Conservation of momentum

Equipment

• Two carts m₁, m₂ on a horizontal plane (3D canvas, drag to rotate the view)
• Mass sliders m₁ (kg) and m₂ (kg)
• Initial-velocity sliders u₁ (m/s) and u₂ (m/s)
• External impulse J (N·s) and duration Δt (s) sliders
• Readout panel “P trước / P sau” (kg·m/s)

Procedure

1. Set masses and initial velocities

   In section 1, move the four sliders m₁ (kg), m₂ (kg), u₁ (m/s), u₂ (m/s) — try u₁ > 0 and u₂ < 0 so the carts move toward each other (positive direction is to the right). Read the line “P trước = m₁u₁+m₂u₂” below and check it against $P = m_1u_1 + m_2u_2$ computed from the slider values.

2. Check that total momentum stays constant

   Keep the external impulse in section 2 at J = 0. Vary m₁, m₂, u₁, u₂ in section 1 and record P trước each time; the readout always states “P sau bằng P trước” when J ngoài ≈ 0 — the system is isolated horizontally so total momentum is conserved even though each cart changes velocity. Compare with $m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2$.

3. Try a nonzero external force

   In section 2, move the “Xung lượng ngoài J (N·s)” slider to positive then negative values, and also vary “Thời gian Δt (s)”. The readout “P sau = P trước + J ngoài” shows total momentum is no longer conserved: it shifts by exactly J, matching the impulse form of Newton's second law $\Delta P = J_{\mathrm{ext}}$ with mean external force $F = J/\Delta t$.

4. Predict and compare

   Choose m₁ = m₂ and u₂ = −u₁; predict P trước, then compare with the readout (expecting P = 0 — the momentum arrows cancel on the canvas). Then set J ≠ 0 and estimate P sau with $P_{\text{after}} = P_{\text{before}} + J$ before reading the value; repeat with two other (m, u) pairs to check when the conservation law applies.

Simulation

Experiment history

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