One particle has a mass of 4.06x10^-3 kg

Question

One particle has a mass of 4.06 x 10^-3 kg and a charge of +6.27 uC. A second particle has a mass of 7.71 x 10^-3 kg and the same charge. The two particles are initially held in place and then released. The particles fly apart, and when the separation between them is 0.132 m, the speed of the 4.06 x 10^-3 kg particle is 165 m/s. Find the initially separation between the particles.

I somehow got 3.18 mm which was incorrect.

Answer 1

I agree with Ryan that you need to use conservation of energy, but I do not agree that you need to know the initial separation of the particles (which is the very thing that they ask you for). You can apply conservation of energy to just one particle, namely the particle whose velocity you know at a separation of 0.132 m. You can do this because the electrical force is conservative, and therefore derivable from a potential energy function.

Let's declare some variables.

r_i = initial separation

r_f = final separation

Particle 1:

m₁ = 4.06 x 10^-3 kg

q = 6.27 x 10^-6 C

v_1i = 0 m/s (initial speed)

v_1f = 165 m/s (final speed)

Particle 2:

q = 6.27 x 10^-6 C

The mass, initial speed, and final speed of Particle 2 do not matter. Only its charge is important.

Now answer these questsions:

1) What is the total energy of Particle 1 when the separation between the particles is r_i? Write an expression in terms of the variables that I have delcared.

2) What is the total energy of Particle 1 when the separation between the particles is r_f? Again, use the variables that I have declared.

If you equate the two expressions for the total energy, then you will have an equation that has just one unknown, namely r_f. Please respond with your answers to my questions 1 and 2.

PS: I got 6 mm for the intitial separation.

Answer 2

Hi Erin,

I’m not going to solve the problem for you, but I can give you some advice. Actually, you need to know the initial distance between the particles. I’m assuming you have that info. If so then apply conservation of energy. Initially, potential energy is stored in the electric field. When the particles are allowed to move energy changes from potential to kinetic but the total mechanical energy remains the same. You cannot use basic kinematics in this case because the acceleration of each particle is not constant. I hope this helps. Also, I hope another tutor does not answer this with step by step instructions. Although that is much easier it does not help you learn. Good luck . Let me know if you are not given the initial separation between the particles.