Problem — Ranking kinetic energies (car, ball, bicycle, golf)

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

Solution

Apply $E_k = \tfrac{1}{2}mv^2$ to each object. Note: speed enters squared, so even very small masses with high speeds do not close the gap with large masses.

$E_k^{(A)} = \tfrac{1}{2}(1500)(20)^2 = \tfrac{1}{2}(1500)(400) = 3{,}0\cdot 10^5\;\mathrm{J}$

$E_k^{(B)} = \tfrac{1}{2}(0{,}1)(30)^2 = \tfrac{1}{2}(0{,}1)(900) = 45\;\mathrm{J}$

$E_k^{(C)} = \tfrac{1}{2}(80)(10)^2 = \tfrac{1}{2}(80)(100) = 4{,}0\cdot 10^3\;\mathrm{J}$

$E_k^{(D)} = \tfrac{1}{2}(0{,}05)(80)^2 = \tfrac{1}{2}(0{,}05)(6400) = 160\;\mathrm{J}$

Ranking the values $45 < 160 < 4000 < 300000$:

$\ev{B < D < C < A}$

Physical reading. The car dominates because it has both large mass and high speed (and $v^2 = 400$). The golf ball (D), although very fast, remains well below the bicycle (C): its tiny mass ($0{,}05\;\mathrm{kg}$) is not enough to compensate. The ball (B) is lowest: small mass and moderate speed.

Collegamenti

Argomenti: Lavoro ed energia Concetti: Energia cinetica Competenze: Ragionamento di ranking