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=
q2=
(b) Find the mass of particle 2
answer in kg
To find the charge on each particle, we can use Coulomb's law, which states that the force between two charged particles is given by:
F = k * (|q1| * |q2|) / r^2
where F is the magnitude of the force, k is Coulomb's constant (k = 8.99 * 10^9 N m^2/C^2), q1 and q2 are the charges on each particle, and r is the separation between the particles.
First, let's find the force experienced by each particle:
For particle 1:
F1 = m1 * a1 = (5.75 * 10^-6 kg) * (4.25 * 10^3 m/s^2) = 24.4375 * 10^-3 N
For particle 2:
F2 = m2 * a2 = m2 * (8.6 * 10^3 m/s^2)
Since both particles have identical positive charges, let's assume q1 = q2 = q. Therefore, the force experienced by each particle is the same:
F1 = F2
Therefore, we can equate the two expressions for force:
m1 * a1 = m2 * a2
Plugging in the given values:
(5.75 * 10^-6 kg) * (4.25 * 10^3 m/s^2) = m2 * (8.6 * 10^3 m/s^2)
Simplifying the equation:
(5.75 * 4.25) / 8.6 = m2
m2 ≈ 2.828 * 10^-6 kg
The mass of particle 2 is approximately 2.828 * 10^-6 kg.
Now, let's find the charge on each particle. We can substitute the values of the forces and charges into Coulomb's law equation:
k * (|q1| * |q2|) / r^2 = F1
Simplifying the equation for q:
|q1| * |q2| = (F1 * r^2) / k
Substituting the given values:
|q|^2 = (24.4375 * 10^-3 N * (2.65 * 10^-2 m)^2) / (8.99 * 10^9 N m^2/C^2)
Simplifying the equation:
|q|^2 = 2.591225 / 8.99
|q| ≈ √(2.591225 / 8.99)
|q| ≈ 0.4968 C
Since both particles have the same charge, q1 = q2 = ±0.4968 C.
Therefore:
q1 ≈ 0.4968 C
q2 ≈ 0.4968 C
So, the charge on each particle is approximately 0.4968 C.