PCS 125 Lecture Notes - Lecture 3: Inertial Frame Of Reference, Gravitational Energy, Centripetal Force

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8 Jan 2018

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The total gravitational potential energy of the system is the sum over all pairs of particles. The absolute value of utotal represents the work needed to separate the particles by an infinite distance. Assume an object of mass m moving with a speed v in the vicinity of a massive object of mass m. Also assume m is at rest in an inertial reference frame. The total energy is the sum of the system"s kinetic and potential energies. In a bound system, e is necessarily less than 0. An object of mass m is moving in a circular orbit about m. The total mechanical energy is negative in the case of a circular orbit. The kinetic energy is positive and is equal to half the absolute value of the potential energy. The absolute value of e is equal to the binding energy of the system.

Related Questions

The Hubble Space Telescope orbits the Earth at an altitude of approximately 612 km. Its mass is 11,100 kg and the mass of the Earth is 5.97×1024 kg. The Earth's radius is 6.38×106 m. Assume the Hubble's orbit is circular. (a) What is the gravitational potential energy of the Earth-Hubble system? (Assume that it is zero when their separation is infinite.) (b) What is the Hubble's KE? (c) What is the Hubble's total energy?

(A) A satellite of mass m is in circular orbit about theearth.
The radius of the orbit is r0 and the mass of the earth isME.
Find the total mechanical energy of the satellite.

(B) Now suppose that the satellite moves in the extreme upper
atmosphere of the earth where it is retarded by a constant
weak frictional force f. The satellite will slowly spiral intoward
the earth. Since the friction force is weak, the change
in radius will be very slow. We can therefore assume that
at any instant the satellite is effectively in a circular orbitof
average radius r. Find the approximate change in radius r
per revolution of the satellite.

(C) Calculate r for these parameters: r = 1.045 RE; f =
\ensuremath{1.300\times 10Ë{-4}} N; m = 91 kg.

(D) Find the approximate change of kinetic energy of the
satellite K per revolution, for the same parameters as (C).
Express the result as the fraction of the current kineticenergy.
Is K positive or negative? Explain briefly.

A block of mass 6o kg is sitting on a platform that in turn sits ona spring with a spring constant k=2500 N/m. The block is initiallyat rest. Assume that the gravitational
potential energy and elastic potential energy of the system is zeroat this point.

a. What is the total mechanical energy of the system?

The platform is depressed a distance of 0.3 m and held there.

b. What are the kinetic, gravitational potential, and elasticpotential energies of the system?

c. What is the new mechanical energy of the system?

The platform is released, ejecting the block in the verticaldirection .

d. What are the kinetic, gravitational potential, and elasticpotential energies when the mass reaches its highest point?

e. How high above the platform does the mass go (measure from theoriginal un-depressed position)?

PCS 125 Lecture Notes - Lecture 3: Inertial Frame Of Reference, Gravitational Energy, Centripetal Force

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