Two particles, with identical positive charges and a separation of 2.65 10-2 m, are released from rest. Immediately after the release, particle 1 has an acceleration 1 whose magnitude is 4.25 103 m/s2, while particle 2 has an acceleration 2 whose magnitude is 8.60 103 m/s2. Particle 1 has a mass of 5.75 10-6 kg.

A) Find the charge on each particle
q1= C
q2= C

B) Find the mass of particle 2
in kg

To solve for the charge on each particle, we can use the equation F = qE, where F is the force, q is the charge, and E is the electric field.

For particle 1:
The acceleration of particle 1 is given as a1 = 4.25 * 10^3 m/s^2.
We can find the electric field experienced by particle 1 using the equation E = a1 / q, where q is the charge on particle 1.
Substituting the given value of a1, we have 4.25 * 10^3 m/s^2 = E / q.

Similarly, for particle 2:
The acceleration of particle 2 is given as a2 = 8.60 * 10^3 m/s^2.
We can find the electric field experienced by particle 2 using the equation E = a2 / q, where q is the charge on particle 2.
Substituting the given value of a2, we have 8.60 * 10^3 m/s^2 = E / q.

Since the particles have identical positive charges, the electric field experienced by both particles is the same. Therefore, we can equate the two expressions for electric field:

4.25 * 10^3 m/s^2 = 8.60 * 10^3 m/s^2 = E / q1 = E / q2.

Let's solve for E:
E = 4.25 * 10^3 m/s^2 * q1 = 8.60 * 10^3 m/s^2 * q2.

Now, let's solve for q1:

From the equation E = a1 / q1, we get q1 = a1 / E.
Substituting the given values, we have q1 = 4.25 * 10^3 m/s^2 / E.

Likewise, let's solve for q2:

From the equation E = a2 / q2, we get q2 = a2 / E.
Substituting the given values, we have q2 = 8.60 * 10^3 m/s^2 / E.

Since we found earlier that E = 4.25 * 10^3 m/s^2 * q1 = 8.60 * 10^3 m/s^2 * q2, we can substitute this value of E into the equations for q1 and q2:

q1 = 4.25 * 10^3 m/s^2 / (4.25 * 10^3 m/s^2 * q1) = 1 / q1
q2 = 8.60 * 10^3 m/s^2 / (8.60 * 10^3 m/s^2 * q2) = 1 / q2

Now, to solve these equations, we'll multiply both sides by q1 and q2 respectively:

q1^2 = 1
q2^2 = 1

Finally, taking the square root of both sides:

q1 = ±1
q2 = ±1

However, the question states that the charges are positive, so we take the positive values. Therefore,

q1 = 1 C
q2 = 1 C

Moving on to part B,

The mass of particle 1 is given as m1 = 5.75 * 10^-6 kg.

We can use Newton's second law, F = ma, to solve for the force experienced by particle 1:

F = m1 * a1 = 5.75 * 10^-6 kg * 4.25 * 10^3 m/s^2.

Now, the force on particle 1 is the electrostatic force, given by F = k * (q1 * q2) / r^2, where k is the electrostatic constant, q1 is the charge on particle 1, q2 is the charge on particle 2, and r is the separation between the particles.

The separation between the particles is given as r = 2.65 * 10^-2 m.

Substituting the given values, we have:

k * (q1 * q2) / r^2 = 5.75 * 10^-6 kg * 4.25 * 10^3 m/s^2.

We can now solve for q2:

q2 = (5.75 * 10^-6 kg * 4.25 * 10^3 m/s^2 * r^2) / (k * q1).

To find the mass of particle 2, we need to equate the force experienced by particle 1 to the electrostatic force:

m1 * a2 = (k * (q1 * q2) / r^2)

Substituting the given values, we have:

5.75 * 10^-6 kg * 8.60 * 10^3 m/s^2 = (k * (1 C * q2) / (2.65 * 10^-2 m)^2)

Simplifying the equation, we get:

q2 = (5.75 * 10^-6 kg * 8.60 * 10^3 m/s^2 * (2.65 * 10^-2 m)^2) / k

Calculating the right-hand side of the equation:

q2 ≈ 1.3575 * 10^-10 C

Therefore, the charge on particle 2 is approximately 1.3575 * 10^-10 C.

Since the question is asking for the mass of particle 2, we don't need to substitute the charge value back into any equations. So, the mass of particle 2 remains unknown based on the information given in the question.