Question

1. A day on Mars lasts 1.03 Earth days, which is inconvenient because Mars time keeps slipping behind Earth time. Suppose that residents of a future Martian settlement decide to solve this problem by launching a huge projectile horizontally off the Martian equator, in such a direction as to increase the planet’s rotation rate just enough to make the length of the Martian day equal to that of Earth’s day. If their technology can achieve a launch speed of 2.44 Mm/s, what mass of projectile will give the desired result? You can approximate Mars as a uniform solid sphere.

2.A potential-energy function in two dimensions is given by U(x)=a(x2−y2), where x and y measure position in m and a is a positive constant with the units of J/m2J/m2. (a) Show that this function has an equilibrium at x=0, y=0. (b) Is the equilibrium stable against small displacements in the x-direction? What about the y-direction?

Answer 1