If you were to separate all of the electrons and protons in 1 g (0.001 kg) of matter, you’d have about 96,000 C of positive charge and the same amount of negative charge. If you placed these charges 5 m apart, how strong would the attractive forces between them be?
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To calculate the strength of the attractive forces between the separated charges, we can use Coulomb's law, which states that the force of attraction or repulsion between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
Let's break down the steps to find the answer:
Step 1: Convert the mass of matter from grams to kilograms.
In this case, 1 g is equal to 0.001 kg.
Step 2: Calculate the number of protons and electrons in 0.001 kg of matter.
Since matter is electrically neutral, the number of protons is equal to the number of electrons in an atom. Each atom consists of one proton and one electron. To find the number of protons and electrons, we can use Avogadro's number, which states that there are 6.022 x 10^23 particles (atoms or molecules) in one mole of a substance. The molar mass of hydrogen is 1 g/mol, so 0.001 kg of matter contains:
(0.001 kg) / (0.001 kg/mol) x (6.022 x 10^23 particles/mol) = 6.022 x 10^20 particles
Step 3: Calculate the total charge in Coulombs (C).
Given that each proton and electron carries a charge of 1.6 x 10^-19 C, the total charge can be calculated as follows:
Total charge = (6.022 x 10^20 particles) x (1.6 x 10^-19 C/particle) = 9.6352 C
Step 4: Calculate the strength of the attractive forces between the charges using Coulomb's law.
Coulomb's law formula is given by:
Force = (k * (charge1 * charge2)) / distance^2
where k is the electrostatic constant, equal to 8.99 x 10^9 Nm^2/C^2.
Using the given values:
Force = (8.99 x 10^9 Nm^2/C^2) * (9.6352 C * 9.6352 C) / (5 m)^2
Simplifying the equation will give you the strength of the attractive forces between the separated charges in Newtons (N).
F = k Q^2/R^2
k is the Coulomb coefficient. Look it up.
Q = 96000 C
R = 5.0 m
The answer will be in newtons.