Question

In a cathode ray tube in an old TV, electrons are acceler-ated from rest with a constant acceleration of magnitude 7.03 × 10 13 m/s 2 during the first 2.0 cm of the tube’s length; then they move at essentially constant velocity another 45 cm before hitting the screen. (a) 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?

Answer 1

First, let's ignore relativistic effects.

a) Now let's use this kinematics equation for the motion of the electrons:

Vf² = Vi² + 2ad

Vf is the final velocity, Vi is the initial velocity, a is the acceleration, and d is the distance covered.

Given values:

Vi = 0m/s

a = 7.03×10¹³m/s²

d = 2.0×10⁻²m

Plug in these values and solve for Vf:

Vf² = 2(7.03×10¹³)(2.0×10⁻²)

Vf = 1.677×10⁶m/s

Round to 2 significant figures:

Vf = 1.7×10⁶m/s

b) For motion under constant velocity, let's use this equation:

d = vΔt

d is the distance covered, v is the velocity, and Δt is the elapsed time.

Given values:

d = 45×10⁻²m

v = 1.677×10⁶m/s

Plug in these values and solve for Δt:

45×10⁻² = 1.677×10⁶Δt

Δt = 2.7×10⁻⁷s