One newly discovered light particle has a mass of m and property q. Suppose it moves within the vicinity of an extremely heavy (fixed in place) particle with a property Q and mass M. When the light particle is xi distance from the heavy particle, it is moving directly away from the heavy particle with a speed of vi. a) What is the lighter particle's speed when it is xf away from the heavy particle? Am¡m2 Consider a new expression for gravitation potential energy as: PE grav ,where A is a constant, m1 and m2 are the masses of the two objects, and r is the distance between them. Moreover, the new particle has an additional interaction with the heavy particle through the following force expression 1 qQ 4περ r2 Fnew where Eo is a constant that is read as epsilon subscript 0, q and Q are their new properties, r is the distance between the new particle and the heavy particle. Solution: We may solve this using two approaches. One involves the Newton's Laws and the other involving Work-Energy theorem. To avoid the complexity of vector solution, we will instead employ the Work-Energy theorem, more specifically, the Conservation of Energy Principle. Let us first name the lighter particle as object 1 and the heavy particle as object 2. Through work-energy theorem, we will take into account all of the energy of the two-charged particle system before and after traveling a certain distance as KE16 + KE2F + PEgravf + Uelasticf + Unewf = KE1¡ + KE2¡ + PEgravi + PEelasticf + Unewi Since the heavy particle remains fixed, before and after the motion of the lighter particle, it does not have any velocity, moreover, there is no spring involved, so KE1F+ KE2F + PEnewf + Unewf = + + + + Unewi (Equation 1) For all energies, we know the following

One newly discovered light particle has a mass of m and property q. Suppose it moves within the vicinity of an extremely heavy (fixed in place) particle with a property Q and mass M. When the light particle is xi distance from the heavy particle, it is moving directly away from the heavy particle with a speed of vi. a) What is the lighter particle's speed when it is xf away from the heavy particle? Am¡m2 Consider a new expression for gravitation potential energy as: PE grav ,where A is a constant, m1 and m2 are the masses of the two objects, and r is the distance between them. Moreover, the new particle has an additional interaction with the heavy particle through the following force expression 1 qQ 4περ r2 Fnew where Eo is a constant that is read as epsilon subscript 0, q and Q are their new properties, r is the distance between the new particle and the heavy particle. Solution: We may solve this using two approaches. One involves the Newton's Laws and the other involving Work-Energy theorem. To avoid the complexity of vector solution, we will instead employ the Work-Energy theorem, more specifically, the Conservation of Energy Principle. Let us first name the lighter particle as object 1 and the heavy particle as object 2. Through work-energy theorem, we will take into account all of the energy of the two-charged particle system before and after traveling a certain distance as KE16 + KE2F + PEgravf + Uelasticf + Unewf = KE1¡ + KE2¡ + PEgravi + PEelasticf + Unewi Since the heavy particle remains fixed, before and after the motion of the lighter particle, it does not have any velocity, moreover, there is no spring involved, so KE1F+ KE2F + PEnewf + Unewf = + + + + Unewi (Equation 1) For all energies, we know the following