THERE ARE A TON OF WORDS TO THIS WORD PROBLEM AND IT BREAKS IT DOWN INTO SIX STE

Question

THERE ARE A TON OF WORDS TO THIS WORD PROBLEM AND IT BREAKS IT DOWN INTO SIX STEPS...HOWEVER, PARTS B -F SEEM VERY SIMPLE ANSWERS. I'M JUST STUCK.

A small charged sphere of radius R1, mass m1, and positive charge q1 is shot head on with speed v1 from a long distance away toward a second small sphere having radius R2, mass m2, and positive charge q2. The second sphere is held in a fixed location and cannot move. The spheres repel each other, so sphere 1 will slow as it approaches sphere 2. If v1 is small, sphere 1 will reach a closest point, reverse direction, and be pushed away by sphere 2. If v1 is large, sphere 1 will crash into sphere 2. For what speed v1 does sphere 1 just barely touch sphere 2 as it reverses direction?

Part A) Begin by drawing a before-and-after visual overview. Initially, the spheres are far apart and sphere 1 is heading toward sphere 2 with speed v1. The problem ends with spheres touching. What is speed of sphere 1 at this instant? How far apart are the centers of the spheres at this instant? How far apart are the centers of the spheres at this instant? Label the before and after pictures with complete information--all in symbolic form.

Part B) Energy is conserved. First we have to identify the "moving charge" q and the "source charge" that creates the potential. Which is the moving charge and which is the source charge?

Part C) We're told the charges start "a long distance away" from each other. Based on this statement, what value can you assign to Vi, the potential of the source charge and the initial position of the moving charge? Explain.

Part D) Now write an expression in terms of the symbols defined above (and any constants that are needed) for the initial energy Ki + qVi          Ki + qVi = ___________________

Part E) Referring to the information on your visual overview, write an expression for the final energy.

Kf + qVf = __________________________

Part F) Energy is conserved, so finish the problem by solving for v1

Explanation / Answer

V = k Q/D this is the electric potential of the large sphere at distance D the initial potential is zero since D is very large W = V q the work required to move small sphere within distance D W = KE = 1/2 m v^2 initial KE = final potential energy 1/2 m v^2 = V q = k Q q / R solve this for v to get the speed required to bring the small sphere to D = R The total energy of the small sphere at any time is E = 1/2 m V^2 + k Q q / D where V is the speed of the small sphere when it is at distance D from the large sphere. (Initially the total energy is 1/2 m v^2 and at distance R the total energy is k q Q / R since V (speed) = 0 if it just reaches the large sphere) (Note: I have used V in two different ways here - once as the electric potential and once as the speed of the small sphere at some intermediate point)

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