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Momentum, Impulse and Collisions: Applied Scenario

≈ 25 min
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Applied Scenario

Apply the idea in context while keeping the assumptions, units, safety and affected people visible.

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 — Applied Scenario: 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 — Applied Scenario: Two cars collide and lock together, moving off as one wreck. Which statement is correct for the isolated two-car system?

Physics — Year 1 — Applied Scenario: 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 applied scenario lesson.

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