Review of Different Force law

Dynamics of a Particle

The study of causes of change in motion of a particle is called dynamics. Newton was the first to study dynamics and explain it through his three laws of motion.

General Equations of Motion

The famous three laws of motion of Newton and the equations of kinematics constitute the general equations of motion.

Types of Forces

There are four types of fundamental forces in nature. In order of their relative strengths, they are the strong nuclear force, electromagnetic force, weak force and gravitational force.

Conservation Laws

In physics, there are certain quantities which do not change after a certain operation and their sum always remains constant. They are related to the underlying symmetry of the universe. Such quantities are energy, linear and angular momenta, charge, number of neutrons and protons, etc. These quantities are conserved and are bounded by the conservation laws, which helps to solve several problems easily for the physicists.

Work-Energy Theorem

The work-energy theorem states that the work done by a force acting on a body is equal to change in kinetic energy of the body. Mathematically,\begin{align*} W=\frac{1}{2}Mv^{2}-\frac{1}{2}Mu^{2}\end{align*}

Conservative and Non-Conservative Forces

A conservative force is a force with the property that the work done in moving a particle between two points is independent of the taken path. Equivalently, if a particle travels in a closed loop, the et work done by a conservative force is zero.

A conservative force is dependent only on the position of the object. If a force is conservative, it is possible to assign a numerical value for the potential at any point. When an object moves from one location to other, the force changes the potential energy of the object by an amount that does not depend on the path taken. If the force is not conservative, then defining a scalar potential is not possible, because taking different paths would lead to conflicting potential differences between the start and end points.

Gravity is an example of conservative force, while friction is an example of a non-conservative force. A force is called a conservative force if it meets any of the three equivalent conditions ie, the curl of force is zero or the net work done in a closed trajectory is zero or the force can be written as the negative gradient of potential.

Non- conservative forces can arise in classical physics due to neglected degrees of freedom or from time-dependent potentials. For instance, friction may be treated without resorting to the use of non-conservative force by considering the motion of individual molecules, however that means every molecule's motion must be considered rather than handling it through statistical methods. For macroscopic systems, the non-conservative approximation is far easier to deal with rather than millions of degrees of freedom. Examples of non conservative forces are friction and non-elastic material stress.

Motion of a Body Near the Surface of the Earth

Motion of a body which can be modeled as a particle, near the surface of the earth ie, when the earth's gravitational field can be approximated to be a constant, can be analyzed by the equations of kinematics by replacing the acceleration by g.

Linear Restoring Force and Potential Energy Curve

A force which is directly proportional to the displacement measured from some fixed point and in a direction tending to reduce the displacement is called the linear restoring force.

The potential energy function of such force, when plotted, gives a parabola.

References

Adhikari, Pitri Bhakta. A Textbook of Physics Volume-I. Kathmandu: Sukunda Pustak Bhawan, 2015.

Feynman, Richard P. The Feynman Lectures on Physics Volume 1. Noida: Dorling Kindersley (India) Pvt. Ltd., 2014.

Mathur, D S. Mechanics. New Delhi: S. Chand & Company Pvt. Ltd., 2015.

Young, Hugh D, Roger A Freedman and A Lewis Ford. University Physics. Noida: Dorling Kindersley (India) Pvt. Ltd., 2014.