Gravitation Field Problem With Equal Masses

[hardygirl989]

Homework Statement

Three objects of equal mass (m) are located at three corners of a square of edge length , as shown in the figure below. Find the magnitude and direction of the gravitational field at the fourth corner due to these objects. (Use any variable or symbol stated above along with the following as necessary: G.)

Image: http://www.webassign.net/serpse8/13-p-025.gif

Homework Equations

The magnitude of the gravitational field is
= GM/R^2 with R = l, and G = gravitation constant, M = mass

The Attempt at a Solution

The field strength of the diagonal mass = GM/(l*√2)^2
and the sum of the field magnitudes from the two neighbored masses is GM*√2/l^2.

So the total magnitude = GM/(2l^2) + GM√(2)/l^2

For the direction, I am not sure what it would be...Would it be 45 degrees or do I need to derive a new formula? If so, how should I go about creating the formula? Thanks!

 

[tiny-tim]

hi hardygirl989!

The field strength of the diagonal mass = GM/(l*√2)^2
and the sum of the field magnitudes from the two neighbored masses is GM*√2/l^2.

So the total magnitude = GM/(2l^2) + GM√(2)/l^2

For the direction, I am not sure what it would be...Would it be 45 degrees

yes of course

the figure is obviously symmetric about that direction (which is why you chose to calculate the components in that direction )