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Chapter 20: Problem 13

Use the two rule-of-thumb approaches (by mass and by cost) to estimate the energy investment in a farm tractor, whose mass is \(2,400 \mathrm{~kg}\) and cost is \(\$ 25,000\). If the results are even within a factor-of-two of each other, we can conclude that the estimate is probably pretty decent as a rough guide.

Short Answer

Expert verified
Answer: No, the factor of difference between the two estimates (9.6) is greater than two, which means that they are not within a decent range as a rough guide.

Step by step solution

01

Estimate Energy Investment by Mass

To estimate the energy investment by mass, we can use the rule of thumb that states the energy investment is about \(50 \,\mathrm{~MJ / kg}\). So, for a tractor with a mass of \(2,400 \,\mathrm{~kg}\), we can calculate the energy investment as follows: Energy in MJ = mass of tractor (kg) x 50 MJ/kg Energy in MJ = \(2,400 \, \mathrm{~kg} \times 50 \,\mathrm{~MJ / kg} = 120,000 \, \mathrm{~MJ}\) The energy investment by mass is approximately 120,000 MJ.
02

Estimate Energy Investment by Cost

To estimate the energy investment by cost, we can use the rule of thumb that states the energy investment is about \(0.5 \,\mathrm{~MJ / \$}\). So, for a tractor with a cost of \(25,000\), we can calculate the energy investment as follows: Energy in MJ = cost of tractor (\() x 0.5 MJ/\) Energy in MJ = \(\$25,000 \times 0.5 \,\mathrm{~MJ / \$} = 12,500 \,\mathrm{~MJ}\) The energy investment by cost is approximately 12,500 MJ.
03

Compare the Two Estimates

Now, let's compare the two estimates to check if they are within a factor of two of each other: - Energy investment by mass: 120,000 MJ - Energy investment by cost: 12,500 MJ Factor of difference = \(\frac{\mathrm{Energy\, investment \,by\, mass}}{\mathrm{Energy\, investment \,by\, cost}} = \frac{120,000 \,\mathrm{~MJ}}{12,500 \,\mathrm{~MJ}} ≈ 9.6\) Since the factor of difference is greater than 2, we cannot conclude that the estimates are decent as a rough guide.

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