Newtonian Dynamics in the Absence of Frictional Forces

An important concept of dynamics is the work w performed by an external force acting through a distance. If force F is applied through differential distance dr, the differential work is defined as 

The dot product between vectors F = (Fx, Fy, Fz) and dr = (dx, dy, dz) can be written more explicitly in terms of Cartesian components as 

Note from (2.58) that force F has the physical units of (mass)(length)(time)-2 [SI newton (N)], while work w has units of (mass)(length)2(time)-2 [SI joule (J)]. Attention to dimensional units of a physical quantity, as well as facility in switching from one set of units to another, will facilitate understanding of thermodynamics and its applications in diverse fields of knowledge. 

As illustrative examples of the work concept, let us develop expressions for two well-known types of work, using the general definition (2.60)  

Extending a spring. For a simple Hooke s law spring, the force of extending the spring increases in proportion to extension distance r (with proportionality force constant k), Fspring = Kr. In this case, 

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