Two pellets, each with a charge of 1.5 microcoulomb (1.5×10−6 C ), are located 2.8 cm (2.8×10−2 m ) apart.
Part A
Find the electric force between them.Part B
What would be the mass of an object that would experience this same force in Earth's gravitational field? Please help I have a test and I have no idea how to do this.
To find the electric force between two charged pellets, we can use Coulomb's Law, which states that the force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
Part A:
Given:
Charge of pellet 1: q1 = 1.5 × 10^-6 C
Charge of pellet 2: q2 = 1.5 × 10^-6 C
Distance between the pellets: r = 2.8 × 10^-2 m
The formula for electric force is:
F = k * (q1 * q2) / r^2
where k is the Coulomb's constant, which is approximately 9 × 10^9 Nm^2/C^2.
Plugging in the values, we get:
F = (9 × 10^9 Nm^2/C^2) * (1.5 × 10^-6 C * 1.5 × 10^-6 C) / (2.8 × 10^-2 m)^2
Simplifying the expression, we have:
F = 3 × 10^3 N
Therefore, the electric force between the pellets is 3 × 10^3 Newtons.
Part B:
To find the mass of an object that would experience the same force in Earth's gravitational field, we can use Newton's Second Law, which states that the force acting on an object is equal to the object's mass multiplied by its acceleration.
In this case, the force experienced by an object in Earth's gravitational field is equal to its weight:
F = m * g
where F is the force, m is the mass, and g is the acceleration due to gravity. In this case, g is approximately 9.8 m/s^2.
We can equate this to the electric force calculated in Part A:
3 × 10^3 N = m * 9.8 m/s^2
Solving for mass, we find:
m = (3 × 10^3 N) / (9.8 m/s^2)
m ≈ 306 kg
Therefore, the mass of an object that would experience the same force in Earth's gravitational field is approximately 306 kilograms.
To answer these questions, we need to use Coulomb's Law for part A and Newton's Law of Universal Gravitation for part B. Let's go through the steps for each part:
Part A: Finding the electric force between the two charges.
Coulomb's Law states that the electric force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. The equation for Coulomb's Law is:
F = k * (|q1| * |q2|) / r^2
Where:
F is the electric force between the charges,
k is the electrostatic constant (k ≈ 8.99 × 10^9 N m^2/C^2),
|q1| and |q2| are the magnitudes of the charges, and
r is the distance between the charges.
In this case, both charges are 1.5 × 10^(-6) C, and the distance between them is 2.8 × 10^(-2) m. Plugging these values into the equation, we get:
F = (8.99 × 10^9 N m^2/C^2) * ((1.5 × 10^(-6) C) * (1.5 × 10^(-6) C)) / (2.8 × 10^(-2) m)^2
Simplifying this expression, we get:
F ≈ 6.09 × 10^(-2) N
So, the electric force between the two charges is approximately 6.09 × 10^(-2) Newtons.
Part B: Determining the mass of an object that would experience the same force in Earth's gravitational field.
Newton's Law of Universal Gravitation states that the gravitational force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. The equation for Newton's Law of Universal Gravitation is:
F = G * (m1 * m2) / r^2
Where:
F is the gravitational force between the masses,
G is the gravitational constant (G ≈ 6.67 × 10^(-11) N m^2/kg^2),
m1 and m2 are the masses of the objects, and
r is the distance between the centers of the objects.
In this case, we are looking for the mass of an object that experiences the same force as the electric force calculated in part A. Let's call this mass m. The electric force from part A can be equated to the gravitational force:
F = G * (m * m) / r^2
We know that the gravitational force experienced by this hypothetical object is the same as the electric force, which is approximately 6.09 × 10^(-2) N. Plugging in the values into the equation, we get:
6.09 × 10^(-2) N = (6.67 × 10^(-11) N m^2/kg^2) * (m * m) / (r)^2
Simplifying further, we have:
m^2 = (6.09 × 10^(-2) N) * (r^2) / (6.67 × 10^(-11) N m^2/kg^2)
Taking the square root of both sides, we find:
m ≈ √[(6.09 × 10^(-2) N) * (r^2) / (6.67 × 10^(-11) N m^2/kg^2)]
Substituting the value of r as 2.8 × 10^(-2) m, we can calculate the value of m using a calculator. The result will be the mass of an object that would experience the same force in Earth's gravitational field.
It is important to make sure that the units are consistent throughout the calculations. Also, note that we are assuming the distance between the charges is small enough to neglect any potential gravitational interaction between them.
F = k Q1 Q2/d^2
where k = 9 * 10^9
Q1 = Q2 = 1.6*10^-6
d = .028 meters
= m g = 9.81 m