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 +7.62 x 105 m/s to a final velocity of 2.56 x 106 m/s while traveling a distance of 0.0778 m. The electron's acceleration is due to two electric forces parallel to the x axis: = 7.80 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 can 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 by multiplying the mass of the electron by its acceleration. The acceleration can be determined using the final velocity, initial velocity, and the distance traveled. We can use the following equation:
Final velocity squared (vf^2) = Initial velocity squared (vi^2) + 2 * acceleration (a) * distance (d)
Rearranging the equation to solve for the acceleration (a), we have:
a = (vf^2 - vi^2) / (2 * d)
Plugging in the values:
a = [(2.56 x 10^6 m/s)^2 - (7.62 x 10^5 m/s)^2] / (2 * 0.0778 m)
Calculating the acceleration using a calculator, we get:
a ≈ 1.23 x 10^14 m/s^2
Now, we can find the net force by multiplying the mass of the electron by the acceleration:
Net force (Fnet) = mass (m) * acceleration (a)
Fnet = (9.11 x 10^-31 kg) * (1.23 x 10^14 m/s^2)
Calculating the net force using a calculator, we get:
Fnet ≈ 1.12 x 10^-16 N
Therefore, the magnitude of the net force acting on the electron is approximately 1.12 x 10^-16 N.
(b) To find the magnitude of the electric force , we need to consider the fact that the net force acting on the electron is the vector sum of the electric forces and . These forces have opposite directions, so we can subtract their magnitudes to find the net force using the equation:
Fnet = -
Since the net force is already known from part (a) to be approximately 1.12 x 10^-16 N, we can rearrange the equation to solve for :
= - Fnet
= - (1.12 x 10^-16 N)
Plugging in the values:
= - 7.80 x 10^-17 N
Calculating the electric force using a calculator, we get:
≈ 7.04 x 10^-17 N
Therefore, the magnitude of the electric force is approximately 7.04 x 10^-17 N.