mech_6_energy - Energy - Currency between different...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Energy - Currency between different disciplines e.g. Chemistry, Thermodynamics - Kinetic, potential; strain m j m i F i f ij f ij r j r i Consider a system of particles. F i - External force on i th particle f ij - Internal force on i th particle due to j and ff ij ji =− For i th particle Ff m ii j j += && r ji ( 1 ) Multiply (1) by & r i Fr f r m r r m d dt r i i i j i iii i i •+ •= = & & & 1 2 2 & & (2) Also for each fr ij i ji j , there is one and () f r r ij i ji j ij i j ij ij && & & +=− = where is the relative velocity between particle i and j . & r ij Summing up for all particles (2) becomes d dt mr i i j j i i ∑∑ 1 2 2 i & We have d dt i i ij ij ij i i 1 2 2 & (3) Integrate (3) w.r.t. time, we have F dr dt dt f dr dt dt m r i i i ij ij ij i 1 2 1 2 2 1 2 & or Fdr f dr i ij ij ij i 1 2 1 2 2 1 2 & (4) W.D. by W.D. by change in K.E. external force internal force 1
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Kinetic energy of a rigid body From (4), K.E. = 1 2 2 mr ii i For rigid body in plane motion, particle velocity is && rr iG =+× i ω ρ therefore () K.E. =+ × + × × × ∑∑ 1 2 1 2 1 2 2 r m r m i G i i i i G i i i ωρ z y x r i r G G m i ρ i 1st term, 1 2 1 2 1 2 22 r
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 05/10/2009 for the course MXXM 2XX9 taught by Professor Gxxy during the Spring '09 term at City University of Hong Kong.

Page1 / 6

mech_6_energy - Energy - Currency between different...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online