Question 1: Newton's and Euler-Langrange's methods Assume a particle of mass m subject to a force F = F(z). It's velocity at time ta is va and at a later time t, > ta its velocity is v. (1a) - Express the Newton's 2nd law of motion for this particle. - Prove the conservation of energy theorem for conservative and non-conservative forces. - If the force is conservative show that the sum of the particle's kinetic and potential energy is constant in time. (1ь) - Define the particle's Lagrangian function assuming the force is conservative. - Express the Euler-Lagrange (E-L) equation-of-motion for this particle. - Show that the E-L equations lead to the Newton's 2nd law. (lc) What is the work of the force on the particle from time t, to time t, if v, - 2 m/s and Us - 1 m/s and m - 1 kg. If the force is conservative and the potential energy at time ta is zero, then what is its potential energy at time t,?

Question 1: Newton's and Euler-Langrange's methods Assume a particle of mass m subject to a force F = F(z). It's velocity at time ta is va and at a later time t, > ta its velocity is v. (1a) - Express the Newton's 2nd law of motion for this particle. - Prove the conservation of energy theorem for conservative and non-conservative forces. - If the force is conservative show that the sum of the particle's kinetic and potential energy is constant in time. (1ь) - Define the particle's Lagrangian function assuming the force is conservative. - Express the Euler-Lagrange (E-L) equation-of-motion for this particle. - Show that the E-L equations lead to the Newton's 2nd law. (lc) What is the work of the force on the particle from time t, to time t, if v, - 2 m/s and Us - 1 m/s and m - 1 kg. If the force is conservative and the potential energy at time ta is zero, then what is its potential energy at time t,?

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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