True or false about collisions

Problem

State whether the following statements are true or false, briefly justifying your answer: (a) in an elastic collision momentum is conserved but not kinetic energy; (b) in a perfectly inelastic collision the two bodies move together; (c) in a collision the external friction force always invalidates conservation of momentum; (d) an isolated system conserves total momentum even during an explosion.

Solution

(a) FALSE. The very definition of an elastic collision is that total kinetic energy is conserved, in addition to momentum. The statement denies exactly what characterises an elastic collision. (b) TRUE. In a perfectly inelastic collision the bodies stick together and continue with a single common velocity. This is the case in which the maximum kinetic energy compatible with conservation of momentum is lost. (c) FALSE. During the collision the internal (impulsive) forces are enormous and act for a very short time; the impulse of the external friction, being a finite force as $\Delta t \to 0$, is negligible. So momentum is conserved to a very good approximation during the collision, even in the presence of friction. Friction matters instead over long times (before and after). (d) TRUE. In an isolated system the resultant of the external forces is zero, so total momentum is conserved. In the explosion the forces are all internal: the fragments move off in such directions that the total momentum stays equal to the initial one (zero, if the system was at rest). $\ev{\text{(a) F};\quad \text{(b) T};\quad \text{(c) F};\quad \text{(d) T}}$

Links

Topics: Quantità di moto e urti Concepts: Urto elastico · Urto anelastico · Conservazione della quantità di moto · Esplosione