Halliday, Resnick & Walker — Potential Energy and Conservation of Energy: Problem 124_CALC

The magnitude of the gravitational force between a particle of mass \( m_1 \) and one of mass \( m_2 \) is given by \[ F(x) = G \frac{m_1 m_2}{x^2} \] where \( G \) is a constant and \( x \) is the distance between the particles. (a) What is the corresponding potential energy function \( U(x) \)? Assume that \( U(x) \to 0 \) as \( x \to \infty \) and that \( x \) is positive. (b) How much work is required to increase the separation of the particles from \( x = x_1 \) to \( x = x_1 + d \)?