Question

Suppose your hair grows at the rate 1/34 in. per day. Find the rate at which it grows in nanometers per second. Because the distance between atoms in a molecule is on the order of 0.1 nm, your answer suggests how rapidly layers of atoms are assembled in this protein synthesis.

Answer 1

1 inch= 0.0254m  

1m= 1x10^9nm  

0.0254m= 2.54x10^7nm  

1/32(2.54x10^7)= 7.9375x10^5nm  

1 day= 24 hrs  

= (24x60)min  

= (24x60x60)sec  

= 8.64x10^4sec  

In 8.64x10^4 seconds, the hair grows by 7.9375x10^5nm  

Therefore, the amount by which the hair grows in 1 second  

= (7.9375x10^5)/(8.64x10^4)  

= 9.19nm  

The rate of growth is thus 9.19nm/sec.  

I hope this helps. Good luck!

Answer 2

Answer:

Concept:

Protein synthesis, also known as protein biosynthesis, is a fundamental biological activity that takes place inside of cells to counteract the loss of cellular proteins (via export or degradation) by producing new proteins. As structural proteins, hormones, or enzymes, proteins serve a variety of important biological purposes.

Explanation:

Given:

Suppose your hair grows at the rate 1/34 inches per day.

The distance between atoms in a molecule is on the order of 0.1 nm.

Find:

The rate at which it grows in nanometers per second.

Solution:

$Apply \ the \ following \ conversion \ factors: 1 \ in =2.54 \mathrm{~cm}, 1 \mathrm{~d}=86400 \mathrm{~s}, 100 \mathrm{~cm}=1 \mathrm{~m} , and 10^{9} \mathrm{~nm}=1 \mathrm{~m} .$

Then, the rate of hair growth per second is

$rate = \left(\frac{1}{34} \mathrm{in} /\right. day ) \frac{(2.54 \mathrm{~cm} / \mathrm{in})\left(10^{-2} \mathrm{~m} / \mathrm{cm}\right)\left(10^{9} \mathrm{~nm} / \mathrm{m}\right)}{86400 \mathrm{~s} / \mathrm{day}}$

        $=8.65 \mathrm{~nm} / \mathrm{s}$  

This means the proteins are assembled at a rate of many layers of atoms each second.

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