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,?

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter2: Newtonian Mechanics-single Particle

Section: Chapter Questions

Problem 2.50P: According to special relativity, a particle of rest mass m0 accelerated in one dimension by a force...

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