Critical analisys of Newton's second law in the form F_res = dp∕dt with p = mv and variable m

In classical mechanics, variable mass is not allowed in Newton's second law in the form F_res = dp∕dt, with p = mv. We think there is some confusion about it both in academia and also in the literature, and we made some effort to discuss this matter in an accessible and rigorous manner. This paper has also a practical nature, providing some help for problem solving in classical mechanics when there is mass variation by increase and/or loss of matter. The concept of variable mass in the special theory of relativity is also discussed – which can be disregarded by those who are interested only in classical mechanics.

Keywords:
Newton's second law; linear momentum; variable mass; relativistic mass