theorem 19.38 Work–energy theorem

open in the book · parts/03-classical-mechanics/02-newtonian-dynamics.tex:1126 · p. 746

Rests on

depends_on definition 19.29 Kinetic energy ¶
- depends_on definition 18.10 Velocity ¶
  - depends_on definition 7.26 Derivative of a function at a point ¶
    - depends_on definition 7.16 Limit ¶
      - depends_on definition 7.2 Absolute value ¶
      - depends_on definition 7.9 Real function ¶
    - depends_on definition 7.9 Real function ¶ ↺
  - depends_on definition 18.9 Position ¶
    - depends_on definition 18.7 Frame of reference ¶
      - depends_on definition 18.3 Particle ¶
    - depends_on definition 18.3 Particle ¶ ↺
  - depends_on definition 13.9 Tangent vector to a curve ¶
    - depends_on definition 13.8 Curve ¶
- depends_on definition 19.3 Mass ¶
  - depends_on definition 18.3 Particle ¶ ↺
  - depends_on postulate 19.1 Inertia ¶
    - depends_on definition 18.8 Inertial frame of reference ¶
      - depends_on definition 18.7 Frame of reference ¶ ↺
      - depends_on definition 18.6 Free particle ¶
    - depends_on definition 18.3 Particle ¶ ↺
depends_on definition 19.34 Work ¶
- depends_on definition 18.3 Particle ¶ ↺
- depends_on postulate 19.8 Newton's second law ¶
  - depends_on definition 19.5 Linear momentum ¶
    - depends_on definition 18.10 Velocity ¶ ↺
    - depends_on definition 19.3 Mass ¶ ↺
  - depends_on postulate 19.6 Newton's first law ¶
    - depends_on definition 18.8 Inertial frame of reference ¶ ↺
    - depends_on definition 19.5 Linear momentum ¶ ↺
depends_on equation 19.4 eq:newt-fma ¶
proves proof ch:02-newtonian-dynamics@proof-12 ¶

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Edges

type	direction	node	provenance	where
`depends_on`	→	Kinetic energy	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:1132
`depends_on`	→	Work	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:1132
`depends_on`	→	eq:newt-fma	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:1132
`proves`	←	ch:02-newtonian-dynamics@proof-12	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:1135