Respuesta :
Answer:
(a). The magnitude of the force is 0.38416 N.
(b). The original length is 0.0869 m.
Explanation:
Given that,
Tensile strength = 196 MPa
Maximum strain = 0.380
Diameter = 50.0 μm
Length = 12.0 cm
We need to calculate the area
Using formula of area
[tex]A=\dfrac{\pi}{4}\times d^2[/tex]
Put the value into the formula
[tex]A=\dfrac{\pi}{4}\times(50.0\times10^{-6})^2[/tex]
[tex]A=1.96\times10^{-9}\ m^2[/tex]
We need to calculate the magnitude of the force
Using formula of force
[tex]F=\sigma A[/tex]
Put the value into the formula
[tex]F=196\times10^{6}\times1.96\times10^{-9}[/tex]
[tex]F=0.38416\ N[/tex]
(b). If the length of a strand of the hair is 12.0 cm at its breaking point
We need to calculate the unstressed length
Using formula of strain
[tex]strain=\dfrac{\Delta l}{l_{0}}[/tex]
[tex]\Delta l=strain\times l_{0}[/tex]
Put the value into the formula
[tex]\Delta l=0.380\times l_{0}[/tex]
Length after expansion is 12 cm
We need to calculate the original length
Using formula of length
[tex]l=l_{0}+\Delta l[/tex]
Put the value into the formula
[tex]I=l_{0}+0.380\times l_{0}[/tex]
[tex]l=1.38l_{0}[/tex]
[tex]l_{0}=\dfrac{l}{1.38}[/tex]
[tex]l_{0}=\dfrac{12\times10^{-2}}{1.38}[/tex]
[tex]l_{0}=0.0869\ m[/tex]
Hence, (a). The magnitude of the force is 0.38416 N.
(b). The original length is 0.0869 m.
