13 - Kinematics of a Partcile : Force and Acceleration

13.1 Newton's Second Law of Motion



Chapter Objectives

To state Newton's Second Law of Motion and to define mass and weight. To analyze the accelerated motion of a particle using the equation of motion with different coordinate systems.To investigate central-force motion and apply it to probles in space mechanics.

Kinetics is a branch of dynamics that deals with the relationship between the change in motion of a body and the forces that cause this change. The basis for kinetics is Newton's second law, which statet that when an unbalanced forces acts on a particle, the particle will accelerate in the direction of the force with a magnitude that is proportional to the force.

This law can be verified experimentally by applying a known unbalanced force (F) to a particle, and then measuring the acceleration (a). Since the force and acceleration are directly proportional, the constant of proportinality, (m), may be detemined from the ratio m=F/a. This positive scalar (m) is called the mass of the particle. Being constant during any acceleration, m provides a quantitative measure of the resistance of the particle to a change in its velocity, that is its inertial.

If the mass of the particle is m, Newton's second law of motion may be written in mathematical form as

F=ma

The above equation, which is referred to as the equation of motion, is one of the most important formulations in mechanics. As previously stated, its validity is based on solely on experimental evidence. In 1905, however, Albert Einstein developed the theory of relativity and placed limitations on the use of Newton's second law for describing general particle motion. Through experiments it was proven that time is not an absolute quantity as assumed by Newton;
and as a result, the equation of motion fails to predict the exact behavior of particle, especially when the particle's speed approaches the speed of light (0.3Gm/s). Developments of the theory of quantum mechanics by Erwin Schrodinger and others indicate further that conclusions drawn from using this equation are also invalid when particles are the size of an atom and move close to one another. For the most part, however, these requirements regarding particle speed and size are not encountered in engineering problems, so their effect will not be considered in this book.