1) After graduating as a mechanical engineer you get a job at NASA. They have discovered a small crack starting to form on the outside of the International Space Station. Your first assignment is to find a new way to weld cracked metal parts in the vacuum of space. $60 - X You cannot use electric arc welding because the electrical currents it creates could damage the electronics and signals inside. It is known that gas welding does not work well in a vacuum. After thinking about the problem for a few days you come up with an idea. You will use electric charges to accelerate small metal particles to high speed, with enough energy that when they strike the metal part to be welded they and the metal will locally melt together - which is how welding works. A large number of particles can fill the crack with metal, all welded together. In designing the equipment to accelerate the particles you find that nearby there is a large charge O on a detector used to make measurements on the charged particles in the solar wind. It is located at a distance d at an angle of 60 from the origin of your coordinates as shown. You want the electric field everywhere on the x axis to point directly left along the -x axis, not pointing up or down, to accelerate the particles in that direction. In this problem work only with integers, not decimals. a) Where could you put another charge so the electric field anywhere on the x axis only points in the -x direction? What charge magnitude, at what position, do you need? (suggestion: think in terms of symmetry, to eliminate any y components) i) Draw this charge on the drawing, showing and labeling exactly where it is. b) You want to place a charge of 80 at a position s along the positive x axis as shown in the drawing, to help create the acceleration field. You calculate that the net electric field at the origin created by the three charges needs to be She 2, pointing left of course. What distance s do you need to use? Remember the values of the sine and cosine of 60, 1/2 and V3/2. c) You need to know the magnitude of the electric field on the x axis at a distance d to the left of the origin as shown. Find it, completely simplifying your expression. d) Find the net electric potential at the origin, where you will release particles of mass m and charge 10 0