To solve this problem it is necessary to apply the concepts related to the Conservation of Energy, for which it is necessary that any decrease made through the potential energy, is equivalent to the gain given in the kinetic energy or vice versa.
Mathematically this can be expressed as
![KE_i+PE_i = KE_f+PE_f](https://tex.z-dn.net/?f=KE_i%2BPE_i%20%3D%20KE_f%2BPE_f)
Since there is no final potential energy (the height is zero), and the initial potential energy is equivalent to the work done we have to
![W = KE_f-KE_i-PE_i](https://tex.z-dn.net/?f=W%20%3D%20KE_f-KE_i-PE_i)
![W = \frac{1}{2}mv_f^2-\frac{1}{2}mv_i^2 -mgh](https://tex.z-dn.net/?f=W%20%3D%20%5Cfrac%7B1%7D%7B2%7Dmv_f%5E2-%5Cfrac%7B1%7D%7B2%7Dmv_i%5E2%20-mgh)
![W =\frac{1}{2} m(v_f^2-v_i^2)-mgh](https://tex.z-dn.net/?f=W%20%3D%5Cfrac%7B1%7D%7B2%7D%20m%28v_f%5E2-v_i%5E2%29-mgh)
![W= \frac{1}{2}(73)(8.5^2-1.6^2)-(73*9.8*1.6)](https://tex.z-dn.net/?f=W%3D%20%5Cfrac%7B1%7D%7B2%7D%2873%29%288.5%5E2-1.6%5E2%29-%2873%2A9.8%2A1.6%29)
![W= 1399.045J](https://tex.z-dn.net/?f=W%3D%201399.045J)
![W= 1.4kJ](https://tex.z-dn.net/?f=W%3D%201.4kJ)
Therefore the non-conservative work was done on the boy is 1.4kJ
The electrons are removed from the rod and transferred to the silk cloth. This leaves the rode positively charged and the cloth negatively charged.
This can be solve using snell's law. snell's law equation is :
N1 / N2 = sin a2 / sin a1
where N1 is the index of refraction of the air which is equal to 1
N2 is the index of refraction of the medium
a2 is the angle of refraction
a1 is the incident angle
subsitute the given values
1 / N2 = 0.173 / 0.217
N2 = 1 ( 0.217 / 0.173)
N2 = 1.25 is the index of refraction