Imagine two 1.0 g bags of protons, one at the earth's north pole and the other at the south pol

step 1 So first let's write down the known information. So we know the mass of each bag, let's call tha

Imagine two 1.0 g bags of protons, one at the earth's north...

Key Concepts

Comparison of Force Strengths

Understanding the relative magnitude of different forces, such as gravitational and electric forces, is crucial in physics. This concept highlights that although gravity is a universal force experienced by all masses, its effects are often negligible compared to the much stronger electric forces at the microscopic level.

Coulomb's Law

Coulomb's law describes how charged particles interact, stating that the electric force between two point charges is proportional to the product of their charges and inversely proportional to the square of the distance between them. This law is a fundamental aspect of electromagnetism and is critical when analyzing forces in systems involving electric charges.

Newton's Law of Universal Gravitation

Newton's law states that every two masses attract each other with a force proportional to the product of their masses and inversely proportional to the square of the distance between their centers. This principle is a cornerstone of classical mechanics and is used to calculate gravitational interactions between objects.

Mass-to-Particle Conversion

This involves using the mass of a single particle to determine the total number of particles present in a given mass sample. It is a fundamental principle in both chemistry and physics that connects macroscopic quantities of matter with its microscopic constituents.

Quantization of Charge

This concept refers to the fact that electric charge is not continuous but exists in discrete units, with the proton carrying one elementary charge. It is essential for converting a given mass of protons into the total number of particles, as each proton contributes a fixed, quantized amount to the overall charge.

Transcript

00:01 So first let's write down the known information.

00:04 So we know the mass of each bag, let's call that mb, and that's given to be 10 to the power minus 3 kgs.

00:16 And we also know the gravitational constant.

00:19 That's equal to 6 .67 times 10 to the power minus 11 newton times meter square over.

00:30 Kg square and this gravitational constant are we are going to use this further in this problem and we are given that one bag is at the north pole of earth and the other one is at the south pole so we can find the distance between the two bags and that will be equal to twice of the radius of the earth where the radius of the earth is 6 .3.

01:03 6 .371 times 10 to the power 6 meter.

01:09 So that's the radius of the earth.

01:11 So using that we can find the distance between the two backs.

01:16 Now in the first part we have to find the number of protons in each bag.

01:24 So we know that mp the mass of the proton is equal to 1 .67 times 10 to the part.

01:34 Minus 27 kg so this is the mass of one single proton therefore nb will be equal to number of protons inside each bag times mass of the proton so from here we can find n which will be equal to mb the mass of each back over mass of each proton and that will give us 6 times 10 to the power 23 after substituting the values.

02:07 So this is the number of protons in each pack.

02:17 So that's the first part.

02:19 Now in the second part, we have to find the electric force and gravitational force.

02:27 So the electric force is given by 1 over 1.

02:35 4 pi epsilon 0 square of like multiplication of all the charges of both the charges of the two bags over square of the distance between them that is d and here since both the charges are equal so because they have the same number of protons so this will then be equal to q square where q is the amount of charge in each back over d square and let's write this factor one 4x0 as k...

Please give Ace some feedback