I've managed to figure out question B but cannot figure out A, any help appreciated
Two particles, with identical positive charges and separation of 3.04 × 10-2 m, are released from rest. Immediately after the release, particle 1 has an acceleration a1 whose magnitude is 6.05 × 103 m/s2, while particle 2 has an acceleration a2 whose magnitude is 8.74 × 103 m/s2. Particle 1 has a mass of 8.14 × 10-6 kg. Find (a) the charge on each particle and (b) the mass of particle 2.
To find the charge on each particle, you can use Coulomb's law and the equation for the electric force between two charged particles:
F = k * |q1 * q2| / r^2
Where:
- F is the magnitude of the electric force between the two particles
- k is Coulomb's constant, approximately 9 x 10^9 Nm^2/C^2
- q1 and q2 are the charges on particles 1 and 2, respectively
- r is the separation between the particles
We are given the following information:
- The separation between the particles, r, is 3.04 x 10^-2 m.
- The mass of particle 1, m1, is 8.14 x 10^-6 kg.
- The acceleration of particle 1, a1, has a magnitude of 6.05 x 10^3 m/s^2.
- The acceleration of particle 2, a2, has a magnitude of 8.74 x 10^3 m/s^2.
For particle 1, we know that the net force acting on it is given by F = m1 * a1. Since the only force acting on particle 1 is the electric force exerted by particle 2, we can equate the two forces:
m1 * a1 = k * |q1 * q2| / r^2
Solving for q1 * q2:
q1 * q2 = (m1 * a1 * r^2) / k
Similarly, for particle 2, we have:
q1 * q2 = (m2 * a2 * r^2) / k
Since the charges on the two particles are equal, we can equate these two equations:
(m1 * a1 * r^2) / k = (m2 * a2 * r^2) / k
Simplifying and solving for m2:
m2 = (m1 * a1 * r^2) / (a2)
To find the charge on each particle (a), substitute the given values into the equation for q1 * q2. To find the mass of particle 2 (b), substitute the given values into the equation for m2.