Randall D. Knight — Work and Kinetic Energy: Problem 53

The gravitational attraction between two objects with masses \(m_A\) and \(m_B\), separated by distance \(x\), is \(F = Gm_Am_B/x^2\), where \(G\) is the gravitational constant. a. How much work is done by gravity when the separation changes from \(x_1\) to \(x_2\)? Assume \(x_2 < x_1\). b. If one mass is much greater than the other, the larger mass stays essentially at rest while the smaller mass moves toward it. Suppose a \(1.5 \times 10^{13} \text{ kg}\) comet is passing the orbit of Mars, heading straight for the sun at a speed of \(3.5 \times 10^4 \text{ m/s}\). What will its speed be when it crosses the orbit of Mercury? Astronomical data are given in the tables at the back of the book, and \(G = 6.67 \times 10^{-11} \text{ Nm}^2/\text{kg}^2\).