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**Help! Conservation of Energy**

The apparatus to be used is a classic one for measuring q/m for electrons. A photo of the cathode-ray tube together with a simplified graphic are shown below. A filament heated with a 6.3-V AC source "boils" off some electrons. These electrons have very little energy initially. However, some of them enter a uniform electric field between two plates maintained at a constant potential difference of V1. The electrons are accelerated in the field and leave the plates through an aperture at Q. The electrons then enter another electric field between two deflection plates a distance L long and separated by distance d. The plates are maintained at a constant potential difference of V2. Between the plates the electrons follow a parabolic path characteristic of charged particle motion in a uniform electric field.

Homework Statement

The apparatus to be used is a classic one for measuring q/m for electrons. A photo of the cathode-ray tube together with a simplified graphic are shown below. A filament heated with a 6.3-V AC source "boils" off some electrons. These electrons have very little energy initially. However, some of them enter a uniform electric field between two plates maintained at a constant potential difference of V1. The electrons are accelerated in the field and leave the plates through an aperture at Q. The electrons then enter another electric field between two deflection plates a distance L long and separated by distance d. The plates are maintained at a constant potential difference of V2. Between the plates the electrons follow a parabolic path characteristic of charged particle motion in a uniform electric field.

Homework Statement

Begin this problem by determining an equation for the velocity, vo, of electrons as they leave the accelerating plates and enter the deflection plates. This is a conservation of energy problem. Clearly indicate your initial and final states and start with a correct statement for the law of conservation of energy as it applies to this problem. Assume that the electrons have negligible kinetic energy as they enter the region between the accelerating plates at point P. Give your result for vo in terms of V1 and q/m.

## Homework Equations

Initial Energy = Final Energy

U = qV

a = qE/m

## The Attempt at a Solution

I know that initial and final energy are equal so:

1/2mvi^2 + Ui = 1/2mvf^2 + Uf

I replace Ui and Uf with qVi and qVf

solving for initial velocity (v0 or vi) I get

v0 = sqrt (mvf^2 + 2(Ua + Ub) )

I need to get the equation down to terms of V1 and q/m, that's where I'm stumped