Question

3. Two charged particles of charge e and mass mare sliding directly toward each other along a frictionless horisontal surface which is attached to a scale and is located in a locally uniform gravitational fieldē a) when the Sparticles come instantaneously to rest at separation des what is the weight measuked by the scale b) What is the weight when the particles each have speed & and are far apart? c) Assuming negligible Wadiation emission, how are your answeis to Yandb) related?

Answer 1

3) a) Two Particles of mass m and charege q are sliding towards each other along a frictionless horipantal talle. At the instantaneous boint when sul rest being seperation by a distance l, their total potential energy is converted into mass - energy as zme² = are e rest mass-energy potential energy 72m = Mcomposete = 4 esl the speed of % weight measured by the seale is W = Mg = a ut el 2 q = 20 where eis the light. le) Now when the particles are face apart and only hare Kinetic energy, since they are moving with speed w's. then again conservation of mass-energy follows as 28 me ² = 1 {mine + 18 mat where = 1 = this is due to cultivistica effect. 12 e 2

- am = my² the total weight of the system ez . Now is uz = Mg = (8m + 8m)q=28 mg = 2 m 4 e). The answers to a) & 6) are enclated af {23m x 2) = atte, teme? & Kinetic envegry of the system fare apart is equal to the potential energy when they are at rust. when o o , the total eust mass energy is obtained from the potential energy.