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Momentum, Impulse and Collisions: Worked Reasoning

≈ 25 min
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Worked Reasoning

Make each reasoning step visible: identify the knowns, choose the governing idea, apply it and check the result.

This extension applies that lens specifically to Momentum, Impulse and Collisions.

Linear momentum is p⃗=mv⃗\vec{p} = m\vec{v}, measured in kg⋅m/s\text{kg}\cdot\text{m/s}. Newton's second law in its original form reads

∑F⃗=dp⃗dt\sum \vec{F} = \frac{d\vec{p}}{dt}

Integrating over a time interval gives the impulse–momentum theorem:

J⃗=∫F⃗ dt=Δp⃗\vec{J} = \int \vec{F}\,dt = \Delta \vec{p}

If the net external force on a system is zero, its total momentum is constant — the conservation of linear momentum. For two bodies:

m1u⃗1+m2u⃗2=m1v⃗1+m2v⃗2m_1\vec{u}_1 + m_2\vec{u}_2 = m_1\vec{v}_1 + m_2\vec{v}_2

Momentum is conserved in every collision of an isolated system. Kinetic energy is conserved only in an elastic collision; in an inelastic one some kinetic energy becomes heat, sound and permanent deformation. When the bodies stick together, the collision is perfectly inelastic.

Worked example. A 0.15 kg0.15\ \text{kg} cricket ball arrives at a bat at 30 m/s30\ \text{m/s} and leaves along the same line at 40 m/s40\ \text{m/s} in the opposite direction.

Take the outgoing direction as positive, so u=−30 m/su = -30\ \text{m/s} and v=+40 m/sv = +40\ \text{m/s}:

J=Δp=m(v−u)=0.15(40−(−30))=0.15(70)=10.5 N⋅sJ = \Delta p = m(v - u) = 0.15\big(40 - (-30)\big) = 0.15(70) = 10.5\ \text{N}\cdot\text{s}

If the contact lasted 2.0 ms2.0\ \text{ms}, the average force was F=J/Δt=10.5/0.0020=5250 NF = J/\Delta t = 10.5/0.0020 = 5250\ \text{N} — which is why bats break.

Physics — Year 1 — Worked Reasoning: What is the magnitude of the momentum of a 1200 kg1200\ \text{kg} bakkie travelling at 15 m/s15\ \text{m/s}? Give the answer in kg⋅m/s\text{kg}\cdot\text{m/s}.

Physics — Year 1 — Worked Reasoning: Two cars collide and lock together, moving off as one wreck. Which statement is correct for the isolated two-car system?

Physics — Year 1 — Worked Reasoning: A 0.15 kg0.15\ \text{kg} cricket ball travelling at 30 m/s30\ \text{m/s} is struck and returns along the same straight line at 40 m/s40\ \text{m/s}. What is the magnitude of the impulse delivered to the ball, in N⋅s\text{N}\cdot\text{s}?

Name the original topic being extended by this worked reasoning lesson.

Which statement is the best evidence-led starting point for Momentum, Impulse and Collisions: Worked Reasoning?