Brilliant oriented solution manual

So these days I have been working through the problems contained in the book Introduction to classical mechanics by D. Morins. I will say I really liked the problems. Apart from some problems with solutions, the book contains over 350 exercise problems with no solutions. So I was thinking we could make a solution manual for the book.

Facts about the book

The problems in the book, have different stars labeled on them;

1-star(plenty) - requires good concept of the subject to solve.
2-star(plenty) - excellent grasp of the topic
3-star(scarce) - profound mastery of the subject
4-star(very rare) - the Harvard professors who created the book, won't give them to their students.

The problems are excellent, and have the Brilliant.org feel to them. I was hoping that every week, I will post a couple of the problems, and after gathering ideas and solutions, One solution will be selected (maybe more if they have different approaches), for that particular problem. In a sense it would be a Brilliant.org solution manual.

Please comment below, if you agree with the idea.

Mardokay has shared a link to the book.

And I have worked my way through some of the book, and if you have ideas not clear I would be happy to help.

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[example link](https://brilliant.org)

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print "hello world"

Math

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Remember to wrap math in $ ... $ or \[ ... \] to ensure proper formatting.

2 \times 3

2 \times 3

2^{34}

2^{34}

a_{i-1}

a_{i-1}

\frac{2}{3}

\frac{2}{3}

\sqrt{2}

\sqrt{2}

\sum_{i=1}^3

\sum_{i=1}^3

\sin \theta

\sin \theta

\boxed{123}

\boxed{123}

Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

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Markdown	Appears as
`italics` or `_italics_`	italics
`bold` or `__bold__`	bold
- bulleted - list	bulleted list
1. numbered 2. list	numbered list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1 paragraph 2	paragraph 1 paragraph 2
`[example link](https://brilliant.org)`	example link
`> This is a quote`	This is a quote
# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"	# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"

Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

I think it is a good idea, by the way it is a good book thanks for sharing. I found an online pdf format of this book yay we don't have to buy it Introduction to classical mechanics.I will re-share this.

Mardokay Mosazghi - 7 years ago

Glad you think so, Thanks for sending the link to the book, now everybody can join.

Beakal Tiliksew - 7 years ago

But the pdf is with solutions...

Anish Puthuraya - 7 years ago

@Anish Puthuraya – The exercise problems have no answer.

@Beakal Tiliksew – Ok...I have submitted the solution to your third problem...Please check and see if the answer is correct..If not, I will make the necessary changes..

@Anish Puthuraya – Yeah, it looks correct. That is the answer I got. The thing is no one knows the answer to this problems,

@Beakal Tiliksew – Well, if others can confirm it, then there is no doubt that the solution is correct.

@Beakal Tiliksew – Could you check the second solution?

@Anish Puthuraya – Nice, thats what I got before posting them, I agree, lets wait for an objective , then take it as a solution

@Anish Puthuraya – Don't you think there should be tension force in the rope? Because friction cannot act on the hanging part as it can act only on surfaces in contact and only tension can pull it and support its weight.

Sudeep Salgia - 7 years ago

@Sudeep Salgia – I think that that tension is developed due to the friction..If there were no friction, then there would be no tension in the string...Also, since there is equilibrium, we can say that the friction force (total) is equal to the tension in the string (look at the last piece of the rope, which is just about to leave contact from the incline)

@Anish Puthuraya – No, I did not mean to say in that manner. It is true that that tension is developed only due to friction. However, your solution considers that the entire friction is acting on the point which is just about leave contact from the incline. If you consider the FBD of the part lying on the incline then there would be three forces along the incline acting on the part which is not hanging namely, friction, tension and the component of its weight. As their resultant is zero, it is evident that tension will differ in magnitude from friction. This is what I feel.

@Sudeep Salgia – If the tension in the string is $\displaystyle T$ , then it is evident that :

$2T\sin\theta = \lambda (fl)g$

As you mentioned, the tension will be different from the friction...That is true..Considering the forces for the part of the rope which is in contact with the incline,

$F = \frac{1-f}{2}mg\sin\theta + T$

And we know that, the friction force $\displaystyle F$ is simply $\displaystyle \mu N = 1\cdot \frac{1-f}{2}mg\cos\theta$ .

From these equations, we get,

$f = \frac{\cos\theta\sin\theta - \sin^2\theta}{\cos\theta\sin\theta + \cos^2\theta}$

And, we can find the maximum value for this function easily..Is this correct?

@Anish Puthuraya – Yeah, I think this is correct. The maximum value is attained at $\frac{\pi }{8}$ as @Mardokay Mosazghi mentioned in the note with the question, right?

@Sudeep Salgia – Yes..

@Sudeep Salgia – Wait that it right, i was convinced that it was $pi/4$ as @Anish Puthuraya said @Sudeep Salgia

@Mardokay Mosazghi – Do you want to say that the original solution which Anish had posted initially was correct and not this one?

@Sudeep Salgia – I think he meant to say that he was convinced that my original solution was correct, and that the answer was $\frac{\pi}{4}$

@Anish Puthuraya – Oh... Okay.

@Anish Puthuraya – yes that is what i meant

@Sudeep Salgia – Yeah, that seems correct...you have any suggestions as to how to approach it?

@Anish Puthuraya – Sorry, that I have become unresponsive, I am flying out in an hour to the US, I am going to be out for a week.

@Beakal Tiliksew – Attending the event, are you?

@Beakal Tiliksew – Probably @Anish Puthuraya will keep a lot solutions ready by then, making your work easier. :D

@Sudeep Salgia – I agree.

@Sudeep Salgia – I seem to have solved it...Ill reply to you in a minute

Hey thanks for the link. BTW, can you give the E&M by david morin too?

Kartik Sharma - 6 years, 6 months ago

Sorry @Kartik Sharma there is no pdf for that one i searched and searched but couldnot find it,try it and tell me

Mardokay Mosazghi - 6 years, 6 months ago

Let's do it

Josh Silverman Staff - 7 years ago

Great lets just wait a couple of days, for people to see this, and start.

It really sounds interesting. I would love to join in.

Same here : )

Karthik Kannan - 7 years ago

Glad you think so, i have included some of the statics problem, as a sample, check it out here

This is not going to be the real thing.

Me too

How many per week, would you guys say is optimal?

Personaly I am here everyday so the planning goes for others

hey

jatasia hudson - 6 years, 6 months ago

Good idea. I will try to help.

Chew-Seong Cheong - 6 years, 5 months ago

Good idea.........

Vishal Bambhaniya - 6 years, 4 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$