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Problem A newly discovered light positively charged particle has a mass of mand charge q. Suppose it moves within the vicinity of an extremely heavy (fixed in place) particle with a positive charge Qand mass M. When the light partidle is xi distance from the heavy particle, it is moving directily 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? (Consider the Newtonian Gravitation acting between the two charged particles. Ignore the effects of external forces) 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 KE1F+ KE24 + PENawtonianf+ Uelasticf + Uelectricf = KE1 + KE2j + PENewtoniani + + Uslectrici 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 in involved, so KE1+ +Uelectricf= + Uelectrici (Equation 1) For all energies, we know the following 1. KE - Gm, m2 PENewtonan -- Uatostic " kx? Velectric = (1/ where in we have m, = m, m2 = M. 91 = q and a2 =Q By substituting all these to Equation 1 and then simplifying results to = sart( v m ) - ) - (1/x ) ) + Take note that capital letters have different meaning than small letter variables/constants.

Problem A newly discovered light positively charged particle has a mass of mand charge q. Suppose it moves within the vicinity of an extremely heavy (fixed in place) particle with a positive charge Qand mass M. When the light partidle is xi distance from the heavy particle, it is moving directily 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? (Consider the Newtonian Gravitation acting between the two charged particles. Ignore the effects of external forces) 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 KE1F+ KE24 + PENawtonianf+ Uelasticf + Uelectricf = KE1 + KE2j + PENewtoniani + + Uslectrici 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 in involved, so KE1+ +Uelectricf= + Uelectrici (Equation 1) For all energies, we know the following 1. KE - Gm, m2 PENewtonan -- Uatostic " kx? Velectric = (1/ where in we have m, = m, m2 = M. 91 = q and a2 =Q By substituting all these to Equation 1 and then simplifying results to = sart( v m ) - ) - (1/x ) ) + Take note that capital letters have different meaning than small letter variables/constants.

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Problem A newly discovered light positively charged particle has a mass of m and charge q. Suppose it moves within the vicinity of an extremely heavy (fixed in place) particle with a positive charge Q and mass M. When the light partidle is xi distance from the heavy particle, it is moving directily 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? (Consider the Newtonian Gravitation acting between the two charged particles. Ignore the effects of external forces) 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 KE1F+ KE2F + PENewtonianf + Uelasticf + Uelectricf = KE1i + KE2i + PENewtoniani + + Uelectrici 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 in involved, so KE1+ + Uelectricf = + Uelectrici (Equation 1) For all energies, we know the following KE -mv Gm, m2 PENewtonan-- Uebstic kr? Uelectric " (1/ X where in we have my = m, m2 = M. q1 = q and a2 = Q By substituting all these to Equation 1 and then simplifying results to = sqrtl m ) - ) - (1/x )) + Take note that capital letters have different meaning than small letter variables/constants.
Transcribed Image Text:Problem A newly discovered light positively charged particle has a mass of m and charge q. Suppose it moves within the vicinity of an extremely heavy (fixed in place) particle with a positive charge Q and mass M. When the light partidle is xi distance from the heavy particle, it is moving directily 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? (Consider the Newtonian Gravitation acting between the two charged particles. Ignore the effects of external forces) 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 KE1F+ KE2F + PENewtonianf + Uelasticf + Uelectricf = KE1i + KE2i + PENewtoniani + + Uelectrici 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 in involved, so KE1+ + Uelectricf = + Uelectrici (Equation 1) For all energies, we know the following KE -mv Gm, m2 PENewtonan-- Uebstic kr? Uelectric " (1/ X where in we have my = m, m2 = M. q1 = q and a2 = Q By substituting all these to Equation 1 and then simplifying results to = sqrtl m ) - ) - (1/x )) + Take note that capital letters have different meaning than small letter variables/constants.
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