Question

In an x-ray tube, an electron with mass 9.1x10^-31 kg moves with a velocity of 9.8x10^6 m/s. It hits the metal target and rebounds with a speed of 7.5x10^4 m/s after 5.0x10^-6 s. Determine:

A) The initial and final momentum of the electron
B) The impulse
C) The average force, F

Answer 1

The initial momentum of the electron is 8.918 x 10^-24 kg m/s and the final momentum is 6.825 x 10^-26 kg m/s. The impulse is -8.835 x 10^-24 kg m/s and the average force is -1.767 x 10^-18 N.

Step-by-step explanation:

A) Initial and final momentum of the electron:

The initial momentum of the electron can be calculated using the formula:

Pi = mass * velocity

Pi = (9.1 x 10^-31 kg) * (9.8 x 10^6 m/s) = 8.918 x 10^-24 kg m/s

The final momentum of the electron can be calculated using the same formula:

Pf = mass * velocity

Pf = (9.1 x 10^-31 kg) * (7.5 x 10^4 m/s) = 6.825 x 10^-26 kg m/s

B) The impulse:

The impulse can be calculated using the formula:

I = Pf - Pi

I = (6.825 x 10^-26 kg m/s) - (8.918 x 10^-24 kg m/s) = -8.835 x 10^-24 kg m/s

C) The average force:

The average force can be calculated using the formula:

F = I / t

Given that the time is 5.0 x 10^-6 s, the average force is:

F = (-8.835 x 10^-24 kg m/s) / (5.0 x 10^-6 s) = -1.767 x 10^-18 N