Q35P - Fundamentals Of Physics

Question

An old English children’s rhyme states, “Little Miss Muffet sat on a tuffet, eating her curds and whey, when along came a spiders who sat down beside her. . . .” The spider sat down not because of the curds and whey but because Miss Muffet had a stash of 11 tuffets of dried flies. The volume measure of a tuffet is given by 1 tuffet ${}^{\mathbf{=}}$ 2 pecks ${}^{\mathbf{=}}$ 0.50 Imperial bushel, where 1 Imperial bushel ${}^{\mathbf{=}}$ 36.3687 liters (L). What was Miss Muffet’s stash in (a) pecks, (b) Imperial bushels, and (c) liters?

Step-by-Step Solution

Answer

1.  Miss Muffet’s stash is${}^{\mathbf{22}\mathbf{ }\mathbf{pecks}}$.

2.  Miss Muffet’s stash is${}^{\mathbf{5}\mathbf{.}\mathbf{5}\mathbf{ }\mathbf{imperial}\mathbf{ }\mathbf{bushels}}$.

3.  Miss Muffet’s stash is ${}^{\mathbf{200}\mathbf{ }\mathbf{liters}}$.

Step 1: Given data

Miss Muffet had a stash of 11 tuffets

$\mathbf{1}\mathbf{ }\mathbf{tufet}\mathbf{=}\mathbf{2}\mathbf{ }\mathbf{pecks}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{50}\mathbf{ }\mathbf{lmperial}\mathbf{ }\mathbf{bushe}$

$\mathbf{1}\mathbf{ }\mathbf{lmperial}\mathbf{ }\mathbf{bushel}\mathbf{=}\mathbf{36}\mathbf{.}\mathbf{3687}\mathbf{ }\mathbf{liters}$

Step 2: Understanding the conversion factor

Unit conversion is the conversion between different units of measure for the same quantity, usually through multiplier conversion factors. Here, pecks and imperial bushels are the different units for the quantity volume.

Step 3: (a) Determination of stash in pecks

Use the given conversion factors to covert tuffets into pecks.

$$\begin{gathered} \mathbf{11}\mathbf{ }\mathbf{tuffets}\mathbf{=}\mathbf{11}\mathbf{ }\mathbf{tuffets}\mathbf{\times }\frac{\mathbf{2}\mathbf{ }\mathbf{peck}}{\mathbf{1}\mathbf{tuffet}} \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{=}\mathbf{22}\mathbf{ }\mathbf{pecks} \end{gathered}$$

Thus,${}^{\mathbf{11}\mathbf{ }\mathbf{tuffets}}$  are equivalent to 22 pecks.

Step 4: (b) Determination of stash in imperial bushels

Use the given conversion factors to convert tuffets into imperial bushels.

$$\begin{gathered} \mathbf{11}\mathbf{ }\mathbf{tuffets}\mathbf{=}\mathbf{11}\mathbf{ }\mathbf{tuffets}\mathbf{\times }\frac{\mathbf{0}\mathbf{.}\mathbf{50}\mathbf{ }\mathbf{Imperial}\mathbf{ }\mathbf{bushels}}{\mathbf{1}\mathbf{ }\mathbf{tuffet}} \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{=}\mathbf{5}\mathbf{.}\mathbf{5}\mathbf{ }\mathbf{Imperial}\mathbf{ }\mathbf{bushels} \end{gathered}$$

Thus, ${}^{\mathbf{11}\mathbf{ }\mathbf{tuffets}}$ are equivalent to 5.5 imperial bushels.

Step 5: (c) Determination of stash in liters

Use the given conversion factors, to convert imperial bushels to liters.

$$\begin{gathered} \mathbf{5}\mathbf{.}\mathbf{5}\mathbf{ }\mathbf{Imperial}\mathbf{ }\mathbf{bushels}\mathbf{=}\mathbf{5}\mathbf{.}\mathbf{5}\mathbf{ }\mathbf{Imerial}\mathbf{ }\mathbf{bushels}\mathbf{\times }\frac{\mathbf{36}\mathbf{.}\mathbf{3687}}{\mathbf{1}\mathbf{ }\mathbf{Imperial}\mathbf{ }\mathbf{bushels}} \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{=}\mathbf{200}\mathbf{.}\mathbf{02}\mathbf{ }\mathbf{liters} \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{=}\mathbf{200}\mathbf{ }\mathbf{liters} \end{gathered}$$

Thus,${}^{\mathbf{11}\mathbf{ }\mathbf{tuffets}}$ are equivalent to ${}^{\mathbf{200}\mathbf{ }\mathbf{liters}}$.