Ranking momenta

Problem

Four moving objects: (A) car $1500\;\text{kg}$ at $20\;\text{m/s}$; (B) ball $0{,}1\;\text{kg}$ at $30\;\text{m/s}$; (C) bicycle plus cyclist $80\;\text{kg}$ at $10\;\text{m/s}$; (D) golf ball $0{,}05\;\text{kg}$ at $80\;\text{m/s}$. Rank the magnitudes of momentum from smallest to largest.

Solution

The magnitude of momentum is $p = m\,v$ (straight-line motion, so just the magnitude is needed). Computing for each object: $\begin{aligned} p_A &= 1500 \cdot 20 = 30\,000\ \mathrm{kg\,m/s}\\ p_B &= 0{,}1 \cdot 30 = 3\ \mathrm{kg\,m/s}\\ p_C &= 80 \cdot 10 = 800\ \mathrm{kg\,m/s}\\ p_D &= 0{,}05 \cdot 80 = 4\ \mathrm{kg\,m/s} \end{aligned}$ Ranking from smallest to largest: the ball (B, $3$) and the golf ball (D, $4$) have tiny momenta despite the high speed, because the mass is very small; next come the bicycle with cyclist (C, $800$) and finally the car (A, $30\,000$), which dominates thanks to its huge mass. $\ev{p_B < p_D < p_C < p_A \qquad (3 < 4 < 800 < 30\,000\ \mathrm{kg\,m/s})}$

Links

Topics: Momentum and collisions Concepts: Momentum Skills: Ranking reasoning