The electrons that produce the picture in a TV set are accelerated by a very large electric force as they pass through a small region in the neck of the picture tube. This region is
1.4 cm in length, and the electrons enter with a speed of 1× 105 m/s and leave with a speed of 1.5 × 108 m/s.
a. What is their acceleration over this 1.4 cm length? Answer in units of m/s2.
b. How long is the electron in the accelerating region? Answer in units of s.
Tip: Write down the values you have and are looking for:
s=1.4cm
v=1*105m/s
u=1.5*108m/s
You must use an equation like s=v-ut/2, in order to find the time.
Isolate the t.
a. Why did the electron cross the road? To accelerate, of course!
To calculate the acceleration, we can use the formula:
acceleration = (change in velocity) / (change in time)
The change in velocity is the final velocity minus the initial velocity:
change in velocity = (1.5 × 10^8 m/s) - (1 × 10^5 m/s) = 1.499 × 10^8 m/s
Now, we need to convert the length from centimeters to meters:
length = 1.4 cm = 0.014 m
We can rearrange the formula to solve for the acceleration:
acceleration = (change in velocity) / (length)
acceleration = (1.499 × 10^8 m/s) / (0.014 m) ≈ 1.07 × 10^10 m/s^2
So, the acceleration of the electrons over this 1.4 cm length is approximately 1.07 × 10^10 m/s^2.
b. How long is the electron in the accelerating region? Well, it seems like the electron has a quicker exit strategy than most! To find out how long it stays in the region, we can use the formula:
time = (length) / (speed)
time = (0.014 m) / (1.5 × 10^8 m/s) ≈ 9.33 × 10^-11 s
Therefore, the electron stays in the accelerating region for approximately 9.33 × 10^-11 seconds.
To find the acceleration of the electrons, we can use the formula:
acceleration = (change in velocity) / (time taken)
To find the change in velocity, we subtract the initial velocity from the final velocity:
change in velocity = final velocity - initial velocity
Given:
Initial velocity, u = 1 × 10^5 m/s
Final velocity, v = 1.5 × 10^8 m/s
Length, s = 1.4 cm = 0.014 m (converted to meters)
a. To find the acceleration, we use the formula:
acceleration = (final velocity - initial velocity) / (time taken)
Since the length is given and we need to find the time taken, we can rearrange the formula to solve for time:
time taken = length / (final velocity - initial velocity)
Substituting the given values:
time taken = 0.014 m / (1.5 × 10^8 m/s - 1 × 10^5 m/s)
Calculating the time taken:
time taken ≈ 9.34 × 10^-11 s
Now that we have the time taken, we can calculate the acceleration:
acceleration = (final velocity - initial velocity) / (time taken)
acceleration = (1.5 × 10^8 m/s - 1 × 10^5 m/s) / (9.34 × 10^-11 s)
Calculating the acceleration:
acceleration ≈ 1.424 × 10^17 m/s^2
Therefore, the acceleration of the electrons over the 1.4 cm length is approximately 1.424 × 10^17 m/s^2.
b. To find the time it takes for the electron to pass through the accelerating region, we already calculated the time taken as 9.34 × 10^-11 s.
Therefore, the electron is in the accelerating region for approximately 9.34 × 10^-11 seconds.
i did not understand that! I NEED HELP!
BE CAREFUL OF UNITS
The neck length is in cm!
For a constant acceleration:
s = distance
v1 = initial velocity
v2 = final velocity
a = acceleration
t = time
s = (v1)(t) + (1/2)(a)(t^2)
s and v1 are given
v2 = v1 + (a)(t)
so (a)(t) = v2 - v1
v1 and v2 are given
substitute for (a)(t) in the first equation to solve for time.
acceleration = dv/dt = (v2 - v1)/t