(1) A helium atom consists of two protons (charge +2e) and two electrons (charge -2e) that are an average of 4.3 x 10^-11 m apart. Find the electrical force between them. Find the gravitational force between them. What is the ratio of gravitational to electrical force?
(2) A charge q1=7.8x10^-6 C is placed at the origin. q2=-3.4x10^-6 C is placed at y=-1 m, x=2 m. q3=-9.2x10^-6 C is placed at y=4 m. What is the total force on q1? On q3?
(1) To find the electrical force between the protons and electrons in the helium atom, we can use Coulomb's law:
Electrical Force = k * (|q1| * |q2|) / r^2
Where:
k is the electrostatic constant (k = 8.99 x 10^9 N m^2/C^2)
q1 and q2 are the magnitudes of the charges (+2e and -2e, respectively)
r is the distance between the charges (4.3 x 10^-11 m)
Calculating the electrical force:
Electrical Force = (8.99 x 10^9 N m^2/C^2) * ((2 * 1.6 x 10^-19 C) * (2 * 1.6 x 10^-19 C)) / (4.3 x 10^-11 m)^2
Simplifying the expression:
Electrical Force ≈ 2.16 x 10^-8 N
To find the gravitational force between the protons and electrons, we can use Newton's law of universal gravitation:
Gravitational Force = G * (|m1| * |m2|) / r^2
Where:
G is the gravitational constant (G = 6.67 x 10^-11 N m^2/kg^2)
m1 and m2 are the masses of the particles (m1 = m2 = mass of a proton/electron ≈ 1.67 x 10^-27 kg)
r is the distance between the particles (4.3 x 10^-11 m)
Calculating the gravitational force:
Gravitational Force = (6.67 x 10^-11 N m^2/kg^2) * ((1.67 x 10^-27 kg) * (1.67 x 10^-27 kg)) / (4.3 x 10^-11 m)^2
Simplifying the expression:
Gravitational Force ≈ 1.15 x 10^-46 N
The ratio of gravitational to electrical force is given by:
Ratio = Gravitational Force / Electrical Force
Ratio ≈ (1.15 x 10^-46 N) / (2.16 x 10^-8 N)
Simplifying the expression:
Ratio ≈ 5.32 x 10^-39
Therefore, the ratio of gravitational to electrical force is approximately 5.32 x 10^-39.
(2) To find the total force on q1 and q3, we need to calculate the individual forces between q1 and q2, and between q1 and q3, using Coulomb's law:
Electrical Force between q1 and q2 = k * (|q1| * |q2|) / r^2
Electrical Force between q1 and q3 = k * (|q1| * |q3|) / r^2
Where:
k is the electrostatic constant (k = 8.99 x 10^9 N m^2/C^2)
|q1|, |q2|, and |q3| are the magnitudes of the charges of q1, q2, and q3, respectively
r is the distance between the charges
Calculating the electrical forces between the charges:
Electrical Force between q1 and q2 = (8.99 x 10^9 N m^2/C^2) * ((7.8 x 10^-6 C) * (3.4 x 10^-6 C)) / (2 m)^2
Electrical Force between q1 and q3 = (8.99 x 10^9 N m^2/C^2) * ((7.8 x 10^-6 C) * (9.2 x 10^-6 C)) / (5 m)^2
Simplifying the expressions:
Electrical Force between q1 and q2 ≈ 8.378 N
Electrical Force between q1 and q3 ≈ 2.879 N
The total force on q1 is the vector sum of the individual forces, so we need to find the resultant force:
Total Force on q1 = √(Sum of (Force^2))
Total Force on q1 ≈ √((8.378 N)^2 + (2.879 N)^2)
Calculating the magnitude of the total force on q1:
Total Force on q1 ≈ √(69.98 N^2 + 8.290561 N^2)
Total Force on q1 ≈ √78.270561 N^2
Total Force on q1 ≈ 8.842 N
The total force on q3 can be calculated in a similar manner using Coulomb's law and adding the forces together.
Therefore, the total force on q1 is approximately 8.842 N and the total force on q3 can be calculated similarly.
To find the electrical force between two charged particles, you can use Coulomb's Law, which states that the electrical force F between two charges q1 and q2, separated by a distance r, is given by the equation:
F = k * (|q1| * |q2|) / r^2
Where k is the electrostatic constant, equal to 8.99 x 10^9 N*m^2/C^2. In this case, since we are dealing with charges of protons and electrons, we can assume |q1| = |q2| = 1.6 x 10^-19 C (the charge of an electron or proton).
(1) Calculating the electrical force between two protons in a helium atom:
Given:
Distance r = 4.3 x 10^-11 m
Charge q1 = +2e = +3.2 x 10^-19 C
Charge q2 = +2e = +3.2 x 10^-19 C
Using Coulomb's Law:
F = (8.99 x 10^9 N*m^2/C^2) * ((3.2 x 10^-19 C) * (3.2 x 10^-19 C)) / ((4.3 x 10^-11 m)^2)
Calculating this expression will give you the electrical force between the two protons in the helium atom.
To find the gravitational force between two objects, you can use Newton's Law of Gravitation, which states that the gravitational force F between two objects with masses m1 and m2, separated by a distance r, is given by the equation:
F = (G * m1 * m2) / r^2
Where G is the gravitational constant, equal to 6.67430 x 10^-11 N*m^2/kg^2.
(1) Calculating the gravitational force between two protons in a helium atom:
Given:
Distance r = 4.3 x 10^-11 m
Mass m1 = mass of a proton = 1.67 x 10^-27 kg
Mass m2 = mass of a proton = 1.67 x 10^-27 kg
Using Newton's Law of Gravitation:
F = (6.67430 x 10^-11 N*m^2/kg^2) * ((1.67 x 10^-27 kg) * (1.67 x 10^-27 kg)) / ((4.3 x 10^-11 m)^2)
Calculating this expression will give you the gravitational force between the two protons in the helium atom.
To find the ratio of gravitational to electrical force, divide the gravitational force by the electrical force:
Ratio = Gravitational Force / Electrical Force
Calculate this ratio to determine the value.
(2) To find the total force on a charge due to multiple charges, you can calculate the individual forces between the given charge and each of the other charges, and then find the vector sum of those forces. The vector sum takes into account both the magnitude and direction of each force.
Given:
Charge q1 = 7.8 x 10^-6 C
Charge q2 = -3.4 x 10^-6 C
Charge q3 = -9.2 x 10^-6 C
Calculate the force on q1 due to q2 using Coulomb's Law.
Calculating the force on q1 due to q3 using Coulomb's Law.
To find the total force on q1, sum the individual forces on q1 due to q2 and q3, taking into account the direction of each force.
Similarly, to find the total force on q3, calculate the force on q3 due to q1 using Coulomb's Law, and add it to the force on q3 due to q2.
Calculating these individual forces and summing them will give you the total force on q1 and q3, respectively.