DYNAMICS · WORK–ENERGY THEOREM
Work and Energy
Explore how gravity converts potential energy into kinetic energy and howfriction and inelastic collisions dissipate mechanical energy. Calculate work done by each force and check the energy balance at any time.
Physical Parameters
Simulation and Energy Balance
True-Scale Geometry 1:1: horizontal and vertical metres use the same scale. The incline and the motion use the same coordinate transform.
Energy and Work at Selected Time
During frictionless motion with no external work, E = K + U is conserved. At an end stop the body undergoes a perfectly inelastic impact with permanent stopping, which dissipates energy: the mechanical system is not conservative.
Work Done by Each Force and Dissipation
Synchronized Energy and Motion Graphs
Click a graph or enter an exact time. Impact discontinuities are highlighted; they do not represent a continuous change in energy.
Kinetic Energy K(t) and Potential Energy U(t)
Mechanical Energy E(t) and Energy Balance
Accumulated Work of Forces (J)
Position s(t)
Velocity v(t)
Values Table
| t (s) | s (m) | v (m/s) | K (J) | U (J) | E (J) | W gravity (J) | W external (J) | W friction (J) | W impacts (J) | Residual (J) | Regime |
|---|
SI units, comma-separated, decimal point.
Model Assumptions
The body is treated as a point particle on a rigid incline of length L, constant angle θ, with uniform gravity. The normal component of weight is balanced by the surface. The normal force does no work because it is perpendicular to displacement.
The forces acting along the incline are constant: gravity, an external force parallel to the plane, and Coulomb static and kinetic friction. Static friction can maintain rest without doing work; kinetic friction always does negative work during sliding.
The energy graphs accumulate work along the actual distance travelled, including after a reversal. The impact balance accounts for instantaneous kinetic energy loss; the body locks at the boundary without bouncing.
Air drag, rotational motion, deformation and explicit heating are excluded. Lost mechanical energy is recorded as dissipation; it does not disappear from the total energy of the environment.
FROM FORCES TO ENERGY BALANCE
Step-by-Step Calculations
General equations, dimensional substitutions, intermediate steps and results in joules.
Calculations retain full internal precision; only displayed results are rounded. Each equation appears on its own line, with MathML fallback.
Other Experiments: Pulleys · Inclined Plane · Forces and Newton · Physics Lab