Separating the universe into point models of objects and force vector models of everything else

1. Constructing Free-Body DiagramsA Step-by-Step Method modeled on the multiple representation technique ofDr. Alan Van Heuvelan at Rutgers University Separating the universe into point models of objects and force vector models of everything else Leo Takahashi The Beaver Campus of The Pennsylvania State University

2. Constructing Free-Body Diagrams for Interacting Objects Featuring Newton’s Third Law  L. H. Takahashi, August 2007

4. a v a v  m m M

5. a a FN2 F FN1 fk1  FT fk2 FT fk1 mg Mg FN1  m v M v FBD Block FBD Slab

6. FBD Slab FBD Block FN2 F FN1 fk1 FT  fk1 fk2 FT a a mg Mg FN1

7. +y +X FBD Block F FN1  FT fk1 a mg Fx = max FCos - FT – fk1 = ma Fy = may FN1 + FSin - mg = 0

8. +y +x FBD Slab FN2 fk2 fk1 FT Mg a FN1 FT - fk1 - fk2 = Ma Fx = Max FN2 - FN1 - Mg = 0 Fy = May

9. FCos - FT - fk1 = ma FN1 + FSin - mg = 0 FT - fk1 - fk2 = Ma FN2 - FN1 - Mg = 0 fk1 = k1FN1 fk2 = k2FN2 Block Equations Slab Equations Friction Equations