Momentum

Equipment

• «1. Động lượng p=mv» canvas: the momentum vector along the motion axis; drag to rotate the view
• «Khối lượng m» (mass, 1–10 kg) and «Vận tốc v» (velocity, −8…8 m/s) sliders
• «2. Xung lượng đổi động lượng» canvas: vectors pᵢ before and p_f after the impulse
• «Lực trung bình F» (average force, −20…20 N) and «Thời gian Δt» (duration, 0.1–1.0 s) sliders
• «Tạm dừng chuyển động» (pause) button; readouts «Động lượng p = mv = …» and «Xung lượng J = FΔt = …; p sau = …»

Procedure

1. Measure p = mv vs m and v

   In section 1, hold «Vận tốc v» fixed and raise «Khối lượng m» from 1 to 10 kg: the p arrow lengthens and the «p = mv» readout grows linearly. Then set v negative — the vector reverses and p takes a negative sign relative to the rightward axis. Verify several pairs against $p = mv$.

2. Compute the impulse J = FΔt

   In section 2, set «Lực trung bình F» = 8 N and «Thời gian Δt» = 0.4 s (slider at 4): the readout gives J = 3.2 N·s. Double Δt to 0.8 s and watch J double; set F negative and see J and the p_f vector reverse — a force opposing the motion reduces momentum.

3. Verify p_f = pᵢ + J

   Choose m = 4 kg, v = 5 m/s (pᵢ = 20 kg·m/s), then set F and Δt so that J = −25 N·s: the «p sau» readout must show −5 kg·m/s — the p_f vector reverses relative to pᵢ on the canvas. Repeat with J > pᵢ and J ≈ −pᵢ to see the body speed up, reverse, or stop; each time check $p_f = p_i + F\Delta t$.

4. Predict before changing conditions

   Predict: keeping J fixed but splitting it differently (F = 20 N for 0.4 s vs F = 8 N for 1.0 s) — is p_f the same? Test on the simulation and explain why only the product FΔt matters (airbags lengthen Δt to reduce F for the same reason). Press «Tạm dừng chuyển động» to compare the pᵢ and p_f vectors.

Simulation

Experiment history

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