Question

The force between a 100 kg man and the Earth is 980 N. How close must two protons (1.6 X 10-19 C) be to generate the same force?

Answer 1

The distance between two protons to generate 950N of force is 0.49 X 10⁻¹⁵ m

Explanation:

Given:

Mass of man, m = 100 kg

Force between man and earth = 980 N

Charge of proton, q = 1.6 X 10⁻¹⁹C

Same force is generated between them

Distance between two protons, r = ?

According to Coulomb's law:

$F = k\frac{q_1q_2}{r^2}$

where,

k is Coulomb's constant

k = 9 X 10⁹ Nm²/C²

According to the question:

$950 = k\frac{q_1q_2}{r^2}$

Solving the equation:

$950 = (9X10^9) X\frac{(1.6 X 10^-^1^9 X 1.6 X 10^-^1^9)}{r^2} \\\\r^2 = \frac{(9 X 10^9) (1.6 X 10^-^1^9 X 1.6 X 10^-^1^9)}{950} \\\\r^2 = 0.024 X 10^-^2^9\\\\r^2 = 0.24 X 10^-^3^0\\\\r = 0.49 X 10^-^1^5 m$

Therefore, the distance between two protons to generate 950N of force is 0.49 X 10⁻¹⁵ m