the mass or the carth is Me, show thnat thegravitational potential energy of a body of mass m locateda distance r from the center of the earth is V, = -GM¸m/r.Recall that the gravitational force acting between the earthand the body is F = G(M¸m/P), Eq. 13-1. For thecalculation, locate the datum at r→ ∞. Also, prove that F isa conservative force.

Answered: Image /qna-images/answer/39317f93-91d7-475b-ab55-6dd5c442f4d3.jpg

Answered: the mass or the carth is Me, show thnat…

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter7: Hamilton's Principle-lagrangian And Hamiltonian Dynamics

Section: Chapter Questions

Problem 7.35P

See similar textbooks

Similar questions

A body of mass m is suspended by a rod of length L that pivots without friction (as shown). The mass is slowly lifted along a circular arc to a height h. a. Assuming the only force acting on the mass is the gravitational force, show that the component of this force acting along the arc of motion is F = mg sin u. b. Noting that an element of length along the path of the pendulum is ds = L du, evaluate an integral in u to show that the work done in lifting the mass to a height h is mgh.
Let's consider a simple pendulum, consisting of a point mass m, fixed to the end of a massless rod of length l, whose other end is fixed so that the mass can swing freely in a vertical plane. The pendulum's position can be specified by its angle Φ from the equilbrium position. Prove that the pendulum's potential energy is U(ϕ)=mgl(1−cosϕ). Write down the total energy E as a function of Φ and ϕ˙. Show that by differentiating E with respect to t you can get the equation of motion for Φ. Solve for Φ(t). If you solve properly, you should find periodic motion. What is the period of the motion?
In the above question let us consider the position of mass when the spring is relaxed as x = 0, and the left to right direction as the positive direction of the x-axis.Provide x as a function of time t for the oscillating mass, if at the moment we start the stopwatch (t = 0), the mass is:( i ) at the mean position,( ii ) at the maximum stretched position, and( iii ) at the maximum compressed position.
Show that the one-dimensional p(x) = Ae−ikx and three-dimensional expression p(x, y, z) = Ae−ikr is asolution to the Cartesian form of the Helmholtz equation, ∇2p + k2p = 0
A 0.4 Gram mass is required to stretch a soap film confined in arectangular frame by 2mm downward before the film breaks. If the length of the movable bar is 2.5 cm, what will be the surface tension and change in surface free energy of the soap film?
Show that the Force of Gravity is conservative.
A pendulum of mass 50 gm and length 90 cm is left to swing from an intial angle of 30 degrees, and seen to raise up to an angle of 28 degrees when it reaches the otherside. How much will it be in the difference in height? How much energy is lost?
calculate the reverberation time at 500hz for a conference room that is 12 ft wide, 20 ft long and 12 ft high. It has a carpeted floor, curtains on both sides, plasterboard (or equivalent) short sides, and a plasterboard ceiling. what will the reverberation tiume be if it is occupied by twenty people in comfortable upholstered seats?
find the potential energy of a particle moving around in F(r,θ,z) = -kr^3 ˆr
Suppose we let the radius approach zero. What would happen to the self-potential energy?
Since the initial potential energy and final kinetic energy are zero, our equation now becomes EP,f = EK,i. We can then substitute the formula for kinetic energy, EK = 1/2mv2, and the formula for gravitational potential energy, EP = mgh, mghf = 1/2mvi2. Now it's just a matter of doing the algebra, solving for the final height hf, and substituting values to find hf. Notice that the mass m divides out of both sides of the equation, so the value of the mass is not needed to find the final height. Calculate the maximum height of the ball in meters. hf = __________ m
In considering question #4, how fast is the mass moving when it is half way between the equilibrium and maximum amplitude, AND what is the kinetic and potential energies at that location?

SEE MORE QUESTIONS

Recommended textbooks for you

Classical Dynamics of Particles and Systems

Physics

ISBN:

9780534408961

Author:

Stephen T. Thornton, Jerry B. Marion

Publisher:

Cengage Learning

Principles of Physics: A Calculus-Based Text

Physics

ISBN:

9781133104261

Author:

Raymond A. Serway, John W. Jewett

Publisher:

Cengage Learning

Classical Dynamics of Particles and Systems

Physics

ISBN:

9780534408961

Author:

Stephen T. Thornton, Jerry B. Marion

Publisher:

Cengage Learning

Principles of Physics: A Calculus-Based Text

Physics

ISBN:

9781133104261

Author:

Raymond A. Serway, John W. Jewett

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS