An electron is a subatomic particle (m = 9.11 10-31 kg) that is subject to electric forces. An electron moving in the +x direction accelerates from an initial velocity of +5.06 105 m/s to a final velocity of +2.03 106 m/s while traveling a distance of 0.034 m. The electron's acceleration is due to two electric forces parallel to the x axis: vector F 1 = +6.89 10-17 N, and vector F 2, which points in the -x direction. Find the magnitudes of the net force acting on the electron and the electric force vector F 2.

To find the magnitudes of the net force acting on the electron and the electric force vector F2, we need to use Newton's second law of motion.

Newton's second law states that the net force acting on an object is equal to the product of its mass and acceleration:

F_net = m * a

In this case, the electron's mass (m) is given as 9.11 x 10^-31 kg. The acceleration (a) can be found using the initial and final velocities and the distance traveled.

1. Calculate the acceleration of the electron:
The average acceleration (a_avg) can be calculated using the formula:

a_avg = (v_f - v_i) / t

Since the distance (d) traveled by the electron is given as 0.034 m, and the initial velocity (v_i) is 5.06 x 10^5 m/s, we can rearrange the formula to solve for the final velocity (v_f).

d = v_i * t + (1/2) * a_avg * t^2

0.034 = (5.06 x 10^5) * t + (1/2) * a_avg * t^2

To simplify the calculation, we can neglect the second term because it is small compared to the first term. Solving for t:

t = d / v_i

Substituting the given values:

t = 0.034 m / (5.06 x 10^5 m/s)

Calculate t to find the average acceleration.

2. Calculate the net force:
Using the acceleration (a) calculated in step 1 and the given mass (m), we can substitute these values into Newton's second law to find the net force acting on the electron:

F_net = m * a

Substitute the values to find the net force.

3. Calculate the electric force vector F2:
Since F_net is the sum of F1 and F2, we can find F2 by subtracting F1 from F_net:

F_net = F1 + F2

Rearrange the equation to solve for F2.

4. Calculate the magnitudes of the net force and F2:
Determine the magnitudes of F_net and F2 by taking the absolute values of the respective forces.

Now, you have the steps to find the magnitudes of the net force acting on the electron and the electric force vector F2. Start by calculating the acceleration of the electron, then use that value to find the net force and F2.