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Section 13.3 Analysis Model: Particle in a Field (Gravitational)
14. (a) Compute the vector gravitational field at a point P on the perpendicular
bisector of the line joining two objects of equal mass separated by a distance 2a as
shown in Figure P13.14. (b) Explain physically why the field should approach
zero as r → 0. (c) Prove mathematically that the answer to part (a) behaves in this
way. (d) Explain physically why the magnitude of the field should approach
2GM/r2 as r →∞. (e) Prove mathematically that the answer to part (a) behaves
correct in this limit.
Figure P13.14
15. Three objects of equal mass are located at three corners of a square of edge length
ℓ, as shown in Figure P13.15. Find the magnitude and direction of the
gravitational field at the fourth corner due to these objects.
Figure P13.15
16. A spacecraft in the shape of a long cylinder has a length of 100 m, and its mass
with occupants is 1 000 kg. It has strayed too close to a black hole having a mass