Question

An electron (mass = 9.11 X 10^-31 kg) leaves one end of a TV picture tube with zero initial speed and travels in a straight line to the accelerating grid, which is 1.80 cm away. It reaches the grid with a speed of 3.00 X 10^6 m/s. If the accelerating force is constant, compute (a) the acceleration(b) the time to reach the grid(c) the net force, in newtons. (You can ignore the gravitational force on the electron.)

Answer 1

Answer: a) 2.5 * 10^14, b) t = 1.2*10^-8 s, c) F = 2.2775 * 10^-15 N

Explanation: Since it starts from rest, initial velocity = 0, final velocity (v) = 3*10^6 m/s, distance covered (s) = 1.80cm = 1.80/100 = 0.018m

Since the force on the electron is constant, it acceleration will be constant too thus making newton's laws of motion valid.

Question a)

To get the acceleration, we use the formulae that

v² = u² + 2as

But u = 0

v² = 2as

(3*10^6)² = 2*a*(0.018)

9* 10^12 = 0.036*a

a = 9 * 10^12 / 0.036

a = 250 * 10^12

a = 2.5 * 10^14 m/s².

Question b)

To get the time, we use

v = u + at

But u = 0

v = at

3*10^6 = 2.5 * 10^14 * t

t = 3*10^6 / 2.5*10^14

t = 1.2*10^-8 s

Question c)

To get the force, we use the formulae below

F = ma

F = 9.11*10^-31 * 2.5 * 10^14

F = 22.775 * 10^-17

F = 2.2775 * 10^-15 N