A scrum has two distinct physics phases. First the hit: both packs sprint the engagement gap at the chosen closing speed and collide almost inelastically — they lock and share a common velocity, exactly like a perfectly inelastic collision:
Hit: p_A = m_A·v, p_B = m_B·v (opposing directions)
v_combined = (p_A − p_B) / (m_A + m_B)
Impulse J = |p_A| + |p_B|
Peak engagement force F ≈ J / Δt_impact (Δt_impact ≈ 0.15 s)
Then the sustained drive: each pack's forwards apply a push force that scales with their own mass (more forwards/heavier forwards = more thrust) and a technique factor capturing binding, body height and leg drive efficiency, opposed by the other pack's force and by friction between boots and turf:
F_A = k · m_A · technique_A, F_B = k · m_B · technique_B
F_net = F_A − F_B − μ·N·sign(v), N = (m_A+m_B)·g
a = F_net / (m_A + m_B)
v(t+dt) = v(t) + a·dt, x(t+dt) = x(t) + v(t)·dt
- Pack mass — heavier packs both hit harder (more momentum at engagement) and sustain more push force during the drive.
- Technique factor — same mass, more (or less) usable force: good technique (low body height, tight bind, synchronised leg drive) converts mass into force more efficiently than raw bulk alone.
- Closing speed at hit — how fast each pack sprints into the engagement; higher speed means a larger momentum exchange and a bigger (sometimes penalised, in real rugby) engagement force spike.
- Ground friction μ — higher μ (dry turf, good studs) resists motion more, so both packs need more surplus force to actually shift the scrum; low μ (wet/muddy pitch) lets even a small force advantage translate into rapid ground gained.
- Engage Scrum — runs the hit (computing the inelastic collision above) then the drive phase in real time until the scrum reaches the sideline or stalls.
Real-world relevance: this is the same momentum/impulse and net-force reasoning that explains any rugby collision — tackles just compress the same physics into a single instant instead of a sustained push. This 2D companion swaps the 3D version's fixed drive-power sliders for mass and technique, so you can see how the same push force can come from either raw bulk or better technique.