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Path: ...!news.mixmin.net!news2.arglkargh.de!news.karotte.org!fu-berlin.de!uni-berlin.de!individual.net!not-for-mail From: Luigi Fortunati <fortunati.luigi@gmail.com> Newsgroups: sci.physics.research Subject: Re: The hidden error Date: Sat, 29 Mar 2025 00:38:53 PDT Organization: A noiseless patient Spider Lines: 54 Approved: Jonathan Thornburg [remove -color to reply]" <dr.j.thornburg@gmail-pink.com (sci.physics.research) Message-ID: <vs8681$o1vk$1@dont-email.me> References: <vs1ovt$2ikcp$1@dont-email.me> <vs3bfd$3pfg$1@dont-email.me> Reply-To: fortunati.luigi@gmail.com X-Trace: individual.net EZof12duUlp/nIFuhBHmpAi40CPggYMvrGcusSdG69/lSLszwg5y4yGqHF Cancel-Lock: sha1:Av6gVr9Gy2PyLmPEN+FzFS0USGA= sha256:5QIhCWB4EYQxdfxYJBr4BqUSm2AoKQE8vWKc0sqyhZA= X-Forwarded-Encrypted: i=2; AJvYcCXumRbEiEd3EX1r/Rk5NoW7mfMT5+ENmQCcSIu9rz1viOyRa8Nt/tP6WoreQ0Nbsdgg1UyTWqipnqWCduwRxA==@gmail.com X-Auth-Sender: U2FsdGVkX1/IZL/mi+0wKh/6/ppPjCHAFzSkBlRVAmnIVVcRfnZhp8WWYCWMN4AF X-ICQ: 1931503972 Bytes: 3335 Mikko il 28/03/2025 06:16:16 ha scritto: > On 2025-03-27 08:26:11 +0000, Luigi Fortunati said: > >> I have completed the animation of the elastic collision >> https://www.geogebra.org/classic/hxvcaphh >> and the inelastic one >> https://www.geogebra.org/classic/atdrbrse >> where, in both cases, I noticed a strange phenomenon. >> >> In the inelastic collision, body A with mass m_A=1 exerts a force >> F_AB=+v on body B, because it increases its speed from vi_B=-v to >> vf_B=0. > > In a collision the force is not constant in time. It is initilally > sero and finally sero but if it is always zero there is no collision. > How the force varies duriong the collision depends on details that > are not discussed below. In the special case of zero duration of the > collision the force is infinite. Zero duration does not exist, the time of the collision is very short but it is never zero. [[Mod. note -- I think Mikko was trying to describe the limit where the duration goes to zero, with the force scaling proportionally to 1/duration. In this limit, the force is a Dirac delta function, https://en.wikipedia.org/wiki/Dirac_delta_function#History and isn't actually a real-valued function. It can be rigorously defined via the theory of distributions, https://en.wikipedia.org/wiki/Distribution_(mathematics) but the intuitive notion of an infinitely narrow and infintely tall "spike" of finite area is relatively simple and often sufficient. Another representation is that a Dirac delta function is the derivative of a Heaviside step function. I suspect a Dirac delta function can also be defined via non-standard analysis, but I'm not sure of this. -- jt]] I obtained the force from Newton's second law F=ma, knowing <m> and knowing <a>. When body A has mass m_A=1, in the inelastic collision the acceleration= of body B is a_B=+v, so the force acting on B is equal to +v (the mass of B being equal to 1) And when the mass of body A doubles to m_A=2, the acceleration of body B and the force acting on B increase only from +v to +4/3v instead of doubling from +v to +2v. Why does the force on body B increase but not double if the mass A that exerts it doubles? This was the question. Luigi Fortunati