An electron is a subatomic particle (m = 9.11 x 10-31 kg) that is subject to electric forces. An electron moving in the +x direction accelerates from an initial velocity of +5.08 x 105 m/s to a final velocity of 2.63 x 106 m/s while traveling a distance of 0.0895 m. The electron's acceleration is due to two electric forces parallel to the x axis: = 8.35 x 10-17 N, and , which points in the -x direction. Find the magnitudes of (a) the net force acting on the electron and (b) the electric force

To find the magnitudes of the net force acting on the electron and the electric force, we need to use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.

(a) The net force acting on the electron can be found using the equation:
net force = mass x acceleration

Given:
mass of the electron (m) = 9.11 x 10^(-31) kg
initial velocity (v1) = +5.08 x 10^5 m/s
final velocity (v2) = 2.63 x 10^6 m/s
distance traveled (d) = 0.0895 m

First, we need to find the acceleration (a) of the electron. We can use the following equation of motion:

v2^2 = v1^2 + 2ad

Rearranging the equation, we have:

a = (v2^2 - v1^2) / (2d)

Substituting the given values, we can calculate the acceleration:

a = ((2.63 x 10^6 m/s)^2 - (5.08 x 10^5 m/s)^2) / (2 x 0.0895 m)

Once we have the acceleration, we can now calculate the net force acting on the electron:

net force = mass x acceleration

Substituting the mass and acceleration:

net force = (9.11 x 10^(-31) kg) x (acceleration)

(b) To find the magnitude of the electric force, we need to consider that the net force acting on the electron is the sum of the two electric forces acting in opposite directions:

net force = - F1 + F2

Substituting the given values of F1 and F2, we get:

net force = (8.35 x 10^(-17) N) + (electric force)

Rearranging the equation, we can find the magnitude of the electric force:

electric force = net force - (8.35 x 10^(-17) N)

By using the values of the net force calculated in part (a), you can find the magnitude of the electric force.