Kinematics Electrons In a Cathode Ray Tube

[nycjay222]

A) In a cathode ray tube, electrons are accelerated from rest by a constant electric force of magnitude 6.22 x 10−17 N during the first 2.00 cm of tube's length; then they move at essentially constant velocity another 46.5 cm before hitting the screen. Find the speed of the electrons when they hit the screen.

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

 

[rl.bhat]

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[tomcue]

A) To find the speed of the electrons when they hit the screen, we can use the kinematic equation v^2 = u^2 + 2as, where v is the final velocity, u is the initial velocity (in this case, 0 m/s), a is the acceleration (in this case, the constant electric force), and s is the distance traveled (in this case, 48.5 cm). Plugging in the values, we get v = √(0^2 + 2(6.22 x 10^-17 N)(0.485 m)) = 1.41 x 10^6 m/s. This is a very high speed, which is expected for electrons accelerated by a strong electric force.

B) To find the time it takes for the electrons to travel the length of the tube, we can use the kinematic equation s = ut + 1/2at^2, where s is the distance traveled (48.5 cm), u is the initial velocity (0 m/s), a is the acceleration (6.22 x 10^-17 N), and t is the time. Solving for t, we get t = √(2s/a) = √(2(0.485 m)/(6.22 x 10^-17 N)) = 6.97 x 10^-9 s. This is a very short amount of time, which is expected for electrons traveling at high speeds in a cathode ray tube.