In a cathode ray tube, electrons initially at rest are accelerated by a uniform electric field of magnitude 4.71 x 105 N/C during the first 5.49 cm of the tube's length; then they move at essentially constant velocity another 47.9 cm before hitting the screen. Find the speed of the electrons when they hit the screen

Question

In a cathode ray tube, electrons initially at rest are accelerated by a uniform electric field of magnitude 4.71 x 105 N/C during the first 5.49 cm of the tube's length; then they move at essentially constant velocity another 47.9 cm before hitting the screen. Find the speed of the electrons when they hit the screen

How long does it take them to travel the length of the tube?

Answer 1

1/2 m v^2= Eqd solve for v.

then, find the time to move .05 (d) at V/2 (avg velocity during acceleration), and the time to move .479 at V.
add the times.

Answer 2

To find the speed of the electrons when they hit the screen, we can use the acceleration formula:

acceleration = change in velocity / time

Given that the electrons are initially at rest and are accelerated by a uniform electric field, the initial velocity is 0 m/s. We can assume that the acceleration remains constant during the first 5.49 cm, so we will use the time it takes to travel that distance to calculate the acceleration.

First, let's convert 5.49 cm to meters:
5.49 cm = 5.49 / 100 = 0.0549 m

We also know the magnitude of the uniform electric field is 4.71 x 10^5 N/C.

Now, we can use the acceleration formula to find the acceleration:
acceleration = change in velocity / time
4.71 x 10^5 N/C = v / 0.0549 m

Rearranging the formula to solve for the change in velocity, we get:
change in velocity = acceleration × time
change in velocity = 4.71 x 10^5 N/C × 0.0549 m

Next, we need to find the time it takes for the electrons to travel the entire length of the tube, which is 5.49 cm + 47.9 cm.

The total length of the tube is:
5.49 cm + 47.9 cm = 53.39 cm

Converting this to meters, we get:
53.39 cm = 53.39 / 100 = 0.5339 m

To calculate the time needed to travel this distance, we can use the formula:

time = distance / velocity

And since we already know the acceleration, we can use it to find the velocity.

Finally, we can substitute the value of the acceleration into the velocity formula and solve for speed.

Once we have obtained the speed, we can divide the distance traveled (0.5339 m) by the speed to find the time it takes to travel the length of the tube.