What Is the Work Done When Moving a Mass from X to Y?

[DumbNut]

Homework Statement

X & Y are two points at respective distances R and 2R from the centre of the Earth, where R is greater than the radius of the Earth. The gravitational potential at X is -800kJkg^-1. When a 1kg mass is taken from X to Y, what is the work done on the mass?

Homework Equations

Gravitational Potential = -GM/r
U= -GMm/r

The Attempt at a Solution

I have thought over this question and tried using integration to make sense of it since gravitational potential and U varies w/ r. But when I tried thinking along the lines of integration, I find myself wondering what does the integrated value of graph U against r represent as it does not concur with what I am trying to find with regards to the concept of homogeneity. Is my idea of trying to integrate wrong? Or is my concept wrong to begin with? Please help, thank you.

 

[cepheid]

Welcome to PF,

I don't think you need to integrate. Since you know the gravitational potential (often called $\psi$ or $\phi$) at R, you can easily figure out what it is at 2R, since the form of the function $\phi(r)$ is known.

Once you get the potential at 2R, you know the potential energy that this particular mass therefore has at 2R. You can compare that to the potential energy it had back when it was only at R. Recall that the work done by a conservative force on an object is equal to the negative of that object's change in potential energy.

 

[DumbNut]

Thank you! I guess I thought about it too mathematically, now it makes sense to me.

 

[Pi-Bond]

The work done in moving a mass between two points is the difference in the potential energy (U). As far as I know, integrating U doesn't have any physical significance. By definition, U is the work done by the gravitational field of an object to move it from a point to infinity. Thus if you consider the difference in the potential energies at any two points, you can find the work required to move a body between those two points.

EDIT: Looks like someone else beat me to it!

 

[DiracRules]

Sorry, but I can't understand your question.
However, why don't you use the property that gravitational field is a conservative one?

 

[DumbNut]

Yeap, I tried that and it worked :D thanks guys.