True or false (impulse and collisions)

Problem

True or false? (a) In a perfectly inelastic collision, momentum is conserved. (b) In an elastic collision, both $\vv{p}$ and $E_c$ are conserved. (c) In an inelastic collision energy is lost, so momentum is not conserved either. (d) Impulse is a vector quantity. (e) In an isolated system the velocity of the centre of mass can vary.

Solution

(a) TRUE. In any collision between isolated bodies total momentum is conserved, whether elastic or inelastic. In the inelastic case kinetic energy is lost, not momentum.

(b) TRUE. This is precisely the definition of an elastic collision: both momentum $\vv{p}$ and kinetic energy $E_c$ are conserved.

(c) FALSE. Kinetic energy is lost (transformed into heat, deformation, sound), but momentum continues to be conserved: they are independent quantities. Conservation of $\vv{p}$ depends only on the absence of external forces, not on energy.

(d) TRUE. Impulse $\vv{J} = \vv{F}\,\Delta t = \Delta \vv{p}$ has magnitude, direction and sense: it is a vector.

(e) FALSE. In an isolated system the resultant of the external forces is zero, so $\vv{p}_\text{tot}$ is constant and the velocity of the centre of mass $\vv{v}_\text{cm} = \vv{p}_\text{tot}/M$ stays constant.

Final result: $\ev{\text{(a) T,\ (b) T,\ (c) F,\ (d) T,\ (e) F}}$

Links

Topics: Quantità di moto e urti Concepts: Conservazione della quantità di moto · Urto elastico · Urto anelastico · Impulso · Centro di massa