Problem — Ranking powers (three machines)

Problem

Three machines lift different objects:

• A: $20\;\mathrm{kg}$ lifted $3\;\mathrm{m}$ in $5\;\mathrm{s}$;
• B: $50\;\mathrm{kg}$ lifted $2\;\mathrm{m}$ in $20\;\mathrm{s}$;
• C: $10\;\mathrm{kg}$ lifted $5\;\mathrm{m}$ in $2\;\mathrm{s}$.

Rank the powers used from smallest to largest.

Solution

Power is the work (here $L = m\,g\,h$) divided by time: $P = \frac{m\,g\,h}{t}$ Calculating for each machine (using $g = 9{,}8\;\mathrm{m/s^2}$): $P_A = \frac{20\cdot 9{,}8\cdot 3}{5} = \frac{588}{5} \approx 118\;\mathrm{W}$ $P_B = \frac{50\cdot 9{,}8\cdot 2}{20} = \frac{980}{20} = 49\;\mathrm{W}$ $P_C = \frac{10\cdot 9{,}8\cdot 5}{2} = \frac{490}{2} = 245\;\mathrm{W}$ Ranking: $P_B \approx 49\;\mathrm{W} < P_A \approx 118\;\mathrm{W} < P_C \approx 245\;\mathrm{W}$. Machine C does less total work than B, but does it in much less time: it is the most powerful. $\ev{P_C > P_A > P_B}$

Collegamenti

Argomenti: Lavoro ed energia Concetti: Potenza Competenze: Ragionamento di ranking