micro fiber as any fiber with a diameter less than 10 ?m, while others use a cutoff of 1 ?m or even 0.3 ?m. Since the diameter of the nylon fiber is 20 ?m, it is unlikely to be considered a micro fiber by most definitions.