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? ProblemOne newly discovered light particle has a mass of m andproperty q. Suppose it moves within the vicinity of anextremely heavy (fixed in place) particle with a property Q andmass M. When the light particle is xi distance from the heavyparticle, it is moving directly away from the heavy particle witha speed of vi. a) What is the lighter particle's speed when it isxf away from the heavy particle?Consider a new expression for gravitation potential energy as:Am m2PE grav =where A is a constant, mj and m2 are themasses of the two objects, and r is the distance between them.Moreover, the new particle has an additional interaction withthe heavy particle through the following force expression1Fnew =qQ4περ r2where ɛ, is a constant that is read as epsilon subscript 0, qand Q are their new properties, r is the distance between thenew particle and the heavy particle.Solution:We may solve this using two approaches. One involves theNewton's Laws and the other involving Work-Energy theorem.To avoid the complexity of vector solution, we will insteademploy the Work-Energy theorem, more specifically, theConservation of Energy Principle.Let us first name the lighter particle as object 1 and the heavyparticle as object 2.Through work-energy theorem, we will take into account all ofthe energy of the two-charged particle system before and aftertraveling a certain distance asKE1F + KE2F + PEgravf + Uelasticf + Unewf = KE1 + KE2¡ +PEgravi ++ UnewiSince the heavy particle remains fixed, before and after themotion of the lighter particle, it does not have any velocity,moreover, there is no spring involved, soKE1F ++ Since the heavy particle remains fixed, before and after themotion of the lighter particle, it does not have any velocity,moreover, there is no spring involved, soKE16 ++++ Unewf =%3D+++ Unewi+(Equation 1)For all energies, we know the followingKE=Am¡m2PEgravUelastic =Unew = (1/%3Dwhere in we havem1 = m, m2 = M, q1 = q and q2 = QBy substituting all these to Equation 1 and then simplifyingresults tosqrt(2 + ( (|Qm ) -(1/x-) +Take note that capital letters have different meaning thansmall letter variables/constants.

Name: One newly discovered light particle has a mass of m and property q. Su
Uploaded: 2024-03-20T06:57:25.000Z
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Description: 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