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Introduction
Newton's laws of motion help us to analyse many kinds of motion. But the analysis is complicated, requiring details about the motion that we simply do not know.
Expression for Work
Let us consider a situation where the force is acting along the X-axis and the magnitude of the force is varying with position 'x'. Thus, as the ball moves, the magnitude of the work done by the force, on the ball, changes. The adjacent graph shows the plot of a one dimensional variable force.
Kinetic Energy
Energy is a number that we associate with a system of one or more objects. If a force acts on one of the objects, making it move, then the number changes. After countless experiments, scientists and engineers realised that if the scheme by which we assign these energy numbers is planned carefully, then the numbers can be used to predict the outcome of experiments. However, learning how to use the numbering scheme is not easy. Let us focus on one form of energy - kinetic energy.
Power
A contractor wishes to lift a load of bricks from the sidewalk to the top of a building by means of a winch. Since we know the expression for work, we can calculate work to be done by the force applied by the winch to lift the load. We are interested in the rate at which it is done, that is, will the job take 5 minutes or a week.
Work Energy Theorem
According to this principle, work done by a force in displacing a body, gives the measure of the change in kinetic energy of the body.
Gravitational Potential Energy Near the Surface of Earth
As we go higher above the surface of the Earth, the value of acceleration due to gravity decreases. But for those heights which are very small when compared to the radius of the Earth, g (and hence mg) can be assumed to be constant.
Potential Energy of a Spring
Consider a massless spring of natural length 'l', one end of which is fastened to a wall. The other end is attached to a block, which is slowly pulled on a smooth horizontal surface, to extend the spring.
Conservative Forces and Non-Conservative Forces
If the work done by a force depends only on the initial and final states and not on the path taken, then it is a conservative force.
Conservation of Mechanical Energy
We can see many situations in which energy is transferred to or from objects and systems, similar to money being transferred between accounts. In each situation, we assume that the energy that was involved can be accounted for, that is, energy cannot appear or disappear. Energy obeys the law of conservation of energy, which is concerned with the total energy of the system.
Illustration of Conservation of Mechanical Energy
Conversion of gravitational potential energy to kinetic energy: When a body falls from a certain height, its kinetic energy increases.
Elastic and Inelastic Collisions in One and Two Dimensions
A Karate expert strikes a board of mass 0.14 kg and breaks it, with his fist of mass 0.70 kg. He then does the same to a 3.2 kg concrete block.
Head-on Elastic Collision [One Dimensional Elastic Collision]
It is that elastic collision in which the colliding bodies move along the same straight line before and after the collision.
Elastic Collision in Two Dimensions (Oblique Collision)
If the colliding bodies do not move along the same straight line path, then the collision is said to be an oblique collision.
Different Forms of Energy
Energy can manifest itself in a number of forms. We have already seen that it can be in the form of mechanical energy, which is subdivided into kinetic energy and potential energy.
Variation of Mass with Velocity
According to Newton's second law of motion, F = ma.
Einstein's Mass-Energy Equivalence Relation
According to Newton's second law of motion, force acting on a body is defined as the rate of change of its momentum.
Summary
In physics, the concept of energy plays the role of the money. Work is transferred to or from an object by means of force acting on the body. Energy transferred to the body is positive work and the energy transferred from the body is negative work.
