Find the magnitude and direction of the gravitational field at point D in the diagram below. Assume that points A, B, and C have the same mass and that each square represents 1m.

Question

Find the magnitude and direction of the gravitational field at point D in the diagram below. Assume that points A, B, and C have the same mass and that each square represents 1m.

Point A (0,3.5)

Point D (0,2)

Point B (-2,0)

Point C (2,0)

Answer 1

Gravitational field has magnitude GM/d²

In these problems, it pays to graph the points, look at symmetries and draw vectors to indicate components

In this case, you see that the horizontal field components of C and B cancel and the vertical components will add to 2(GM/8 m²) (sqrt(2)/2) downwards (Thet act at 45 degree angles, so the components are sqrt(2)/2 of the full field from one point.

Meanwhile, A produces a field upwards with a magnitude of GM/(1.5 m)²

So the net field will be upwards.