# Textbook Solution Accuracy: Are Rounded Calculations Affecting the Final Answer?

• QED-Kasper
In summary, the textbook solution manual provides incorrect information about the bob's equilibrium position and speed. The bob passes its equilibrium position in 3.17 seconds and has a vibration energy of 0.48J.
QED-Kasper

## Homework Statement

Is the answer provided by the textbook solution manual wrong?
Here is the textbook exercise:

A bob with a mass of 0,500 kg is on the end of a long chord and suspended on a pivot (no friction). The distance of the center of mass of the the bob to the pivot-point is 250 cm. The bob is pulled 70 cm from its equilibrium state and then released.

a. Calculate the period.
b. Calculate the speed at which the bob passes its equilibrium state
c. How big is the Vibration energy?

## Homework Equations

T=2$$\pi$$$$\sqrt{}(l/g)$$
Vmax=2$$\pi$$A/T
Evib=0,5mv2max

## The Attempt at a Solution

a. T=2$$\pi$$$$\sqrt{}(2,5/9,81)$$=3,17187=3,17 s
b. Vmax=2$$\pi$$0,7/3,17187=1.386636=1,4 m/s
c. Evib=0,5 x 0,5 x 1,3866362=0,48 J

for c. the textbook got 0,49 J

The textbook calculations are the same except that they use the rounded answers in each consecutive calculation. I thought that the correct way to calculate is to use the unrounded answers and then round the final answer to the correct significant figures. Am I right? Any help will be so much appreciated. (I'm sorry the equations aren't very pretty, it's my first time trying to use this system)

Last edited:
Well, we're doing this after spring break, so I guess I can't REALLY help.
But, my brother, dad, and aunt have a rant on physics- even though textbooks round every calculation YOU SHOULDN'T. In the end, two decimal places makes a huge difference. Even in high school physics homework. (I was 60 off one time because I put all of my calculations in sig figs)
So anyway, no- don't do that. And yes, books are wrong. Especially if you use Glencoe Physics.

Are you sure I'm doing it right? It happened to me a couple of times now, that I used unrounded answers in my calculations, which made my answer slightly different than the one in the textbook. Perhaps I'm using this rule in the wrong situations :s.

Never round down intermediate results.

If you report them - report them rounded down, as listing zillions of digits looks ugly and doesn't make much sense (they are mostly just noise), but if you are using them for further calcualtions - use them as you got them. If you have to copy them manually you don't need to copy everything, but using 2 or 3 guard digits is a must.

So my answers are correct, and the textbook is wrong?

yes. you are definitely right.

I agree. This rounding business hangs on from the long-dead age of sliderule calculations where anything over two digits was meaningless. It's been a bit over 30 years since calculators supplanted sliderules in general use in college courses, and it takes about one and one half generations for outmoded rules of thumb to die out...

Last edited:
ok thank you very very much guys :)

## 1. Why is the textbook answer wrong?

There could be a variety of reasons why the textbook answer is wrong. It could be due to outdated information, a mistake made during the editing process, or a difference in interpretation or perspective. It is important to critically evaluate and question information presented in textbooks.

## 2. What should I do if I believe the textbook answer is wrong?

If you believe the textbook answer is wrong, you should first gather evidence to support your belief. This could include consulting other credible sources or conducting your own experiments. Once you have sufficient evidence, you can bring your concerns to the attention of your teacher or professor.

## 3. Can I still get a good grade if I challenge the textbook answer?

Yes, you can still get a good grade even if you challenge the textbook answer. In fact, questioning and challenging information is an important aspect of scientific thinking. As long as you have evidence to support your arguments, your teacher or professor should consider your perspective and give you credit for critical thinking.

## 4. Is it common for textbook answers to be wrong?

It is not uncommon for textbook answers to be wrong. Textbooks are often written and edited by multiple authors and go through a rigorous review process, but mistakes can still occur. Additionally, new research and discoveries can challenge previously accepted information, leading to updates and revisions in textbooks.

## 5. How can I ensure the accuracy of textbook answers?

You can ensure the accuracy of textbook answers by consulting multiple sources, such as scientific journals and reputable websites, and comparing the information presented in the textbook. You can also actively engage in critical thinking and questioning of information presented in textbooks, rather than accepting it blindly as fact.

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