Conservation of energy in charge interactions

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MODEL:Check whether there are any dissipative forces that would prevent the mechanical energy from beingconserved.

VISUALIZE:Draw a before-and-after pictorial representation. Define symbols that will be used in the problem,list known values, and identify what you are trying to find.

SOLVE:The mathematical representation is based on the law of conservation of mechanicalenergy:

K_{rm f}+qV_{rm f}=K_{rm i}+qV_{rm i}.

Is the electric potential given in the problem statement? If not, you'll need to use a known potential, such as that of a point charge, orcalculate the potential using the procedure given in Problem-Solving Strategy 29.2.
K_f and K_i are the sums of kinetic energies of all movingparticles.
Some problems may need additional conservation laws, such as conservation of charge or conservation of momentum.
ASSESS:Check that your result has the correct units, is reasonable, and answers thequestion.

ModelThe particles described in this problem interact under the effect of the electric force, which is a conservative force, so the system's mechanicalenergy is conserved.
Learning Goal: To practice Problem-Solving Strategy 29.1 for chargeinteraction problems.

A proton and an alpha particle are momentarily at rest at a distance r from each other. They then begin to move apart. Find the speed of the proton by the time the distance between the proton andthe alpha particle doubles.

Both particles are positively charged. The charge and the mass of the proton are, respectively, e and m. The charge and the mass of the alpha particle are,respectively, 2e and 4m.

Which of the following quantities are unknown?
initial separation of the particles
final separation of the particles
initial speed of the proton
initial speed of the alpha particle
final speed of the proton
final speed of the alpha particle
mass of the proton
mass of the alpha particle
charge of the proton
charge of the alpha particle
Enter the letters of all the correct answers in alphabetical order. Do not use commas. For instance, if A, C, and D are unknowns,enter ACD.

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