Bizzare center of gravity problem.

[quasar987]

Here's the question: "Two equal masses m are separated by a distance a. Find the center of gravity of the two masses relative to a point P on the perpendicular bisector of the line joining them a distance y from the midpoint between them."

(perpendicular bisector definition)

I never heard of a definition of a center of gravity for a system of free particles. Not in my book nor on the net. Any clue?

Thx.

 

[Doc Al]

In most contexts, center of gravity is identical to center of mass. Is that the case here?

 

[quasar987]

Probably not as the next question is: "Show that as y aproaches infinity, the center of gravity approaches the center of mass. What happens when y approaches 0?"

But I wouldn't know anyway because I don't know what the center of gravity is for a system of free particles.

 

[Doc Al]

center of gravity

OK... just checking.

The center of gravity of a system of particles, with respect to some point, is the location where you could put the entire mass and still get the same gravitational force at that point.

So: Find the net gravitational field at point P due to the two masses. Then find where you'd have to put the entire mass (2m) to duplicate that net gravitational field at point P. That point is the center of gravity.

(It's easy.)

 

[quasar987]

Ok, thanks a lot for clarifying that !

 

[daveed]

question- when is center of gravity not identical to center of mass?

 

[Doc Al]

question- when is center of gravity not identical to center of mass?

In a non-uniform gravitational field.