Understanding Purcell's Cube: Attraction to Mass Center?

Click For Summary

Discussion Overview

The discussion revolves around the gravitational attraction of a cube with constant density, as described by Purcell in "Electricity and Magnetism." Participants explore how such a cube interacts with external bodies and the implications of its gravitational field compared to that of point masses and spherical objects.

Discussion Character

  • Exploratory, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant notes that Purcell states a cube does not attract external bodies as if its mass were concentrated at its center, raising questions about how attraction occurs.
  • Another participant explains that while point masses and spheres have spherically symmetric gravitational fields, a cube's gravitational field lacks this symmetry, suggesting that external observers can distinguish its field from that of a point mass.
  • A reference to another thread is provided for further insights into Newton's law of gravitation, indicating a broader context for the discussion.

Areas of Agreement / Disagreement

Participants express differing views on the implications of Purcell's statement, with no consensus reached on how the gravitational attraction of a cube operates compared to that of point masses or spherical objects.

Contextual Notes

The discussion highlights the complexity of gravitational fields and the assumptions involved in comparing different geometries, such as cubes versus spheres and point masses.

fluidistic
Gold Member
Messages
3,934
Reaction score
286
In the Spanish second edition of "Electricity and Magnetism", Berkeley Physics Course, volume II, page 27, Purcell states that a cube with a perfectly constant density does not attract external bodies as if its mass was concentrated in its geometrical center.
However he does not say how does such a cube attract other bodies...

The only thing my intuition tells me is that if I am in front of a cube in such a way that I'm closer to a vertex than any other, I will be more attracted by the vertex than any other part of the cube. However I'm not sure it implies that I'm not attracted by the center of mass of the cube.
The comment from Purcell blows up my intuition.

Can you help me to understand, please?
 
Physics news on Phys.org


A point mass has a gravitational field that is spherically symmetric.

A sphere also has a gravitational field that is spherically symmetric. So if you're outside the sphere and examining the gravitational field, you wouldn't be able to tell if it is the field of a sphere or a point mass.

A cube's gravitational field is not spherically symmetric does not. So if you're outside the cube and examining the gravitational field, you'll be able to tell that it isn't the gravitational field of a point mass.
 


Thanks a lot to both!
 

Similar threads

Undergrad Gravity at Earth's poles vs equator
  • · Replies 12 ·
Replies
12
Views
4K
Center of mass and momentum- A question about systems
  • · Replies 25 ·
Replies
25
Views
2K
Undergrad Magnetic Attraction: Is Bar Magnet Symmetrical?
  • · Replies 3 ·
Replies
3
Views
2K
Center of mass for two small particles
  • · Replies 4 ·
Replies
4
Views
5K
Understanding Acceleration and Center of Mass in Shock Absorption
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Gravity inside an exponential mass disk
  • · Replies 16 ·
Replies
16
Views
2K
Center of Mass involving three cubes
  • · Replies 1 ·
Replies
1
Views
6K
Undergrad Does Changing Material Density Affect the Center of Mass in a Composite Object?
  • · Replies 3 ·
Replies
3
Views
3K
How Far Does m1 Travel Before Colliding with m2?
  • · Replies 4 ·
Replies
4
Views
4K
High School Calculate needed dimensions of table - Center of mass, levers etc
  • · Replies 11 ·
Replies
11
Views
3K