Source of Difficult Newtonian Mechanics Problems?

[Silicon-Based]

I'm looking for a source of harder mechanics problems, preferably with solutions. I'm supposed to use the Young and Freedman book, but I find it rather teadious and superficial; most problems don't match the difficulty and depth of the ones on the exam. I had my mid-term tests recently, and got startled seeing my dynamics score (63%), though math and relativity was a breeze (100% each), so I know that it isn't the math that hinders my progress. I study in the UK if that's relevant. Thank you.

 

[Moayd Shagaf]

Go for Kleppner.

 

[Buffu]

I'm looking for a source of harder mechanics problems, preferably with solutions. I'm supposed to use the Young and Freedman book, but I find it rather teadious and superficial; most problems don't match the difficulty and depth of the ones on the exam. I had my mid-term tests recently, and got startled seeing my dynamics score (63%), though math and relativity was a breeze (100% each), so I know that it isn't the math that hinders my progress. I study in the UK if that's relevant. Thank you.

Problem book by Irodov and Krotov has many difficult problems. They are also free.

 

[Dr.D]

The text Analytical Dynamics by E.T. Whittaker has some real zingers!

 

[password123]

classical mechanics david morin has lot of difficult solved problems. difficult for me anyways. it is 2nd year level.

 

[Buffu]

classical mechanics david morin has lot of difficult solved problems. difficult for me anyways. it is 2nd year level.

I didn't recommend that book because it requires knowledge of Lagrangian mechanics. It is "Too Hard".

 

[vanhees71]

Mechanics without Lagrangians is hard. Whenever you've learned about the Action Principle, you'll not want to miss it again!

 

[Dr.D]

If your intention is to determine motion, Lagrange is often very useful. If your intent is to determine the force acting in a system, then Newton is the only option.

 

[vanhees71]

No, it is much easier to evaluate forces using the Lagrangian method than doing cumbersome free-body diagram analyses!

 

[Dragon27]

No, it is much easier to evaluate forces using the Lagrangian method than doing cumbersome free-body diagram analyses!

What about classical electrodynamics (if it's not too off-topic)? Is this classical field theory much easier with the Lagrangian (or Hamiltonian) approach?

 

[vanhees71]

On a fundamental level the Lagrange-Hamilton method is also very elegant for fields. To "derive" classical electrodynamics you are almost forced to write down the correct Lagrangian by just knowing that the electromagnetic field is a massless gauge field. Then it's also easy to understand, why the observable quantities like energy, momentum and angular momentum of the fields are what they are, using Noether's theorem.

For practical calculations, of course you still have to solve the Maxwell equations. That's the same in mechanics: To finally find the trajectories of the particles in your given system, you have to solve the equations of motion, but often you can find an easier way by analyzing the symmetries and choose the most convenient coordinates.

 

[Dr.D]

, it is much easier to evaluate forces using the Lagrangian method than doing cumbersome free-body diagram analyses!

If that is so, please describe for me how to get the bearing forces at a pinned joint in an accelerating mechanism. I look forward to being enlightened. (Please excuse the bold face, the button seems to be stuck!) I regularly use energy methods to get the system equation(s) of motion , but I know of no way to get the internal forces at joints and non-working forces at anchors (constraints) other than Newton.

 

[vanhees71]

Isn't this a paradigmatic example for the Lagrange method of the first kind to be solved with Lagrange multipliers?