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 springinvolved, soKE14++ Unewf =+ Unewi(Equation 1)For all energies, we know the followingXF -mKE =Am,m2PEgrav =r1Uelastic =kx²Unew = (1//(rwhere in we havem1 = m, m2 = M, q1 = q and q2 = QBy substituting all these to Equation 1 and then simplifying results to= sgrt(2 + ( (Qm ) -Vv) - (1/x) ) + QUESTION 4ProblemOne newly discovered light particle has a mass of m and property q. Suppose it moves within the vicinity of an extremely heavy (fixed inplace) 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 theheavy particle with a speed of vi. a) What is the lighter particle's speed when it is xf away from the heavy particle?Am¡m2Consider a new expression for gravitation potential energy as: PEaray = -where A is a constant, m, and m, are the masses of thertwo objects, and r is the distance between them.Moreover, the new particle has an additional interaction with the heavy particle through the following force expression1Fnew =qQ4πεο r2where En is a constant that is read as epsilon naught, q and Q are their new properties, r is the distance between the new particle and the heavyparticle.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 EnergyPrinciple.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 certaindistance asKE16 + KE2F + PEgravf + Velasticf + Unewf = KE1i + KE2i + PEgravi ++ UnewiSince the heavy particle remains fixed, before and after the motion of the lighter particle, it does not have any velocity, moreover, there is no springinvolved, so

From the energy conservation, we conclude,…

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 + Unewf = + Unewi (Equation 1) For all energies, we know the following KE=-m Am,m2 PEg Fgrav Uelastic = kx? Unew = (1/ where in we have m, = m, m2 = M, q1 = q and q2 = Q By substituting all these to Equation 1 and then simplifying results to = sąrt v 2 + ( ( m ) - ) - (1/x ) ) +

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 + Unewf = + Unewi (Equation 1) For all energies, we know the following KE=-m Am,m2 PEg Fgrav Uelastic = kx? Unew = (1/ where in we have m, = m, m2 = M, q1 = q and q2 = Q By substituting all these to Equation 1 and then simplifying results to = sąrt v 2 + ( ( m ) - ) - (1/x ) ) +

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter9: Relativity

Section: Chapter Questions

Problem 50P

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Qno7 solve asap. Physics expert plz suggest