Physics education research, electronic materials, and the musings of Christopher Moore, Ph.D.

If anybody knows how to find the answer to any or all of these, I would greatly appreciate it and rate you very high.

In Fig. 13-35, a square of edge length 15.6 cm is formed by four spheres of masses m1 = 2.97 g, m2 = 3.60 g, m3 = 3.63 g, and m4 = 3.35 g. In unit-vector notation, what is the net gravitational force from them on a central sphere with mass m5 = 3.22 g?

Fig. 13-35
Problem 8.
Answer: _____ i + _____ j Newtons

Problem 21:
One model for a certain planet has a core of radius R and mass M surrounded by an outer shell of inner radius R, outer radius 2R, and mass 4M. If M = 6.64 × 1024 kg and R = 8.69 × 106 m, what is the gravitational acceleration of a particle at points (a) R and (b) 3R from the center of the planet?

Problem 23:
Certain neutron stars (extremely dense stars) are believed to be rotating at about 0.71 rev/s. If such a star has a radius of 38 km, what must be its minimum mass so that material on its surface remains in place during the rapid rotation? (in kg)

Problem 40:
In deep space, sphere A of mass 69 kg is located at the origin of an x axis and sphere B of mass 130 kg is located on the axis at x = 2.5 m. Sphere B is released from rest while sphere A is held at the origin. (a) What is the gravitational potential energy of the two-sphere system just as B is released? (b) What is the kinetic energy of B when it has moved 0.75 m toward A? (I have a but cant find b)