Gravity in Three Dimensions a point mass ml is held in place at the origin, and another point mass m2 is free to move a distance r away at a point P having coordinates x, y, and z. The gravitational potential energy of these masses is found to be U(r) = -Gm1/m2/r, where G is the gravitational constant (see Exercises 7.34 and 7.35). (a) Show that the components of the force m m2 due to m. are (Hint: First write r in terms of x, y, and z.) (b) Show that the magnitude of the force on m, is F = Gm1m2/r2. (c) Does ml attract or repel m? How do you know?

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Gmymx Gmm2y 2+2) Gmm2z