Please Solve This Physics Problem

Question

An electron and a proton, each starting from rest, are accelerated by the same uniform electric field of 190 N/C. Determine the distance d (in m) and time t (in s) for each particle to acquire a kinetic energy of 1.9 ✕ 10⁻¹⁶ J.

Answer 1

Mass of electron Me = 9.10 x 10^-31 kg

Mass of proton Mp = 1.67 x 10^-27 kg

Charge of both electron and proton Q = 1.60 x 10^-19 C

Force on both proton and electron = 190 n/C x 1.60 x 10^-19 C = 3.0 x 10^-17 N

Final velocity of electron Ve = Sq. Root (2 x KE/ Me) = √(2 x 1.9 x 10^-16 / Me ) = 2.04 x 10^7 m/s

 Final velocity of proton Vp = Sq. Root (2 x KE/ Mp) = √( 2 x 1.9 x 10^-16 / 1.67 x 10^-27) = 4.77 x 10^5 m/s

Work done by field on electron We = F x D = KE, so De = KE / F = 1.9 x 10^-16 / 3.0 x 10^-17 =

6.3 meters (D is distance)

Work done by field on proton Wp = F x d = KE, so Dp = KE / 1.9 x 10^-16/ 3.0 x 10^-17 =  6.3 meters

Both travel same distance.

Time for electron to travel 6.3 m = 6.3 m / (Ve/2) = 6.3 / (2.04 x 10^7 /2) = 6.2 x 10^-7 s

Time for proton to travel 6.3 m = 6.3 m / ( Vp / 2) = 6.3 / (4.77 x 10^5 /2) = 2.6 x 10^-5 s

Note: Average velocity = final velocity – initial velocity / 2 and initial velocity is zero, so Vavg = Vf/2 Check all math!