# Bizzare center of gravity problem.

1. Nov 18, 2004

### 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.

2. Nov 18, 2004

### Staff: Mentor

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

3. Nov 18, 2004

### 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.

4. Nov 18, 2004

### Staff: Mentor

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.)

5. Nov 18, 2004

### quasar987

Ok, thanks a lot for clarifying that !

6. Nov 20, 2004

### daveed

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

7. Nov 20, 2004

### Staff: Mentor

In a non-uniform gravitational field.