Question

Use the work-energy theorem to find the force required to accelerate an electron (m = 9.11 × 10–31 kg) moving along the x axis from 4.00 × 106 m/s to 1.60 × 107 m/s in a distance of 0.0125 m. a. 8.20 × 10–17 N b. 8.75 × 10–15 N Selected:c. 5.47 × 10–22 NThis answer is incorrect. d. 3.56 × 10–19 N e. 1.64 × 10–14 N

Answer 1

force required to accelerate an electron is b. 8.75 × 10–15 N  

Explanation:

work done = change in K E ........................ work energy theorem

change in kinetic energy ΔKE = 1/2 m ( V² final - V² initial )

initial velocity = 4.00 × 10⁶m/s

final velocity = 1.60 × 10⁷ m/s

ΔKE = 0.5 * 9.11 * 10⁻³¹ * (   ( 1.60 × 10⁷ ) ² - ( 4.00 × 10⁶) ²  )

      = 1093.2* 10 ⁻¹⁹ j

so work done = 1093.2* 10 ⁻¹⁹ j

work done = force * displacement

force = work done /displacement

        = 1093.2* 10 ⁻¹⁹  / 0.0125

         = 87456  * 10 ⁻¹⁹

         = 8.75 * 10 ⁻¹⁵ N