CritABCD
A.2 · 5 · A.2 Forces and momentum · momentum and kinetic energy

Momentum vs kinetic energy

Commonly confused, and once argued over for about sixty years.

SL+HLMedium15 minFree
Hook

Two identical carts head towards each other at the same speed. Their total momentum is zero. Is their total kinetic energy zero too?

Commonly misunderstood
1 / 3

Two different quantities

MomentumKinetic energy
Formulap = mvEk = ½mv²
Typevector (has direction)scalar (no direction)
Unitkg m s⁻¹ (= N s)J (= kg m² s⁻²)
Depends on speed asv: double v, double pv²: double v, four times Ek
Can it be negative?yes: the sign shows directionno: always ≥ 0
Isolated system, any collisionalways conservedonly if the collision is elastic
Changed bya net force acting over a TIME: Ft = Δpa force acting over a DISTANCE (work, in A.3)
Two equal carts, equal speeds, opposite directionstotal p = 0total Ek > 0
Check 1 of 4

A body’s speed doubles. Its momentum and kinetic energy become…

Check 2 of 4

In a collision in an isolated system, which is ALWAYS conserved?

Check 3 of 4

Which of these can be negative?

Check 4 of 4

The argument between Descartes and Leibniz was finally described as…

Apply

Two identical carts move towards each other at the same speed and stick together. State what happens to the total momentum and to the total kinetic energy, and explain.

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Remember earlier lessons
From lesson A.2 · 4

Δp_sys = 0 if…

From lesson A.2 · 2

p = …

Summary card

Key points

  • • Momentum p = mv is a vector; kinetic energy E_k = ½mv² is a scalar.
  • • Momentum is always conserved in an isolated system; kinetic energy only in elastic collisions.
  • • They were argued over as one quantity until d’Alembert (1743).

Formulas

  • p = mv
  • Ek = ½mv²

Key terms

Elastic collision
:
kinetic energy is conserved
Inelastic collision
:
kinetic energy is not conserved

Common errors

  • • Treating kinetic energy as conserved in every collision.
  • • Adding momenta without signs.
Checks solved: 0 of 4
← PreviousA.2 · 4 Momentum conservationNext →A.2 · 6 Momentum change: four cases