Force, Work and Energy

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Last Updated: Monday, 11 March 2024 01:14
Published: Monday, 14 August 2023 22:58
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Force:

There are 4 fundamental forces or interactions in nature. All the motion that you see around as are due to forces. These forces may be friction, gravitation, push, etc. They ultimately belong to one of these 4 forces. It's easier to visualize these forces by considering a field, and then this field exerting forces. Force is always a vector as the effective force due to multiple forces is a vector sum of these forces. We are omitting the arrow sign on top of force for simplicity, but it should always be there to indicate it's a vector. The 4 fundamental forces or fields are:

  1. Gravitational force: This is attraction force due to mass of an object, and it's range is infinite. Newton's formula for gravitational force (published in 1686) gives us the formula for this:
    1. Newton's Gravitational Law: Force between 2 bodies of mass m1 and m2 as F = G*m1*m2/R^2, where G=Gravitational Constant of 6.674*10^-11 m^3/(kg*s^2). Here both F and R are vectors.
    2. Gravitation Field is defined as field due to presence of mass M and is given as g = F/m = G*M/R^2. The other mass is removed in eqn here, as F =m*g where g is the Gravitation Field due to mass M,
    3. The value of G wasn't determined at Newton's time. It was used to calculate forces relative to one another. It was in 1798 (>100 years later) that value of G was found out experimentally. It can be seen that this gravitational force is very weak (as G is a very small number), and is only relevant when at least one of the bodies is very large as moons, planets, stars, etc. What in the mass causes gravity or gravitational field is unknown. Even Newton hypothesized that cause of this power is unknown and contrary to sound science.
  2. Electromagnetic Force: This is the attractive or repulsive force due to charge. This force is studied as 2 separate forces - Electric force and Magnetic force. However both of these forces are the same. They appear as Electric or magnetic force depending on the frame of reference of the observer.
    1. Electric force: This force is between charged particle at rest. Coulomb's Law for Electrostatic Force is exactly similar in form to Newton's Gravitational Force. It was published in 1785 by Charles Coulomb and is given by below formula
      1. Coulomb's Law: F=q1*q2/(4*Π*ε*R^2). Here instead of G, we replace it by other constant (1/4*Π*ε).
      2. Electric Field is defined as field due to presence of charge q and is given as E = F/q2 = q/(4*Π*ε*R^2). Electric field is measured in V/m. ε is the permittivity of the material. It measures as to how well the material itself polarizes in response to the Electric Field. This happens due to natural tendency of outside charges to rearrange themselves so that the Field is reduced. If we put the charge Q in a vacuum, then there's nothing in vacuum to neutralize the field, so vacuum will have the lowest permittivity possible. For vacuum, permittivity is ε0 = 8.85*10^-12 F/m. Unit is F/m as ε=Q/E.1/R^2 = Cap.m/m^2=Cap/m=F/m.We take out the constant part (1/4*Π*ε) and call it the Coulomb Constant (ke) = 1/4*Π*ε0 = 9*10^9 N-m^2/C^2  where F =  ke*q1*q2/R^2. Thus it can be seen that force is lot stronger than gravitational force (as ke is very large number). 
      3. Relative Permittivity: Since everything has higher permittivity than vacuum, we talk in terms of relative permittivity εr which is the ratio of the absolute permittivity of medium to permittivity of vacuum. i.e εr= ε/ε0. A metal doesn't allow any Electric field to exist within itself, as any resultant Electric field will make electrons move (as electrons are very loosely bound), and they will keep moving until the Electric Field within the metal is no more there. So, if we put a charge surrounded by metal, metal will have no resultant Electric field, implying infinite ε. Basically electrons will move to one end making that end -ve charged, while leaving the other end +ve charged. Thus a really big dipole is created in the metal which neutralizes the applied Electric field. For any material which is a perfect insulator, electrons can't freely roam whenever there's an Electric field. They are stuck in their positions bound to the nucleus. At an atomic level, the electron cloud in an atom might still get distorted. Electrons might get pushed away a little from the Electric Field creating a dipole. All such atomic dipoles will create an internal electric field in opposite direction to applied Electric field. How strong of the dipole is created is dependent on the material's ability to form such dipoles. Perfect Conductors may be thought of as an extreme case where such dipoles are created along the full length of the material, i.e electrons go on one side and nucleus goes to the opposite side. Polarizing insulators make limited length dipoles. Electrons are still held in place but just shifted a little. So, there is some net Electric field left. More the dipole electric field formed, less is the net electric field and higher is the permittivity of the material. Higher permittivity means you have to apply more charge to hold same potential difference, as some of the applied field will get neutralized. Permittivity is the capacitive ability of a material, and totally different than resistivity (see in Passive elements section). Silicon has εr=12, while SiO2 has εr=4. This means Si will have less Electric field and hence higher ability to retain charge for same Voltage than SiO2. Capacitors have materials known as dielectric with high εr so that they can hold more charge and hence more energy.
    2. Magnetic force: This force is counterpart of Electric force. It's caused by magnetic charges instead of electric charges. The only thing unique to magnetic charges is that they always appear in pair, i.e +ve and -ve magnetic charges will appear together, and can never be separated. Usually Magnetic force or magnetic field is associated with magnets, but anything else can also behave as a magnet under right conditions. A magnet's North and South pole can be thought of as 2 magnetic charges, one at N and other at S, with opposite polarity. A moving electric charge behaves as a magnetic charge and causes magnetic field.

 

Newtonian Laws: