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 thatd-mx².dtGmMx²i.GmMX= 0.dvdv(i.e., the total energy, sum of kinetic and potential energy, is conserved).(b) Using the change of variables var dr, solve the equation of motion and determine the=dxvelocity of the particle v(x) as a function of x assuming it starts with zero velocity at xo. Doesthe particle's speed in x O depend on the initial position?dt'=

Given data: A particle of constant mass m with position x>0 is moving in one space dimension…

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 GmM i. d (2m²² _ GmM) dt = 0. (i.e., the total energy, sum of kinetic and potential energy, is conserved). dv dt' (b) Using the change of variables vd = dy, 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?

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 GmM i. d (2m²² _ GmM) dt = 0. (i.e., the total energy, sum of kinetic and potential energy, is conserved). dv dt' (b) Using the change of variables vd = dy, 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?

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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Question

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
-mx².
dt
GmM
x²
i.
GmM
X
= 0.
dv
dv
(i.e., the total energy, sum of kinetic and potential energy, is conserved).
(b) Using the change of variables var dr, solve the equation of motion and determine the
=
dx
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 O depend on the initial position?
dt'
=

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