Ranking momentum (mv)

Problem

Ranking. Four objects move with mass $m$ and velocity $v$: (A) $m = 2\;\mathrm{kg}$, $v = 6\;\mathrm{m/s}$. (B) $m = 4\;\mathrm{kg}$, $v = 2\;\mathrm{m/s}$. (C) $m = 3\;\mathrm{kg}$, $v = 4\;\mathrm{m/s}$. (D) $m = 1\;\mathrm{kg}$, $v = 5\;\mathrm{m/s}$. Order the magnitudes of momentum $p = mv$ from smallest to largest.

Solution

I calculate $p = m\,v$ for each object: $\begin{aligned} p_A &= 2\cdot 6 = 12\;\mathrm{kg\,m/s} \\ p_B &= 4\cdot 2 = 8\;\mathrm{kg\,m/s} \\ p_C &= 3\cdot 4 = 12\;\mathrm{kg\,m/s} \\ p_D &= 1\cdot 5 = 5\;\mathrm{kg\,m/s} \end{aligned}$ I order the values from smallest to largest: $5 < 8 < 12 = 12$. Objects A and C have the same momentum (both $12\;\mathrm{kg\,m/s}$). $\ev{D < B < A = C}$

Links

Topics: Quantità di moto e urti Concepts: Quantità di moto Skills: Ragionamento di ranking