1) Part A: Two pellets, each with a charge of 3 × 10−6 C,
are located 0.03 m apart.
What is the electric force between
them? The value of the Coulomb
constant is 8.99 × 109 N · m2/C2 and
the universal gravitational constant is
6.67259 × 10−11 m3/kg · s2.
Answer in units of N.
Answer: 8.99 N
Part B: What mass would experience this same gravitational force?
Answer in units of kg. (This is what I need help with.)
Mr. Bob, I got 0.000009439 and it was wrong.
f=GMM/.03^2
F=8.99
M^2=8.9*.03^2/G
solve for M
I agree,that is really wrong. G is a samll number, diviing it into a number makes the number big. Check your exponents.
To find the mass that would experience the same gravitational force as the electric force between the pellets, we need to set up an equation equating the two forces.
Let's start by finding the electric force between the pellets. The electric force can be calculated using Coulomb's Law, which states that the electric force between two charged objects is given by the equation:
Fe = (k * q1 * q2) / r^2
Where Fe is the electric force, k is the Coulomb constant, q1 and q2 are the charges of the two objects, and r is the distance between them.
Given:
Coulomb constant (k) = 8.99 × 10^9 N·m^2/C^2
Charge 1 (q1) = 3 × 10^(-6) C
Charge 2 (q2) = 3 × 10^(-6) C
Distance (r) = 0.03 m
Plugging in the values, we can calculate the electric force (Fe):
Fe = (8.99 × 10^9 N·m^2/C^2 * (3 × 10^(-6) C) * (3 × 10^(-6) C)) / (0.03 m)^2
Fe = (8.0991 × 10^(-6) N)
Now, to find the mass that would experience an equivalent gravitational force, we can use Newton's law of universal gravitation, which states that the gravitational force between two objects is given by the equation:
Fg = (G * m1 * m2) / r^2
Where Fg is the gravitational force, G is the universal gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between them.
We know the gravitational force is equal to the electric force, so we can set up the equation:
Fe = Fg
Plugging in the known values and solving for the mass (m1 or m2) gives us:
(8.0991 × 10^(-6) N) = (6.67259 × 10^(-11) m^3/kg·s^2 * m1 * m2) / (0.03 m)^2
To isolate the mass term, we can rearrange the equation as follows:
m1 * m2 = (8.0991 × 10^(-6) N) * (0.03 m)^2 / (6.67259 × 10^(-11) m^3/kg·s^2)
m1 * m2 ≈ 0.011369 kg^2
To find the individual mass, we take the square root of both sides:
√(m1 * m2) ≈ √(0.011369 kg^2)
m1 ≈ √(0.011369 kg^2)
m1 ≈ 0.1066 kg
Therefore, the mass that would experience the same gravitational force as the electric force between the pellets is approximately 0.1066 kg.