Two protons in a molecule are 3.80 multiplied by 10-10 m apart. Find the electrical force exerted by one proton on the other.
Magnitude
N
(b) State how the magnitude of this force compares with the magnitude of the gravitational force exerted by one proton on the other.
(electrical force / gravitational force)
(c) What if? What must be a particle's charge-to-mass ratio if the magnitude of the gravitational force between two of these particles is equal to the magnitude of electrical force between them?
C/kg
A 4.8-g bullet leaves the muzzle of a rifle with a speed of 324 m/s. What force (assumed constant) is exerted on the bullet while it is traveling down the 0.75-m-long barrel of the rifle?
To find the electrical force exerted by one proton on the other, you can use Coulomb's Law. Coulomb's Law states that the electrical force between two charged particles is proportional to the product of their charges and inversely proportional to the square of the distance between them. The formula is given by:
Electrical force = (k * q1 * q2) / r^2
Where:
k is the electrostatic constant (k = 9.0 x 10^9 N.m^2/C^2),
q1 and q2 are the charges of the two particles (which are both equal to the charge of a proton, q = 1.60 x 10^-19 C), and
r is the distance between the particles (r = 3.80 x 10^-10 m).
(a) Plugging in these values into the formula, we can calculate the electrical force exerted by one proton on the other:
Electrical force = (9.0 x 10^9 N.m^2/C^2) * (1.60 x 10^-19 C) * (1.60 x 10^-19 C) / (3.80 x 10^-10 m)^2
Calculating this expression will give you the magnitude of the electrical force in Newtons.
(b) To compare the magnitude of the electrical force with the magnitude of the gravitational force exerted by one proton on the other, we need to calculate the gravitational force. The gravitational force between two masses is given by Newton's Law of Universal Gravitation:
Gravitational force = (G * m1 * m2) / r^2
Where:
G is the gravitational constant (G = 6.674 x 10^-11 N.m^2/kg^2),
m1 and m2 are the masses of the two particles (which are both equal to the mass of a proton, m = 1.67 x 10^-27 kg), and
r is the distance between the particles (the same as before, r = 3.80 x 10^-10 m).
The magnitude of the gravitational force can be calculated using the same approach as before. Once you have the values, you can compare the magnitude of the electrical force to the magnitude of the gravitational force by taking the ratio of the two forces: (electrical force / gravitational force).
(c) If the magnitude of the gravitational force between two particles is to be equal to the magnitude of the electrical force between them, we set the two forces equal to each other and solve for the charge-to-mass ratio:
(k * q^2) / r^2 = (G * m^2) / r^2
Simplifying the equation, we obtain:
(q^2 / m^2) = (G / k)
Taking the square root of both sides will give you the ratio q/m in C/kg.