In the preceding chapter, most problems dealing with the motion of particles were solved through the use of the fundamental equation of motion F = ma. Given a particle acted upon by a force F, we could solve this equation for the acceleration a; then, by applying the principles of kinematics, we could determine from a the velocity and position of the particle at any time.

Using the equation F = ma together with the principles of kinematics allows us to obtain two additional methods of analysis, the method of work and energy and the method of impulse and momentum. The advantage of these methods lies in the fact that they make the determination of the acceleration unnecessary. Indeed, the method of work and energy directly relates force, mass, velocity, and displacement, while the method of impulse and momentum relates force, mass, velocity, and time.

The method of work and energy will be considered first. In Secs. 13.2 through 13.4, the work of a force and the kinetic energy of a particle are discussed and the principle of work and energy is applied to the solution of engineering problems. The concepts of power and efficiency of a machine are introduced in Sec. 13.5.

Sections 13.6 through 13.8 are devoted to the concept of potential energy of a conservative force and to the application of the principle of conservation of energy to various problems of practical interest. In Sec. 13.9, the principles of conservation of energy and of conservation of angular momentum are used jointly to solve problems of space mechanics.

The second part of the chapter is devoted to the principle of impulse and momentum and to its application to the study of the motion of a particle. As you will see in Sec. 13.11, this principle is particularly effective in the study of the impulsive motion of a particle, where very large forces are applied for a very short time interval.

In Secs. 13.12 through 13.14, the central impact of two bodies will be considered. It will be shown that a certain relation exists between the relative velocities of the two colliding bodies before and after impact. This relation, together with the fact that the total momentum of the two bodies is conserved, can be used to solve a number of problems of practical interest.

Finally, in Sec. 13.15, you will learn to select from the three fundamental methods presented in Chaps. 12 and 13 the method best suited for the solution of a given problem. You will also see how the principle of conservation of energy and the method of impulse and momentum can be combined to solve problems involving only conservative forces, except for a short impact phase during which impulsive forces must also be taken into consideration.