A particle of mass 82 g and charge 80 µC is

released from rest when it is 81 cm from a
second particle of charge −24 µC.
Determine the magnitude of the initial acceleration of the 82 g particle.
Answer in units of m/s
2

F = k |Q1 Q2| / d^2 = 8.99*10^9 * 80*10^-6* 24*10^-6 / 0.81^2

= 26,308 * 10^-3 = 26.308 N
a = F/m = 26.3/ 0.082

A particle (m = 50 g. q = 5.0 µC) is released from rest when it is 50 cm from a second particle (Q = -20 µC). Determine the magnitude of the initial acceleration of the 50-g particle.

Well, that particle must really hate the other one if it's in such a hurry to accelerate away from it!

To determine the magnitude of the initial acceleration, let's use Newton's law of gravitation and Coulomb's law.

Newton's law of gravitation tells us that the gravitational force between two objects is given by:

F_grav = (G * m1 * m2)/(r^2)

where G is the gravitational constant, m1 and m2 are the masses of the particles, and r is the distance between them.

In this case, m1 = 82 g, m2 = (-24 µC), and r = 81 cm.

Now, Coulomb's law tells us that the electrostatic force between two charged objects is given by:

F_elec = (k * |q1 * q2|)/(r^2)

where k is the electrostatic constant, q1 and q2 are the charges of the particles, and r is the distance between them.

In this case, q1 = 80 µC, q2 = (-24 µC), and r = 81 cm.

However, since the problem didn't mention anything about the particles being stationary charged particles, we can assume that the only force acting on the 82 g particle is gravity. So, let's find the magnitude of the gravitational force:

F_grav = (G * m1 * m2)/(r^2)

Converting the masses to kg:
m1 = 82 g = 0.082 kg
m2 = (-24 µC)
Using Coulomb's law: k = 9 * 10^9 N·m^2/C^2

Plugging the values into the formula:
F_grav = (6.674 * 10^-11 N·m^2/kg^2 * 0.082 kg * (-24 µC))/(0.81^2 m)

Calculating the magnitude of the initial acceleration using Newton's second law (F = m * a):
a = F_grav / m1

Plugging the values into the formula:
a = [(6.674 * 10^-11 N·m^2/kg^2 * 0.082 kg * (-24 µC))/(0.81^2 m)] / 0.082 kg

Calculating the magnitude of the initial acceleration:
a ≈ 8.14 m/s^2

So, the magnitude of the initial acceleration of the 82 g particle is approximately 8.14 m/s^2.

To determine the magnitude of the initial acceleration of the 82 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 (9.0 x 10^9 N m^2/C^2), q1 and q2 are the charges of the particles, and r is the distance between them.

In this case, the force acting on the 82 g particle is due to the electric field created by the second particle. Since the 82 g particle is positively charged and the second particle is negatively charged, the force is attractive.

First, let's convert the mass of the particle to kilograms:

mass = 82 g = 0.082 kg

Next, let's convert the charge of each particle to Coulombs:

Q1 = 80 µC = 80 x 10^-6 C
Q2 = -24 µC = -24 x 10^-6 C

Now, we can calculate the force acting on the 82 g particle:

F = k * (Q1 * Q2) / r^2
= (9.0 x 10^9 N m^2/C^2) * (80 x 10^-6 C) * (-24 x 10^-6 C) / (0.81 m)^2

Simplifying the expression gives us:

F ≈ -2.96 N

Newton's second law states that the force acting on an object is equal to its mass multiplied by its acceleration:

F = mass * acceleration

Rearranging the equation to solve for acceleration:

acceleration = F / mass

Plugging in the known values:

acceleration = (-2.96 N) / (0.082 kg)
≈ -36.1 m/s^2

The magnitude of the initial acceleration of the 82 g particle is approximately 36.1 m/s^2.

82/1000 = 0.082