Question

Two equally charged particles, held 4.2 x 10^-3 m apart, are released from rest. The initial acceleration of the first particle is observed to be 7.4 m/s² and that of the second to be 11 m/s². If the mass of the first particle is 5.9 x 10^-7 kg, what are (a) the mass of the second particle and (b) the magnitude of the charge (in C) of each particle?

Answer 1

For every force there is an equal and opposite reaction force.
In this case the force on one particle is equal but opposite to the force on the other particle.
This follows directly from the conservation of momentum principle.
This is because a force is the rate of change of momentum. F=dP/dT For the total momentum of the system to remain constant or zero the rate that one particle picks up momentum must be equal to the rate that the other particle picks up momentum. (Of course the directions of the momentum will be opposite, just as the directions of the forces on each particle are)

a)That means F1 = F2 (dP1/dT = - dP2/dT)

M1a1 = M2 a2
=> 5.9*10^-7 * 7.4 = 11*m

=> m = 3.97*10^-7 Kg

b) For (b) ,you know the force, and you use the equation below to solve for Q1

F=k* Q1Q1 /R^2
F=k* Q1^2 /R^2

F=k* Q1^2 /R^2
=> 5.9*10^-7 * 7.4 = 9*10^9 * Q1^2/ (4.2*10^-3)^2
=> Q1 = Q = 9.25*10^-11 C