2. PHY147 Lecture 8: Imagine you are an astronaut on a pirate spaceship with a. \"cannon" to shoot at other space ships. In this shooting device, two charged spheres are pushed together against an electrical repulsion force due to each of the spheres carrying a charge of 0.8 C. Assume the device is loaded with the two spheres locked in place while touching each other with all the charges uniformly distributed throughout the spheres. (a) What is the potential energy stored in the cannon relative to a conguration in which the charged spheres are very far away from each other assuming the radius of each sphere is 13 cm? Comment on the sign of the potential energy difference: does it make sense? How would the sign of potential energy change if both spheres were positively charged rather than negatively? (b) As another spaceship is passing you, you release the locking mechanism of your device such that the two spheres shoot out in opposite directions due to their electric repulsion. One of the cannon balls hits the command centre of the passing Imperial Star Destroyer while the other one simply shoots away into the void. What is the speed the second sphere will reach when it is very far away from you: assuming the mass of each sphere is lOOkg? Explicitly comment on any symmetry considerations you used in your calculation! (You may assume that all potential energy gets converted to kinetic energy and there are no other forces acting on the sphere, i.e.: there are no other gravitational or electric elds.)