Calculator · Engineering Mechanics
Work–Energy Calculator
Work done by a constant force over a straight displacement, and the work–energy theorem for a particle: T₂ − T₁ = W_net.
Calculation
Force and displacement
Results
| Work W = F · Δr | 30 J |
|---|---|
| Sign | Positive — energy added |
| Reading | The force has a component along the displacement, so it adds energy to the particle. |
Technical reference
T = ½·m·v²
W = F · Δr (constant force only)
ΣW = ΔT
- T
- particle kinetic energy[J]
- m
- particle mass[kg]
- v
- speed[m/s]
- F
- constant force[N]
- Δr
- straight-line displacement[m]
- W
- work of a force[J]
The general definition of work is the path integral W = ∫F·dr; this calculator implements only the constant-force case W = F·Δr = F·d·cosθ over a straight displacement, not a general path integral. The work–energy theorem uses the net work of every force on the particle.
This is particle (translational) kinetic energy only, with no rotational term. For a rigid body, T also includes ½·I·ω², see the Rigid-Body Work–Energy Calculator.
Assumptions
- · Point particle; kinetic energy is ½m|v|² with no rotational term.
- · Work is computed for a CONSTANT force over a straight displacement — no path integral is approximated.
- · The work–energy theorem uses the NET work of every force acting on the particle.
- · A negative final kinetic energy has no physical speed; it is reported as such and never as an imaginary number.
Related tools
- Constant Acceleration
- Projectile Motion
- Circular Motion
- Curvilinear Motion
- Newton's Second Law
- Impulse–Momentum
- Collision
There is no Particle Motion handoff here: a mass, a speed and a scalar amount of work do not define a planar motion model, and an approximate one would be misleading.