Momentum, Impulse and Collisions: Mechanism

≈ 25 min

Mechanism

Follow the mechanism step by step and distinguish what causes the change from what is merely observed.

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

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

\sum \vec{F} = \frac{d\vec{p}}{dt}

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

\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:

m_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 $0.15\ \text{kg}$ cricket ball arrives at a bat at $30\ \text{m/s}$ and leaves along the same line at $40\ \text{m/s}$ in the opposite direction.

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

J = \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 $2.0\ \text{ms}$ , the average force was $F = J/\Delta t = 10.5/0.0020 = 5250\ \text{N}$ — which is why bats break.

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

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

Kinetic energy is conserved but momentum is not

Momentum is conserved but kinetic energy is not

Both momentum and kinetic energy are conserved

Neither momentum nor kinetic energy is conserved

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

Name the original topic being extended by this mechanism lesson.

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

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

\sum \vec{F} = \frac{d\vec{p}}{dt}

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

\vec{J} = \int \vec{F}\,dt = \Delta \vec{p}

If the net external force on a system is zero, its total momentu

Kinematics in One Dimension

Newton's Laws and Free-Body Diagrams

A conclusion needs no observations, calculations or stated assumptions.