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Momentum and impact

Momentum is mass times velocity, and the impulse–momentum principle links it to force over time. In an impact with no external horizontal forces, momentum is conserved, even though kinetic energy can be lost to heat and deformation.

∫F dt=Δ(mv)\int F\,dt = \Delta(mv)the impulse–momentum principle
v′=m1v1+m2v2m1+m2v' = \dfrac{m_1v_1 + m_2v_2}{m_1+m_2}common velocity after a perfectly inelastic impact

Symbols

p=mvp = mvmomentumkg m/s
v′v'common velocity after impactm/s

Example

A 4 kg cart at 6 m/s hits a 2 kg cart at rest and they stick:

v′=(4⋅6+0)/6=4v' = (4\cdot 6 + 0)/6 = 4 m/s.

Only momentum is conserved in an inelastic impact – not kinetic energy.
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Part of Statics and Dynamics: Dynamics.