Physic Labs

Newtonian mechanics

Kinetic energy

Observe how the ball's kinetic energy changes with mass and speed, compare the energy bar with K=12mv2K = \tfrac{1}{2}mv^2, and verify that net work equals the change in kinetic energy ΔK=Wnet\Delta K = W_{\text{net}}.

Middle school

Equipment

  • Virtual rail carrying a moving ball of mass m
  • “Mass m” slider (1–20 kg)
  • “Speed v” slider (0–20 m/s)
  • “Net work W” slider (−100…+100 J)
  • Energy bars for K and W, Pause button, and the K₀ readout

Procedure

  1. Check K ∝ v² at fixed mass

    Keep m = 5 kg and sweep the “Speed v” slider; the K bar grows quadratically. Record the K₀ readout at two speeds and compare the ratio K₂/K₁ with (v₂/v₁)² from K=12mv2K = \tfrac{1}{2}mv^2.

  2. Use work to raise or lower kinetic energy

    Drag the “Net work W” slider positive then negative: the ball speeds up or slows down and the W bar adds to or subtracts from K. Compare the K shift with the work–energy theorem ΔK=Wnet\Delta K = W_{\text{net}}; the model does not allow negative K.

  3. Compare the roles of m and v

    Press “Pause” to read values precisely, then double m and double v in turn. Doubling v quadruples K while doubling m only doubles it — explain with K=12mv2K = \tfrac{1}{2}mv^2 and predict each outcome before moving the slider.

Simulation

Experiment history

Galileo showed experimentally that free-fall distance grows as the square of time, so speed increases uniformly — a precursor of the idea of kinetic energy. In the late seventeenth century Leibniz championed vis viva, mv², as the conserved quantity, against the Cartesian mv; the dispute lasted until the roles of momentum and energy were properly separated. In Newtonian mechanics force relates directly to momentum through the second law, while the line integral of force defines work. During the nineteenth century the works of d'Alembert, Lagrange and especially Gaspard-Gustave Coriolis (1829) — who introduced the factor ½ and the very word “work” — standardized the work–energy theorem ΔK=Wnet\Delta K = W_{\text{net}} illustrated by this simulation.

Related physicists

Galileo GalileiIsaac Newton

Related library topics

Kinetic energy