EQ-WORK-ENERGY · Classical Mechanics
Work–Energy Theorem
W - m*(v_f**2 - v_i**2)/2 = 0
Variables
variable
W
net work done on the body along its path
- Object
- rigid_body
- Property
- Energy
- Context
- inertial_frame
- Constraint
- net_work
variable
m
inertial mass (constant)
- Object
- rigid_body
- Property
- Mass
- Context
- inertial_frame
variable
v_f
final speed (magnitude)
- Object
- rigid_body
- Property
- Speed
- Context
- inertial_frame
- Constraint
- final
variable
v_i
initial speed (magnitude)
- Object
- rigid_body
- Property
- Speed
- Context
- inertial_frame
- Constraint
- initial
Axioms
algebraic classical constant_coefficients deterministic non_relativistic
Assumptions
- m is constant (not variable-mass)
- Classical regime (|v| << c)
- W includes all net external work done on the body
- The body is treated as a point particle
Derivation
- Time integral of Newton's second law along the trajectory: ∫F·dx = ∫m(dv/dt)(dx/dt)dt = ∫m v dv = (1/2)m(v_f²-v_i²)
- Equivalently, the component of Noether's theorem for time translation, restricted to a trajectory segment
References
- Goldstein, Classical Mechanics, 3rd ed., §1.1 Eq. (1.19)
- Halliday/Resnick/Walker, Fundamentals of Physics, 11th ed., §7-3