I'm still a science major but had to take and extended leave for various reasons (don't ask) to be better suited in the long run in multiple facets. Soon I will be going back and which makes things, well, makes me feel there is more to life than negative reinforcement.

There is a sample problem in the text book "Halliday/Resnick/(Walker) Fundamentals of Physics" 7th, 8th and 10th editions at least, where it appears a quantity was simply pulled out of someones ass. Mulling over the problem, as elevator rides provide great opportunity for reflection on things, I wondered: "Where the F* did they get that from?"

In bold.

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Sample Problem 1.01 Estimating order of magnitude, ball of string

The world’s largest ball of string is about 2 m in radius. To the nearest order of magnitude, what is the total length L of the string in the ball?

KEY IDEA

We could, of course, take the ball apart and measure the total length L, but that would take great effort and make the ball’s builder most unhappy. Instead, because we want only the nearest order of magnitude, we can estimate any quantities required in the calculation.

Calculations: Let us assume the ball is spherical with radius R = 2 m. The string in the ball is not closely packed (there are uncountable gaps between adjacent sections of string).

V = (cross-sectional area)(length) =

This is approximately equal to the volume of the ball, given by

which is about

because Pi is about 3. Thus, we have the following

(Note that you do not need a calculator for such a simplified calculation.) To the nearest order of magnitude, the ball contains about 1000 km of string!

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Now, not about the methodology, but say I chose an edge length, not of 4 mm, but 4 km or even light years? How often did one have to guess, and or, deliberately or not screw up in assignments and exams? I would appreciate to hear any personal experiences.

Thanks.

There is a sample problem in the text book "Halliday/Resnick/(Walker) Fundamentals of Physics" 7th, 8th and 10th editions at least, where it appears a quantity was simply pulled out of someones ass. Mulling over the problem, as elevator rides provide great opportunity for reflection on things, I wondered: "Where the F* did they get that from?"

In bold.

---------------------------------------------------------------------------------------------------------------------

Sample Problem 1.01 Estimating order of magnitude, ball of string

The world’s largest ball of string is about 2 m in radius. To the nearest order of magnitude, what is the total length L of the string in the ball?

KEY IDEA

We could, of course, take the ball apart and measure the total length L, but that would take great effort and make the ball’s builder most unhappy. Instead, because we want only the nearest order of magnitude, we can estimate any quantities required in the calculation.

Calculations: Let us assume the ball is spherical with radius R = 2 m. The string in the ball is not closely packed (there are uncountable gaps between adjacent sections of string).

**To allow for these gaps, let us somewhat overestimate the cross-sectional area of the string by assuming the cross section is square, with an edge length d = 4 mm.**Then, with a cross-sectional area of d^2 and a length L, the string occupies a total volume ofV = (cross-sectional area)(length) =

This is approximately equal to the volume of the ball, given by

which is about

because Pi is about 3. Thus, we have the following

(Note that you do not need a calculator for such a simplified calculation.) To the nearest order of magnitude, the ball contains about 1000 km of string!

---------------------------------------------------------------------------------------------------------------------

Now, not about the methodology, but say I chose an edge length, not of 4 mm, but 4 km or even light years? How often did one have to guess, and or, deliberately or not screw up in assignments and exams? I would appreciate to hear any personal experiences.

Thanks.

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