Exploring Frictionless Climbing on a Conical Mountain: Cheap vs Deluxe Lassos

[Nano-Passion]

So I've ordered Taylor's book in classical mechanics and I need some advice.

My plan is to solve as many problems as I can in classical mechanics, since it seems that the type of logical thinking that is needed in classical mechanics will surface time and time again in following physics classes. So I want to get in the habit of knowing how to solve these types of problems and becoming more comfortable with them.

First question, around how long should problems in Taylor's classical mechanics take? Roughly how many can I expect to finish in a given period of time?

Second question, anyone else aiming to study classical mechanics this summer? We can discuss certain materials/h.w. problems and bounce ideas off each other.

Third question, is it reasonable that solving problems in Taylor's classical mechanics will improve my problem solving skills in other physics classes?

 

[SolsticeFire]

So I've ordered Taylor's book in classical mechanics and I need some advice.

My plan is to solve as many problems as I can in classical mechanics, since it seems that the type of logical thinking that is needed in classical mechanics will surface time and time again in following physics classes. So I want to get in the habit of knowing how to solve these types of problems and becoming more comfortable with them.

First question, around how long should problems in Taylor's classical mechanics take? Roughly how many can I expect to finish in a given period of time?

Second question, anyone else aiming to study classical mechanics this summer? We can discuss certain materials/h.w. problems and bounce ideas off each other.

Third question, is it reasonable that solving problems in Taylor's classical mechanics will improve my problem solving skills in other physics classes?

Hey Nano,
I'm reviewing CM this summer but I'm using Morin's book. I'm aiming to cover all the topics and majority of the problems by November (as I'm also reviewing other things). Morin's first chapter is all about problem solving, checking limiting cases, dimensional analysis etc. It was a delight to work through that stuff. So much can be learned just by checking special cases and understanding what the question is really asking! Solving CM questions will definitely help you in other classes. I have done CM, EM, QM and Thermo and problem solving skills I learned through CM have definitely helped in other, more advanced courses.

GL
SolsticeFire

 

[Nano-Passion]

Hey Nano,
I'm reviewing CM this summer but I'm using Morin's book. I'm aiming to cover all the topics and majority of the problems by November (as I'm also reviewing other things). Morin's first chapter is all about problem solving, checking limiting cases, dimensional analysis etc. It was a delight to work through that stuff. So much can be learned just by checking special cases and understanding what the question is really asking! Solving CM questions will definitely help you in other classes. I have done CM, EM, QM and Thermo and problem solving skills I learned through CM have definitely helped in other, more advanced courses.

GL
SolsticeFire

Thanks for the input. I browsed a couple of QM books before and figured that the problem solving in CM would help since they are a bit similar in a couple ways, glad I'm right since that means I can tackle CM problems knowing its a good use of my time.

How long do you think the problems should take? They are very different from what I'm used to in all my previous classes, but I like it.

 

[SolsticeFire]

Well from my experience so far, problems in CM can range from very easy (the type where you can just plug and chug, or just guess the answer by observing limiting cases or dimensional analysis) to very very hard. There are some questions which are near impossible. I have been working on a problem from chapter 2 in Morin's text for two weeks now. To be honest with you, I think problems in CM demand more creativity and imagination than SM (Statistical Mechanics) or EM. :P

SolsticeFire

 

[Nano-Passion]

Well from my experience so far, problems in CM can range from very easy (the type where you can just plug and chug, or just guess the answer by observing limiting cases or dimensional analysis) to very very hard. There are some questions which are near impossible. I have been working on a problem from chapter 2 in Morin's text for two weeks now. To be honest with you, I think problems in CM demand more creativity and imagination than SM (Statistical Mechanics) or EM. :P

SolsticeFire

Well Morin's book is much harder than Taylor's from what I read, and it isn't good for an introduction. Not sure of the validity of this statement though so if someone wants to chime in with experience on both books then feel free to share.

Out of curiosity, what is the problem about that took two weeks?

 

[SolsticeFire]

2.10
A mountain climber wishes to climb up a frictionless conical mountain. He wants to do this by throwing a lasso (a rope with a loop) over the top and climbing up along the rope. Assume that the climber is of negligible height, so that the rope lies along the mountain. At the bottom of the mountain are two stores. One sells cheap lassos (made of a segment of rope tied to a loop of fixed length). The other sells deluxe lassos (made of one piece of rope with a loop of variable length; the loop's length may change without any friction of the rope with itself). When viewed from the side, the conical mountain has an angle of A at its peak. For what angles A can the climber climb up along the mountain if he uses a cheap lasso? A deluxe lasso?

SolsticeFire

PS: When I was looking for a book I was actually split between Morin and Taylor. But my CM class was using Morin so I decided to conform. :P

 

[Nano-Passion]

2.10
A mountain climber wishes to climb up a frictionless conical mountain. He wants to do this by throwing a lasso (a rope with a loop) over the top and climbing up along the rope. Assume that the climber is of negligible height, so that the rope lies along the mountain. At the bottom of the mountain are two stores. One sells cheap lassos (made of a segment of rope tied to a loop of fixed length). The other sells deluxe lassos (made of one piece of rope with a loop of variable length; the loop's length may change without any friction of the rope with itself). When viewed from the side, the conical mountain has an angle of A at its peak. For what angles A can the climber climb up along the mountain if he uses a cheap lasso? A deluxe lasso?

SolsticeFire

PS: When I was looking for a book I was actually split between Morin and Taylor. But my CM class was using Morin so I decided to conform. :P

That looks harder than Taylor's problems for sure. This is a really awkward-looking problem though, for me at least.