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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 Consider a new expression for gravitation potential energy as: PEgray = - , where A is a constant, m1 and m2 are the masses of the two objects, andr r is the distance between them. Moreover, the new particle has an additional interaction with the heavy particle through the following force expression 1 Fnew qQ where Eo 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 the two-charged particle system before and after traveling a certain distance as KE1F + KE2F + PEgravf + Uelasticf + Unewf = KE1j + KE2¡ + PEgravi + + Unewi 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 KE1F + + Unewf = + Unewi (Equation 1) For all energies, we know the following

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 Consider a new expression for gravitation potential energy as: PEgray = - , where A is a constant, m1 and m2 are the masses of the two objects, andr r is the distance between them. Moreover, the new particle has an additional interaction with the heavy particle through the following force expression 1 Fnew qQ where Eo 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 the two-charged particle system before and after traveling a certain distance as KE1F + KE2F + PEgravf + Uelasticf + Unewf = KE1j + KE2¡ + PEgravi + + Unewi 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 KE1F + + Unewf = + Unewi (Equation 1) For all energies, we know the following

College Physics
College Physics
1st Edition
ISBN:9781938168000
Author:Paul Peter Urone, Roger Hinrichs
Publisher:Paul Peter Urone, Roger Hinrichs
Chapter8: Linear Momentum And Collisions
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Problem 35PE: Professional Application Two manned satellites approaching one another, at a relative speed of 0.250...
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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? Amım2 Consider a new expression for gravitation potential energy as: PEgrav where A is a constant, m1 and m2 are the masses of the two objects, and r r is the distance between them. Moreover, the new particle has an additional interaction with the heavy particle through the following force expression Ob 4TTE, p2 1 Fnew where Eo 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 as KE1F + KE2F + PEgravf + Velasticf + Unewf = KE1j + KE2i + PEgravi + + Unewi 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 KE1 + Unewf + + + + + Unewi (Equation 1) + For all energies, we know the following KE mv² 2 Am¡m2 PEgrav r 1 U elastic = kx? kx² Unew = (1/ /(r
Transcribed Image Text: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? Amım2 Consider a new expression for gravitation potential energy as: PEgrav where A is a constant, m1 and m2 are the masses of the two objects, and r r is the distance between them. Moreover, the new particle has an additional interaction with the heavy particle through the following force expression Ob 4TTE, p2 1 Fnew where Eo 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 as KE1F + KE2F + PEgravf + Velasticf + Unewf = KE1j + KE2i + PEgravi + + Unewi 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 KE1 + Unewf + + + + + Unewi (Equation 1) + For all energies, we know the following KE mv² 2 Am¡m2 PEgrav r 1 U elastic = kx? kx² Unew = (1/ /(r
where in we have m1 = m, m2 = M, q1 = q and q2 = Q %3D %3D By substituting all these to Equation 1 and then simplifying results to sqrt( 2 + ( ( m ) - V %D V ) - (1/x ) ) + Take note that capital letters have different meaning than small letter variables/constants.
Transcribed Image Text:where in we have m1 = m, m2 = M, q1 = q and q2 = Q %3D %3D By substituting all these to Equation 1 and then simplifying results to sqrt( 2 + ( ( m ) - V %D V ) - (1/x ) ) + Take note that capital letters have different meaning than small letter variables/constants.
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