Question

Assume that Lee’s foot has a rectangular area of 10cm X 30cm, and that the skin is covered by a uniform layer of carbon atoms. If each carbon atom occupies a square-shaped area of 170pm X 170pm (“pm” is picometer), estimate how much force each carbon atom acts on the ground when Lee is standing with BOTH feet flat on the ground. (Recall that Lee’s mass is 64.5kg.) If we assume this force by each carbon atom is completely supplied by the electric repelling interaction between one electron in the carbon atom and another electron in another atom on the ground, how large the gap between these two atoms would be? Express your final answer in micrometers.

Answer 1

Total force on Lee's foot i.e. on an area of 10cm x 30cm(300 cm² or 0.03 m² ) = Weight of Lee

= 64.5 x 9.8 = 632.1 N

So force on each carbon atom i.e. on an area of 170 pm x 170 pm(i.e. 28900 pm² or 2.89 x 10^-20 m² )

So, force by each carbon atom on the ground must be equals to 6.089 x 10^-16 N.

Force of electrical repulsion between two charge particles is given by

  

Where,

K is a constant and K = 9 x 10⁹ Nm²/C²

q₁ & q₂ is charge on the particle (here electrons have charge 1.602 x 10^-19 C)

r is distance(gap) between two charge particles

According to question,

  

or,   

or,

or,   

or,   

or , r = 0.61 micrometer

For any doubt please comment.