ProblemOne 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 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: PEgrav=, where A is a constant, m, and m, 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 expression1Fnew =4TE0 r2qQwhere Eg 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 asKE1F + KE2F + PEgravf + Velasticf + Unewf = KE11 + KE2¡ + PEgravi ++ UnewiSince the heavy particle remains fixed, beforeafter the motion of the lighter particle, it does not have any velocity, moreover, there is no spring involved, soKE1F ++ Unewf =+ Unewi(Equation 1)For all energies, we know the following1KE =mv Am¡m2PEgrav =rU elastic = kxkx²Unew = (1/where in we havem1 = m, m2 = M, q1 = q and q2 = QBy substituting all these to Equation 1 and then simplifying results to= sgrt(2 + ( (m ) -) - (1/x) ) +VTake note that capital letters have different meaning than small letter variables/constants.

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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

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

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

Chapter11: Gravity, Planetary Orbits, And The Hydrogen Atom

Section: Chapter Questions

Problem 57P

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