Answered

The "lead" in pencils is a graphite composition with a Young's modulus of about 1x10^9 N/m^2 Calculate the change in length of the lead in an automatic pencil if you tap it straight into the pencil with a force of 4.0 N. The lead is 0.50 mm in diameter and 60 mm long. (b) Is the answer reasonable? That is, does it seem to be consistent with what you have observed when using pencils?



Answer :

Answer:

Part a)

[tex]\Delta L = 1.22 mm[/tex]

Part b)

Yes it is reasonable but since this is very small so it is not observable to us while we are using the pencils

Explanation:

As we know that Young's modulus of a given material is

[tex]Y = \frac{stress}{strain}[/tex]

now we have

[tex]stress = \frac{Force}{Area}[/tex]

[tex]stress = \frac{4.0}{\pi r^2}[/tex]

here we know

diameter = 0.50 mm

so we have

[tex]stress = \frac{4.0}{\pi(0.25 \times 10^{-3})^2}[/tex]

[tex]stress = 2.04 \times 10^7 N/m^2[/tex]

now we have

[tex]strain = \frac{stress}{Y}[/tex]

[tex]strain = \frac{2.04 \times 10^7}{1\times 10^9}[/tex]

[tex]strain = 0.0204[/tex]

now we have

[tex]\frac{\Delta L}{L} = 0.0204[/tex]

[tex]\Delta L = (60 mm)(0.0204)[/tex]

[tex]\Delta L = 1.22 mm[/tex]

Part b)

Yes it is reasonable but since this is very small so it is not observable to us while we are using the pencils