A particle of mass 86 g and charge 24 μC is
released from rest when it is 67 cm from a
second particle of charge −12 μC.
Determine the magnitude of the initial ac-
celeration of the 86 g particle.
a = F/m
Use Coulomb's Law for the initial force, F.
F = k*Q1*Q2/R^2
Look up the value of k. Separation distance R should be in meters.
The acceleration direction will be towards the other (negative) particle.
the answer is a positive number. the question asks for magnitude, which is never negative
To determine the magnitude of the initial acceleration of the 86 g particle, we can use Coulomb's Law and Newton's second law of motion.
Coulomb's Law states that the magnitude of the electrostatic force between two charged particles is given by:
F = k * |q1 * q2| / r^2
where F is the force, k is the electrostatic constant, q1 and q2 are the charges of the two particles, and r is the distance between the particles.
The electrostatic force acting on the 86 g particle is:
F = k * |q1 * q2| / r^2
where q1 is the charge of the 86 g particle and q2 is the charge of the other particle.
Next, we can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration:
F = m * a
where F is the force, m is the mass of the object, and a is the acceleration.
In this case, the force acting on the 86 g particle is the electrostatic force between the two particles, and the mass of the particle is 86 g.
Setting the electrostatic force equal to the mass times acceleration, we have:
k * |q1 * q2| / r^2 = m * a
Substituting the given values:
k = 9 * 10^9 Nm^2/C^2 (electrostatic constant),
q1 = 24 * 10^-6 C (charge of the 86 g particle),
q2 = -12 * 10^-6 C (charge of the other particle),
r = 67 cm = 0.67 m (distance between the particles),
m = 86 g = 0.086 kg (mass of the 86 g particle),
we can solve for the acceleration a:
a = k * |q1 * q2| / (m * r^2)
Plugging in the values, we get:
a = (9 * 10^9 Nm^2/C^2) * |(24 * 10^-6 C) * (-12 * 10^-6 C)| / ((0.086 kg) * (0.67 m)^2)
Calculating this expression will give us the magnitude of the initial acceleration of the 86 g particle.