First, you make a diagram of all the forces acting on the system. This is shown in the figure. We have to determine F1 and F4. Let's do a momentum balance. Momentum is conserved so the summation of all momentum is equal to zero. Momentum is force*distance.
To determine F1: (reference is F4, so F4=0)
∑Momentum = 0 = -F2 - F3 + F1
0 = (-4 kg)(9.81 m/s2)(0.25m)-(6kg)(9.81 m/s2)(0.5-0.3m)+F1(0.5-0.1m)
F1 = 53.96 N (left knife-edge)To determine F4: (reference is F1, so F1=0)
∑Momentum = 0 = -F2 - F3 + F4
0 = (-4 kg)(9.81 m/s2)(0.25m)-(6kg)(9.81 m/s2)(0.5-0.2m)+F4(0.5-0.1m)
F4 = 68.67 N (right knife-edge)
Answer:
The electric force is ![F = 11.9 *10^{-9} \ N](https://tex.z-dn.net/?f=F%20%3D%20%2011.9%20%2A10%5E%7B-9%7D%20%5C%20N)
Explanation:
From the question we are told that
The Bohr radius at ground state is ![a_o = 0.529 A = 0.529 ^10^{-10} \ m](https://tex.z-dn.net/?f=a_o%20%20%3D%20%200.529%20A%20%3D%20%200.529%20%5E10%5E%7B-10%7D%20%5C%20m)
The values of the distance between the proton and an electron ![z = 2.63a_o](https://tex.z-dn.net/?f=z%20%3D%20%202.63a_o)
The electric force is mathematically represented as
![F = \frac{k * n * p }{r^2}](https://tex.z-dn.net/?f=F%20%20%3D%20%20%5Cfrac%7Bk%20%2A%20n%20%20%2A%20p%20%7D%7Br%5E2%7D)
Where n and p are charges on a single electron and on a single proton which is mathematically represented as
![n = p = 1.60 * 10^{-19} \ C](https://tex.z-dn.net/?f=n%20%3D%20p%20%20%3D%20%20%201.60%20%2A%2010%5E%7B-19%7D%20%5C%20C)
and k is the coulomb's constant with a value
![k =9*10^{9} \ kg\cdot m^3\cdot s^{-4}\cdot A^2.](https://tex.z-dn.net/?f=k%20%3D9%2A10%5E%7B9%7D%20%5C%20kg%5Ccdot%20m%5E3%5Ccdot%20s%5E%7B-4%7D%5Ccdot%20A%5E2.)
substituting values
![F = \frac{9*10^{9} * [(1.60*10^{-19} ]^2)}{(2.63 * 0.529 * 10^{-10})^2}](https://tex.z-dn.net/?f=F%20%3D%20%20%5Cfrac%7B9%2A10%5E%7B9%7D%20%2A%20%20%5B%281.60%2A10%5E%7B-19%7D%20%5D%5E2%29%7D%7B%282.63%20%2A%200.529%20%2A%2010%5E%7B-10%7D%29%5E2%7D)
![F = 11.9 *10^{-9} \ N](https://tex.z-dn.net/?f=F%20%3D%20%2011.9%20%2A10%5E%7B-9%7D%20%5C%20N)