Calculating the Distance Fallen by an Electron Beam

In summary, the electron beam in a TV set has a horizontal velocity of 2.5 x 107 and travels 40 cm before hitting the screen. By using the equations x = voxt and vy = voy - gt, the time it takes for the electron beam to reach the screen was found to be 1.6 x 10-9 seconds. However, an error was made in the calculation of vy, resulting in a negative value. After correcting the error and solving for time again, the electron beam was found to fall a distance of 1.568 x 10-8 meters while traversing the 40 cm distance.
  • #1
Warmacblu
103
0

Homework Statement



In a TV set, an electron beam moves with horizontal velocity of 2.5 x 107 across the cathode ray tube and strikes the screen, 40 cm away.

The acceleration of gravity is 9.8 m/s2.

How far does the electron beam fall while traversing this distance? Answer in units of m.

Homework Equations



x = voxt

vy = voy - gt

The Attempt at a Solution



I solved for t:

x = voxt

.04 = 2.5 x 107
t = 1.6 x 10-9

Then I plugged t into vy = voy - gt.

vy = 0 - (9.8)(1.6x10-9)
vy = -1.568x10-8

Now I am not sure if I have the correct values plugged in because I do not think I am supposed to come up with a negative answer. I did draw a picture but am not sure if my math corresponds to the picture.

Any suggestions are appreciated,
Thanks.
 
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  • #2
vy = voy - gt
Check this formula.
If vy and g are in the same direction, they must have the same sigh.
 
  • #3
rl.bhat said:
vy = voy - gt
Check this formula.
If vy and g are in the same direction, they must have the same sigh.

Thanks for the quick reply. I will think about it while I sleep and report back tomorrow morning.
 
  • #4
I figured out my mistake. I divided the 40 cm distance by 1000 instead of 100 which gave me the incorrect time. I solved for time again and plugged that into y = 1/2gt^2 which gave me the correct answer.
 

What is an electron beam?

An electron beam is a stream of electrons that are accelerated through an electric field. It is commonly used in various scientific and technological applications, such as in electron microscopes and particle accelerators.

How is the distance fallen by an electron beam calculated?

The distance fallen by an electron beam is calculated using the formula d = 1/2 * a * t^2, where d is the distance, a is the acceleration of gravity (9.8 m/s^2), and t is the time the electron beam has fallen. This formula is derived from the equations of motion.

What factors can affect the distance fallen by an electron beam?

The main factor that affects the distance fallen by an electron beam is the acceleration of gravity, which is a constant value on Earth. However, other factors such as air resistance and the initial velocity of the electron beam can also have an impact on the distance fallen.

Why is calculating the distance fallen by an electron beam important?

Calculating the distance fallen by an electron beam is important in understanding the behavior of electrons in a vacuum and in various scientific experiments. It also helps in designing and optimizing devices that use electron beams, such as cathode ray tubes and electron microscopes.

Can the distance fallen by an electron beam be altered?

Yes, the distance fallen by an electron beam can be altered by changing the initial velocity of the beam or by adjusting the acceleration of gravity. Additionally, the distance can also be affected by external factors such as the presence of a magnetic field or the properties of the vacuum in which the electron beam is travelling.

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