Recoil of a rifle

Problem

Fermi estimate: recoil of a rifle. Estimate the recoil velocity of a $4\;\text{kg}$ rifle that fires a $10\;\text{g}$ bullet at $700\;\text{m/s}$.

Solution

Isolated rifle + bullet system: the total momentum, initially zero, remains zero. So $m_f\,v_f + m_p\,v_p = 0 \;\Rightarrow\; v_f = -\frac{m_p\,v_p}{m_f} = -\frac{0{,}010\cdot 700}{4}$ $\ev{v_f \approx -1{,}75\;\text{m/s}}$ The minus sign indicates recoil, in the direction opposite to the bullet. The velocity is small because the rifle is much more massive than the bullet.

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Topics: Quantità di moto e urti Concepts: Conservazione della quantità di moto · Esplosione Skills: Stime di Fermi