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Mechanics · Momentum

Chapter 1 · 3

The idea

Impulse and momentum as vectors

How a push changes the motion of a particle moving on a plane: the impulse-momentum principle I = mv − mu in i, j components, the velocity after an impulse, the size of an impulse, the angle the motion is turned through, the kinetic energy gained or lost, impulses with an unknown in them, the momentum triangle, and the equal and opposite impulses when two particles collide.

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Mechanics · Momentum

Impulse and momentum as vectors

How a push changes the motion of a particle moving on a plane: the impulse-momentum principle I = mv − mu in i, j components, the velocity after an impulse, the size of an impulse, the angle the motion is turned through, the kinetic energy gained or lost, impulses with an unknown in them, the momentum triangle, and the equal and opposite impulses when two particles collide.

Why it works

Where does the puck go?

A puck PP of mass 0.50.5 kg slides across smooth, level ice with velocity (8i+6j) m s−1(8\mathbf{i} + 6\mathbf{j})\text{ m s}^{-1}, where i\mathbf{i} and j\mathbf{j} are perpendicular unit vectors on the ice. A player's stick strikes it, and it shoots off at 12 m s−112\text{ m s}^{-1}, straight along j\mathbf{j}. How hard was it hit, and which way?10 m s⁻¹12 m s⁻¹struck herebeforeafterijOn a flat surface a direction needs two numbers, so momentum is a vector: mass times velocity, component by component. Before the hit the puck's momentum is 0.5(8i+6j)=(4i+3j)0.5(8\mathbf{i} + 6\mathbf{j}) = (4\mathbf{i} + 3\mathbf{j}) N s, pointing the way the puck moves.

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