In a cathode ray tube, electrons are accelerated from rest by a constant electric force of magnitude 6.2 multiplied by 10-17 N during the first 2.2 cm of the tube's length; then they move at essentially constant velocity another 43 cm before hitting the screen.
(a) Find the speed of the electrons when they hit the screen.
1 Incorrect: Your answer is incorrect. m/s
(b) How long does it take them to travel the length of the tube?
2 Incorrect: Your answer is incorrect. ns
To solve this problem, we can use the equations of motion and the principles of work and energy.
(a) To find the speed of the electrons when they hit the screen, we need to find the initial speed and acceleration during the first 2.2 cm of the tube's length.
Let's use the equation of motion: v^2 = u^2 + 2as
Here, u represents the initial velocity (which is 0 m/s as the electrons start from rest), v represents the final velocity (which we need to find), a represents the acceleration, and s represents the distance.
Given:
Acceleration (a) = 6.2 × 10^-17 N
Distance (s) = 2.2 cm = 0.022 m
Substituting these values into the equation, we get:
v^2 = 0 + 2 * (6.2 × 10^-17) * 0.022
v^2 = 2 * (6.2 × 10^-17) * 0.022
v^2 = 2.744 × 10^-18
v = √(2.744 × 10^-18) = 1.657 × 10^-9 m/s
So, the speed of the electrons when they hit the screen is approximately 1.657 × 10^-9 m/s.
(b) To find the time taken to travel the length of the tube, we can divide the total distance by the constant velocity.
Total distance traveled = 2.2 cm + 43 cm = 45.2 cm = 0.452 m
Time taken = Distance / Velocity
Time taken = 0.452 m / (1.657 × 10^-9 m/s)
Time taken ≈ 2.729 × 10^8 seconds
However, it is worth noting that the question is asking for the answer in "ns" (nanoseconds). To convert the time to nanoseconds, we know that 1 second is equal to 10^9 nanoseconds.
Time taken = 2.729 × 10^8 seconds * 10^9 nanoseconds/second
Time taken ≈ 2.729 × 10^17 nanoseconds
Therefore, the time taken for the electrons to travel the length of the tube is approximately 2.729 × 10^17 nanoseconds.
To find the speed of the electrons when they hit the screen, we can use the concept of work and energy. The work done on an object is equal to the change in its kinetic energy.
(a) To calculate the speed of the electrons, we can use the work-energy theorem:
Work done on the electrons = Change in kinetic energy of the electrons
The work done on the electrons can be found by multiplying the magnitude of the electric force by the distance over which it acts:
Work = Force × Distance
Given:
Electric force = 6.2 × 10^-17 N
Distance = 43 cm = 0.43 m
Work = (6.2 × 10^-17 N) × (0.43 m)
Work ≈ 2.666 × 10^-17 J
The change in kinetic energy can be calculated using the equation:
Change in kinetic energy = 1/2 mv^2 - 0
Where m is the mass of the electrons and v is their final velocity (which we need to find).
Now, using the equation:
Work = Change in kinetic energy
2.666 × 10^-17 J = (1/2)mv^2 - 0
Rearranging the equation:
1/2 mv^2 = 2.666 × 10^-17 J
Simplifying:
mv^2 = 5.332 × 10^-17 J
Since the mass of an electron is very small, we can assume its mass is negligible compared to the magnitude of the electric force. Therefore, we can rewrite the equation as:
v^2 ≈ (5.332 × 10^-17 J) / m
The value of m is not given, so we need information about the mass of the electron to proceed further.