lec02 - Dynamics of a Single Particle(Review(continued 1...

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Cite as: Thomas Peacock and Nicolas Hadjiconstantinou, course materials for 2.003J/1.053J Dynamics and Control I, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. Dynamics of a Single Particle (Review) (continued) 1 2.003J/1.053J Dynamics and Control I, Spring 2007 Professor Thomas Peacock 2/12/2007 Lecture 2 Work-Energy Principle Dynamics of a Single Particle (Review) (continued) Reading: Williams 4–1, 4–2, 4–3 (Momentum Principles) - End of lecture last time Work-Energy Principle This material is covered in Williams 5–1, 5–2, and 5–3. Figure 1: Single particle moving. m moves along r ( t ) and experiences a force, F . Figure by MIT OCW. W 12 =work done going from 1 2 r 2 Integral over sum = F · dr = “Work done by force F(t)” (in going from r 1 to r 2 ) r 1 t 2 = F · vdt (Integration over time) t 1 t 2 d = ( mv ) · vdt where m is constant dt t 1
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Cite as: Thomas Peacock and Nicolas Hadjiconstantinou, course materials for 2.003J/1.053J Dynamics and Control I, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 2 Dynamics of a Single Particle (Review) (continued) t 2 d 1 = mv · v dt dt 2 t 1 = 1 2 mv · v | t t 2 1 = 1 2 mv 2 2 1 2 mv 1 2 Define Kinetic Energy T = 1 2 m | v | 2 W 12 = T 2 T 1 = (Work done is the change in the kinetic energy) Consider the case: ∂V F = ∂r For example, ∂V ∂V F = ( ˆ ı j ˆ) ∂x ∂y r 2 r 2 ∂V W 12 = F · dr = · dr = V 1 V 2 (Potential Energy) ∂r r
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