# Homework Help: Hibbeler 13-34

1. Mar 2, 2014

### c0der

1. The problem statement, all variables and given/known data

In the cathode-ray tube, electrons having a mass m
are emitted from a source point S and begin to travel
horizontally with an initial velocity v0. While passing
between the grid plates a distance l, they are subjected to a
vertical force having a magnitude eV/w, where e is the
charge of an electron, V the applied voltage acting across
the plates, and w the distance between the plates. After
passing clear of the plates, the electrons then travel in
straight lines and strike the screen at A. Determine the
deflection d of the electrons in terms of the dimensions of
the voltage plate and tube. Neglect gravity which causes a
slight vertical deflection when the electron travels from S to
the screen, and the slight deflection between the plates.

See attachment for picture

2. Relevant equations

∑Fy = may

vy = ayt

3. The attempt at a solution

By Newton's 2nd Law,

ay = eV/mw from 0 to l

By kinematics t1 = l/v0
t2 = t1 + L/v0 = l/v0 + L/v0

From 0 to l, by kinematics:

y1 = 1/2*eV/mw*(l/v0^2)
(v1)y = eV/mw*l/v0

Hence, from l to L where ay is zero

y2 = d = 1/2*eV/mw*l^2/v0^2 + eV/mw*L/v0

It appears the solution is missing the left term I keep getting, any idea why?

#### Attached Files:

• ###### Hibbeler 13-34.png
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Last edited: Mar 2, 2014
2. Mar 2, 2014

### Redbelly98

Staff Emeritus
The solution is missing that term because they are neglecting the slight deflection between the plates, as mentioned at the end of the problem statement.