A particle of mass 47 g and charge 54 �C is released from rest when it is 13 cm from a second particle of charge −15 �C.
Determine the magnitude of the initial acceleration of the 47 g particle.
Answer in units of m/s2
To determine the magnitude of the initial acceleration of the 47 g particle, we can use Coulomb's law and Newton's second law.
Coulomb's law states that the force between two charged particles is given by:
F = k * |q1 * q2| / r^2
where F is the force, k is the electrostatic constant (k = 9 * 10^9 Nm^2/C^2), q1 and q2 are the charges of the particles, and r is the distance between the particles.
In this case, the force between the two particles is attractive since one of the charges is positive and the other is negative.
First, let's convert the mass of the particle from grams to kilograms:
mass = 47 g = 0.047 kg
Now, let's calculate the force between the two particles using Coulomb's law:
F = (9 * 10^9 Nm^2/C^2) * (|54 * (-15)|) / (0.13 m)^2
F = (9 * 10^9 Nm^2/C^2) * (54 * 15) / (0.13)^2
F ≈ 1.963 * 10^10 N
According to Newton's second law, the force on an object is equal to its mass times its acceleration:
F = mass * acceleration
We can rearrange this equation to solve for acceleration:
acceleration = F / mass
acceleration = (1.963 * 10^10 N) / (0.047 kg)
acceleration ≈ 4.18 * 10^11 m/s^2
Therefore, the magnitude of the initial acceleration of the 47 g particle is approximately 4.18 * 10^11 m/s^2.
To determine the magnitude of the initial acceleration of the 47 g particle, we can use the equation for the electric force between two charged particles:
\(F = \dfrac{k \cdot |q_1 \cdot q_2|}{r^2}\)
where F is the force, k is the Coulomb's constant (9 × 10^9 N·m^2/C^2), q1 and q2 are the charges of the particles, and r is the distance between them.
First, we need to convert the mass of the particle to kilograms:
\(m = 47 \, \text{g} = 0.047 \, \text{kg}\)
Next, we can calculate the magnitude of the electric force between the two particles using the given values:
\(F = \dfrac{k \cdot |q_1 \cdot q_2|}{r^2} = \dfrac{(9 \times 10^9 \, \text{N·m}^2/\text{C}^2) \cdot |(54 \, \mu\text{C}) \cdot (-15 \, \mu\text{C})|}{(0.13 \, \text{m})^2}\)
where μC represents microcoulombs (10^-6 C) and m represents meters.
Calculating this equation gives us the force between the particles. To find the acceleration, we can use Newton's second law:
\(F = m \cdot a\)
Rearranging this equation to solve for acceleration:
\(a = \dfrac{F}{m}\)
Substituting the known values:
\(a = \dfrac{(9 \times 10^9 \, \text{N·m}^2/\text{C}^2) \cdot |(54 \, \mu\text{C}) \cdot (-15 \, \mu\text{C})|}{(0.13 \, \text{m})^2 \cdot 0.047 \, \text{kg}}\)
Evaluating this expression will give us the magnitude of the acceleration of the particle.