The charge of a proton is 1.6 x 10-19 C. The mass of a proton is 1.673 x 10-27 kg. The constant in the universal law of gravitation is 6.673 x 10-11 Nm2/kg2. The constant in the Coulomb¡¯s law is 9x109 Nm2/C2. Calculate the numerical value of both the gravitational and electrostatic forces between the pair of protons.
Please help me with this question!!!
d is the same for both
I will do F d^2 so you see which wins :)
gravity
Fg * d^2 = G M1 M2
= 6.673*10^-11 * (1.673*10^-27)^2
= 18.7 * 10^-65
electrostatic
Fe d^2 = k Q1Q2
= 9*10^9 (1.6*10^-19)^2
= 23 * 10^-29
it is 10^-65 for gravity and 10^-29 for electricity
Electricy wins big time until you get something the mass of earth with a small charge :)
DIVIDE BOTH BY THE DISTANCE SQUARED TO GET THE FORCE IN NEWTONS :)
To calculate the numerical value of both the gravitational and electrostatic forces between a pair of protons, we can use the formulas for the gravitational force and the electrostatic force.
1. Gravitational Force (Fg):
The formula for the gravitational force between two objects is given by:
Fg = (G * m1 * m2) / r^2
Where:
Fg = Gravitational force
G = Universal gravitational constant (6.673 x 10^-11 Nm^2/kg^2)
m1 = Mass of the first object (1.673 x 10^-27 kg)
m2 = Mass of the second object (1.673 x 10^-27 kg)
r = Distance between the two objects (which we assume to be very close for protons)
So, plugging in the values given:
Fg = (6.673 x 10^-11 Nm^2/kg^2) * (1.673 x 10^-27 kg) * (1.673 x 10^-27 kg) / r^2
2. Electrostatic Force (Fe):
The formula for the electrostatic force between two charged objects is given by Coulomb's Law:
Fe = (k * q1 * q2) / r^2
Where:
Fe = Electrostatic force
k = Coulomb's constant (9 x 10^9 Nm^2/C^2)
q1 = Charge of the first object (1.6 x 10^-19 C)
q2 = Charge of the second object (1.6 x 10^-19 C)
r = Distance between the two objects (which we assume to be very close for protons)
Plugging in the values given:
Fe = (9 x 10^9 Nm^2/C^2) * (1.6 x 10^-19 C) * (1.6 x 10^-19 C) / r^2
Once you have the values for Fg and Fe, you can calculate their numerical values by substituting the distance (r) between the protons into the respective formulas. Remember to square the distance (r) in the denominator.
Note: The distance value is crucial to provide the final numerical values for the forces.