Purchase Solution

Gravity Work required to move a mass radially outward from the c.m. of a planet

Not what you're looking for?

Ask Custom Question

See attachment #1 for diagram showing parameters.

A uniform spherical planet has mass M= 8.5 E 25 kg and radius R= 7.5 E 6 m.
A hole is drilled from the surface to mass m= 360 kg at an initial position r1= 2.5 E 6 m from the center.

PART a. Find the initial gravity force F that the planet exerts on mass m.
PART b. Find the work required to bring mass m to the surface at a constant speed.
PART c. Find the work required to move mass m at constant speed from initial distance r2= 8.2 E 6 m to distance r3= 9.4 E 6 m, from the center of the planet.

Purchase this Solution

Solution Summary

The solution is very detailed in its explanation of the problem and the answers. The initial positions from the center of a spherical planets are given.

Solution Preview

PART a.
The gravity field g at a point is defined as the force per unit mass at that point. In this case, the distance r1 is less than the radius R so the mass m is interior to the planet. For a field within a planet, universal gravitation law;
(1) F= G M m /r^2 will not hold. The field of a planet at interior points is given (as developed in a separate posting in the Solutions Library #6055) by the linear function:
(2) g = (G M/R^3)(r1)
From the definition of g, we can write:
(3) g= F/m.
Equating (2) and (3) and solving for F, we get:
(4) F= (G M ...

Purchase this Solution


Free BrainMass Quizzes
Basic Physics

This quiz will test your knowledge about basic Physics.

Intro to the Physics Waves

Some short-answer questions involving the basic vocabulary of string, sound, and water waves.

The Moon

Test your knowledge of moon phases and movement.

Classical Mechanics

This quiz is designed to test and improve your knowledge on Classical Mechanics.

Introduction to Nanotechnology/Nanomaterials

This quiz is for any area of science. Test yourself to see what knowledge of nanotechnology you have. This content will also make you familiar with basic concepts of nanotechnology.