How can I get started with classical mechanics and solve difficult problems?

[bit188]

Hey, self-studying, I've just started into Marion's Classical Dynamics of Particles and Systems, and I'm having major issues with the problems; I don't even have any idea where to start. I was wondering if somebody would be willing to give some general advice and maybe go through a couple of them with me?

Here's a problem:

A particle is projected with an initial velocity v0 up a slope which makes an angle (alpha) with the horizontal. Assume frictionless motion and find the time required for the particle to return to its starting position.

EDIT: Sorry! Missed the homework forum...

 

[Cyrus]

How much physics have you taken?

 

[bit188]

How much physics have you taken?

Previously? I'd done introductory mechanics. I guess this is the next step?

 

[Cyrus]

You can do it, but its going to be painful .

Have you taken any classes in statics or dynamics?

 

[bit188]

You can do it, but its going to be painful .

Ah hah hah...

Pointers? Advice? Thanks!

 

[bit188]

Have you taken any classes in statics or dynamics?

No classes. All self-teaching, I'm far far too young to be allowed in classes...

 

[Cyrus]

Just work through it and ask questions I guess. How old are you? This book is for seniors/grad students. Its going to assume you know a lot of background material.

 

[bit188]

Between 12 and 14. XD

Background material, I assumed, was introductory mechanics... anything else I should do for prereqs?

 

[Cyrus]

calculus 1,2,3. Ode's, some linear algebra, and statics and dynamics.

How is your math background?

 

[bit188]

Calc 1-3, that's all. I have some books on linear algebra and odes, though.

Statics and dynamics? What's that all about?

 

[Cyrus]

Statics is a course on, statics. :tongue2: You should know this from your mechanics course.

Given your background, I think you could read through the book you have. But it will still be tough unless you have some experience with statics and dynamics.

 

[bit188]

Ah... well, I guess I'll give it a try. Could you help me with that problem I posted?

Thanks for your help!

 

[Cyrus]

I am going to take a very quick stab at it but it might be wrong.

Draw a free body diagram along the incline with all the forces labeled on the particle. You will have gravity acting down, and it will be the only force. Then find the component in the direction opposing motion. Once you do this, write your equations of motion and solve them given your initial conditions.

I got this as the final answer:

$$t= \frac{v_0}{2gsin(\alpha)}$$

Edit: I had the fraction inverted by accident.

Do you know what the answer is?

 

[bit188]

It's the equations of motion that get me. XD

 

[Cyrus]

Show some work. What are you doing/getting?

 

[bit188]

Actually, my main issue is that I have no idea how to begin or what the heck to do. I was hoping for some general advice on starting a problem and what to do?

Sorry, and thank you. This is going to be tough, but I know that I can do this if I work at it.

 

[Cyrus]

For a book of this level, I can't teach you how to write the equations of motion. You have to do that on your own. If you cant, going through this book is going to be hopeless. This book isn't going to hold your hand, so expect things to get a LOT worse than this simple problem.

Write the equations of motion for starters.

Lets be clear, you are reading https://www.amazon.com/dp/0534408966/?tag=pfamazon01-20 book, yes?

 

[bit188]

F = ma = m(dv/dt) = mv0cos(alpha) + mv0sin(alpha)

Is that right?

 

[Cyrus]

Almost, those v_0 are wrong, and you have sign errors.

 

[bit188]

Break velocity into horizontal/vertical components--

v0x = v0 cos x
v0y = v0 sin y

Then compute derivative for acceleration--

ax = -sin x
ay = cos y

F = ma = -m sin x + m cos y

Is that right?

 

[Cyrus]

Velocity components have nothing to do with force balance-velocity is not a force.

You need to use a body fixed coordinate system, not an absolute coordinate system. The x-direction should be pointing up the incline, not horizontally and to the right as your thinking.

Also: this is incorrect and written incorrectly as well:

F = ma = -m sin x + m cos y

F is a vector, everything you do in this book will be for a vector from now on.

F=ma=-msinx (i) + 0(j) + m cosy(k) (This is not correct, but the vector notation is).

If you are struggling with this, I would recommend that you read https://www.amazon.com/dp/0131411675/?tag=pfamazon01-20 book first on statics.

You will learn more about vectors, how to do force balance, moment of inertia etc. Your basics right now are too weak for the book your using.

 

[Cyrus]

Once you finish the statics book, work through this https://www.amazon.com/dp/0131046373/?tag=pfamazon01-20 book.

Once you do these two books, read the book you are reading now.

 

[bit188]

Is there anything online I can use instead?

Plus, could you show me how you worked the problem? Maybe I could get the hang of this, possibly?

Oh, and the vector notation was just a screw-up... I always forget to put in the unit vectors... @_@;;

 

[Cyrus]

I recommend you use those books.

If you need help doing simple force balance, trust me, you are not yet ready to dive into this book.

 

[bit188]

Okay. Thank you, I will!

I'll be back if I need help once I get these books. Thanks so much.

I'll keep going in math as well, I'll be starting into ODEs now. Thanks again!