King Fahd University of Petroleum & Minerals Mechanical Engineering Dynamics ME 201 BY Dr. Meyassar N. Al-Haddad Lecture # 16

Chapter 14 Kinetics of a Particle ; Work & Energy Objectives –To develop the principle of work and energy and apply it solve problems that involve force, velocity, and displacement. –To study problems that involve power and efficiency. –To introduce the concept of a conservative force and apply the theorem of conservation of energy to solve kinetic problems.

Work of a Force F S U = F. S F U = (F cos  S

Work of a Weight

Work of a Spring Force

Work and Energy relation Initial K.E + Work Done = Final K.E

Power and Efficiency Power is defined as the amount of work performed per unit time. “rate of downing work” Mechanical Efficiency :

Example 14-7

CONSERVATIVE FORCE A force F is said to be conservative if the work done is independent of the path followed by the force acting on a particle as it moves from A to B. In other words, the work done by the force F in a closed path (i.e., from A to B and then back to A) equals zero. This means the work is conserved.  rF0  · d x y z A B F A conservative force depends only on the position of the particle, and is independent of its velocity or acceleration.

14.5 Conservative Forces and Potential Energy Conservative Force: independent of the path –Example weight & spring force –The work done by the frictional and applied force -> depends on the path -> non-conservative-> the work is dissipated (heat) Potential Energy: “capacity for doing work” –Energy comes from the motion -> Kinetic energy –Energy comes from the position-> Potential energy

Gravitational potential Energy : Elastic potential energy :

Potential Function: particle subjective to both gravitational and elastic force

Conservation of Mechanical Energy For a system of Particles

Example

Example 14-9

Review Example 14-8 Example Example 14-11