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 find the speed of the electrons when they hit the screen, we can use the concept of work and energy. Since the electric force is constant, we can assume that it does work on the electrons.
(a) First, let's find the work done by the electric force on the electrons during the first 2.2 cm of the tube's length. We can use the formula for work:
Work (W) = Force (F) * Distance (d) * cos(theta)
In this case, theta is the angle between the force and the direction of displacement, which is 0 degrees since the force is in the same direction as the displacement.
From the problem, we know:
Force (F) = 6.2 * 10^-17 N
Distance (d) = 2.2 cm = 0.022 m
Plugging these values into the formula, we get:
W = (6.2 * 10^-17 N) * (0.022 m) * cos(0) = 1.364 × 10^-18 J
The work done by the electric force is equal to the change in kinetic energy of the electrons. So, we can equate the work to the kinetic energy:
1/2 * mass * velocity^2 = 1.364 × 10^-18 J
To find the velocity, we need to know the mass of the electrons. Typically, the mass of an electron is around 9.11 × 10^-31 kg. However, the problem does not mention the mass explicitly. If the mass is not given, we can't calculate the speed accurately.
(b) To find how long it takes for the electrons to travel the length of the tube, we can use the concept of velocity:
Velocity (v) = Distance (d) / Time (t)
We know:
Distance (d) = 43 cm = 0.43 m
Velocity (v) = constant velocity (since the electrons move at essentially constant velocity)
Rearranging the formula, we get:
Time (t) = Distance (d) / Velocity (v) = 0.43 m / constant velocity
Since the problem states that the electrons move at a constant velocity, we can calculate the time it takes for the electrons to travel the length of the tube by dividing the 43 cm by the constant velocity. However, without knowing the exact constant velocity, we cannot determine the time accurately.