Kleppner and Kolenkow difficulty

[Mr Davis 97]

So I have just started my freshman year at college, and I am majoring in physics. For the introductory sequence on mechanics, we are using Kleppner and Kolenkow. After reading the first section on vectors and kinematics, I feel as though I completely understand the material; however, when it comes to the problems, it seems that I could only solve a handful. KK is known for their problem difficulty. However, I want to get to the point where I can solve all of the problems in the chapter. When I can't solve one problem, I get discouraged, and when I can't solve three in a row, I get even more discouraged. I know that problem solving takes persistence, but what should I do when I just can't solve a problem, even though I feel as though I understand all of the reading material? Do I just read the section again?

edit: also, when I DO solve a problem, I always feel as though there is a better, more clever way to get to the solution that I am not doing, which is also discouraging...

 

[axmls]

I know that problem solving takes persistence, but what should I do when I just can't solve a problem, even though I feel as though I understand all of the reading material?

Any time you can't solve a problem, it's because there's a deficiency there--either in your mathematical knowledge or your physics knowledge. That's not a bad thing! When you do solve those problems, it's that much more experience you have solving physics problems. Eventually you start to see common patterns of approaching problems.

That said, the point still stands. If you are having trouble solving the problems, it means you don't fully understand the material. If you understand the entire chapter, that means maybe you should look at other resources and read those. They may have examples that will prepare you for your problem. They may explain a certain aspect of the chapter more clearly. Either way, it's a good thing to get your information from a diverse selection of sources. Go through your text again. Write down the important steps in derivations. If a step is skipped and you aren't 100% sure what happened, write it down and work it out yourself. See if you can rederive things without looking. See what happens if you apply the steps of the derivation to different problems. This is all just general advice.

And of course, find a textbook with easier problems and use those to make sure you're strong in the fundamentals.

also, when I DO solve a problem, I always feel as though there is a better, more clever way to get to the solution that I am not doing, which is also discouraging...

Those solutions will come with practice, and they will certainly come once you learn more mathematically advanced and elegant ways to solve those problems.

 

[micromass]

edit: also, when I DO solve a problem, I always feel as though there is a better, more clever way to get to the solution that I am not doing, which is also discouraging...

Yeah, there usually is a better and more clever way. But I feel that sometimes artificial but clever and elegant solutions are emphasized too much in mathematics or physics. Learning how to solve things the ugly brute way is something you must master first.

Here's a dumb example, but I hope you get the point. Suppose you're asked to compute the limit $\lim_{x\rightarrow 1} \frac{x^2 - 1}{x-1}$. Now the fun thing about these kind of limits is that there is a very general and easy procedure that can solve all of them. It's called L'Hospitals rule. You don't need to think, just differentiate numerator and denominator and you're done. And sure, L'Hospital's theorem is an extremely useful tool that you absolutly need to master. But before you do, you must also master these limits the usual way, that is: factorize the numerator.

In classical mechanics, it's the same thing really. There are often a lot of situation which can be solved with much more advanced methods. Lagrangian mechanics comes to mind as a very cool method to solve things. That doesn't mean that you don't need to know the Newtonian way first.

 

[Student100]

KK is known for their problem difficulty.

This basically sums it up. There are some problems in there that your professor wouldn't be able to solve without his solutions manual; at least, not right away.

Which is what I'm assuming you're probably doing, i.e. looking at the problem and getting discouraged right away because the way forward isn't obvious. Some (read the majority) of the problems in there require you to think and experiment on them for a good amount of time. You also need to be to connect them to concepts you've learned in your other courses.

Reading the section again? Sure go for it, but I feel like the problems are an extension of the section that requires a certain level of work and interactive reading. As it should be. Also, does your class meet for discussion or articulation sessions? Are you going to these?