The three particles interact with each other through pairwis

The three particles interact with each other through pair-wise internal forces. The force between any two particles is central. That means force on particle 1 due to particle 2 (denoted by f12) is equal in magnitude and opposite in direction to f2i and along the line joining 1 and 2. Show that the sum of all internal forces is zero. That is Summation_alpha, beta f_alpha beta = 0

Solution

å_, f _,   = (f₁₂ +f₂₁ )+ (f₂₃ + f₃₂) + (f₃₁ + f₁₃)

there can be only 6 possible interation across the 3- particle as described above.

It is given the forces of interaction are central

f₁₂ = - f₂₁, the forces are equal in magnitude and opposite in direction and

(f₂₃ = - f₃₂) and (f₃₁ = - f₁₃)

each of the above pairs get canceled

and

å_, f _,   = 0