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. What is the lighter particle's speed when it is xf away from the heavy particle? Consider a new expression for gravitation potential energy as: PEgrav = -(A (m1m2)) /r where A is a constant, m1 and m2 are the masses of the two objects, and r is the distance between them.   To avoid the complexity of vector solution 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.   KE1f + KE2f + PEgravf + Uelasticf + Unewf = KE1i + KE2i + PEgravi +  + Unewi   Note that 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.

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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 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. What is the lighter particle's speed when it is xf away from the heavy particle?

Consider a new expression for gravitation potential energy as:

PEgrav = -(A (m1m2)) /r

where A is a constant, m1 and m2 are the masses of the two objects, and r is the distance between them.

 

To avoid the complexity of vector solution 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.

 

KE1f + KE2f + PEgrav+ Uelasticf + Unewf = KE1i + KE2i + PEgravi +  + Unewi

 

Note that 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. 

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