- #1
blackheart
- 10
- 0
1. Three objects of equal mass are located at three corners of a square of edge length d. Find the magnitude and direction of the gravitational field at the fourth corner due to these objects. (Use the following as necessary: G, d, and m.)
2. Homework Equations :
g = Gm/r2
3. My attempt at the solution: I labeled the masses as 1, 2, and 3, where 1 and 3 are adjacent to the fourth corner and 2 is in the opposite corner from the fourth.
g1 = g3 = Gm/d2
g2 = Gm/(d[tex]\sqrt{}2[/tex]2)
gy = g1 + g2y
= Gm/d2 + g2 sin 45
= Gm/d2 + Gm/(d[tex]\sqrt{}2[/tex])2
gx = g3 + g2x
= Gm/d2 + g2 cos 45
= Gm/d2 + Gm(d[tex]\sqrt{}2[/tex])2
g2 = gx2 + gy2
g = [tex]\sqrt{}(2Gm/d2 + Gm/d^2 cos 45[/SUP])[/tex]
2. Homework Equations :
g = Gm/r2
3. My attempt at the solution: I labeled the masses as 1, 2, and 3, where 1 and 3 are adjacent to the fourth corner and 2 is in the opposite corner from the fourth.
g1 = g3 = Gm/d2
g2 = Gm/(d[tex]\sqrt{}2[/tex]2)
gy = g1 + g2y
= Gm/d2 + g2 sin 45
= Gm/d2 + Gm/(d[tex]\sqrt{}2[/tex])2
gx = g3 + g2x
= Gm/d2 + g2 cos 45
= Gm/d2 + Gm(d[tex]\sqrt{}2[/tex])2
g2 = gx2 + gy2
g = [tex]\sqrt{}(2Gm/d2 + Gm/d^2 cos 45[/SUP])[/tex]