Newtonian mechanics

Conservation of mechanical energy

Track the exchange between potential energy $U = mgh$ and kinetic energy $K = \tfrac12mv^2$ of a rolling ball; verify that mechanical energy $E_m = U + K$ is conserved without friction and decreases with friction.

High school

Equipment

Virtual ball sliding on a frictionless curve in the 3D canvas
Sliders “Độ cao ban đầu h” (initial height), “Khối lượng m” (mass), and “Ma sát” (friction)
Buttons “Tạm dừng”/“Chạy tiếp” (pause/resume) and “Thả lại” (release again)
Energy bars U, K, E plus the readout “U = … J · K = … J · Eₘ = … J · v = … m/s”

Procedure

Watch the potential–kinetic exchange
Set «Ma sát» to 0, «Độ cao ban đầu h» to 8 m and «Khối lượng m» to 3 kg. Read the values when the ball is at the bottom: $U$ is near 0 and $K$ peaks; the U and K bars trade height while the yellow Eₘ bar stays fixed. Press «Tạm dừng» at any position and check $U + K = E_m$ , i.e. $mgh + \tfrac12mv^2 = mgh_0$ .
Measure the speed at the lowest point
Press «Thả lại» and read “v = … m/s” as the ball passes the bottom. Compare with the prediction $v = \sqrt{2gh_0}$ (for h₀ = 8 m and g = 9.8 m/s², $v \approx 12.5$ m/s). Change «Khối lượng m» from 3 to 8 kg and repeat: the bottom speed is unchanged because both U and K scale with m, so m cancels.
Enable friction and track the heat
Drag «Ma sát» to about 0.30 and watch: the Eₘ bar shrinks, the readout gains “chuyển thành nhiệt ≈ … J” (converted to heat), and the ball reaches lower peaks each pass. Record Eₘ and the heat term over a few cycles; note that $E_m + Q$ stays constant — mechanical energy is not lost but becomes internal energy.

Simulation

Experiment history

In the early seventeenth century, Galileo Galilei rolled balls on inclined tracks and recognized that a body descending regains nearly its initial height on the opposite slope — this “height traded for speed” idea seeded the conservation of mechanical energy. In 1686, Gottfried Wilhelm Leibniz named the quantity

mv^2

vis viva (“living force”) and argued it is conserved in elastic collisions, disputing the Cartesians who conserved

mv

. The nineteenth century completed the picture: Thomas Young brought the word “energy” into science in 1807, Gaspard-Gustave Coriolis standardized work and kinetic energy

\tfrac12mv^2

in the 1820s, and James Prescott Joule measured the “mechanical equivalent of heat” around 1840–1849 — proving that mechanical energy “lost” to friction is not destroyed but becomes heat, exactly what the simulation shows when you raise the friction slider. Hermann von Helmholtz synthesized the general conservation of energy in 1847.

Related physicists

Isaac Newton Galileo Galilei James Prescott Joule

Equipment

Procedure

Simulation

Experiment history

Related physicists

Related library topics