H2. Suppose a particle of constant mass m with position x > 0, moves in one space dimensionunder the influence of the gravitational force of another point particle of constant mass Msitting at x = 0, i.e. the attracting force isF=(a) Using Newton's second law, show thatGmMx²i.1dr (2m²2² _ GimM)dt= 0.(i.e., the total energy, sum of kinetic and potential energy, is conserved).dx dt(b) Using the change of variables vdy = r, solve the equation of motion and determine thevelocity of the particle v(x) as a function of x assuming it starts with zero velocity at xo. Doesthe particle's speed in x = 0 depend on the initial position?

Given: F=-GmMx2i Solution: Let the velocity has the velocity ,v=vi From the Newton's second law of…

H2. Suppose a particle of constant mass m with position x > 0, moves in one space dimension under the influence of the gravitational force of another point particle of constant mass M sitting at x = 0, i.e. the attracting force is F (a) Using Newton's second law, show that d (2m²² -mx dt GmM x² = GmM = 0. (i.e., the total energy, sum of kinetic and potential energy, is conserved). (b) Using the change of variables vd dr, solve the equation of motion and determine the velocity of the particle v(x) as a function of x assuming it starts with zero velocity at xo. Does the particle's speed in x = 0 depend on the initial position? X

H2. Suppose a particle of constant mass m with position x > 0, moves in one space dimension under the influence of the gravitational force of another point particle of constant mass M sitting at x = 0, i.e. the attracting force is F (a) Using Newton's second law, show that d (2m²² -mx dt GmM x² = GmM = 0. (i.e., the total energy, sum of kinetic and potential energy, is conserved). (b) Using the change of variables vd dr, solve the equation of motion and determine the velocity of the particle v(x) as a function of x assuming it starts with zero velocity at xo. Does the particle's speed in x = 0 depend on the initial position? X

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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