Question

According to one set of measurements, the tensile strength of hair is 196 MPa , which produces a maximum strain of 0.380 in the hair. The thickness of hair varies considerably, but let's use a diameter of 50.0 μm

Part A
What is the magnitude of the force giving this tensile stress?
F = ? N

Part B
If the length of a strand of the hair is 12.0 cm at its breaking point, what was its unstressed length? original length = ?cm

Answer 1

(a). The magnitude of the force is 0.38416 N.

(b). The original length is 0.0869 m.

Step-by-step 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

`A=(\pi)/(4)* d^2`

Put the value into the formula

`A=(\pi)/(4)*(50.0*10^(-6))^2`

`A=1.96*10^(-9)\ m^2`

We need to calculate the magnitude of the force

Using formula of force

`F=\sigma A`

Put the value into the formula

`F=196*10^(6)*1.96*10^(-9)`

`F=0.38416\ N`

(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

`strain=(\Delta l)/(l_(0))`

`\Delta l=strain* l_(0)`

Put the value into the formula

`\Delta l=0.380* l_(0)`

Length after expansion is 12 cm

We need to calculate the original length

Using formula of length

`l=l_(0)+\Delta l`

Put the value into the formula

`I=l_(0)+0.380* l_(0)`

`l=1.38l_(0)`

`l_(0)=(l)/(1.38)`

`l_(0)=(12*10^(-2))/(1.38)`

`l_(0)=0.0869\ m`

Hence, (a). The magnitude of the force is 0.38416 N.

(b). The original length is 0.0869 m.