The common setup

Let us analyse three different problems built on the same physical setup, so that they can be compared. A projectile ($m_p = 0{,}3\;\mathrm{kg}$, $v_A = 900\;\mathrm{m/s}$) travels horizontally and strikes a uniform rod ($M = 4\;\mathrm{kg}$, $L = 2\;\mathrm{m}$) initially at rest, hitting one of its ends.

Two switches generate the three cases:

1. is the rod hinged at the other end (it cannot translate) or free to slide on a frictionless rail?
2. is the collision inelastic (the projectile embeds itself) or elastic (the projectile bounces off)?

In cases 1 and 2 the rod is hinged; in case 3 it is free. Changing these conditions changes which quantities are conserved — momentum, kinetic energy, angular momentum — and with them the number of equations and unknowns in the problem.

The three cases of the projectile–rod problem. In cases 1 and 2 the rod is hinged; in case 3 the hinge slides freely on a horizontal rail. In the elastic collisions (2 and 3) the projectile bounces off without embedding itself.

Collegamenti

Argomenti: Dinamica rotazionale Concetti: Conservazione del momento angolare Oggetti: Asta · Proiettile

Esercizi collegati: Problema — La pattinatrice che si stringe · Esercizio svolto — proiettile contro asta incernierata · Problema — Perché il pattinatore ruota più veloce