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 +5.31 * 10^5 m/s to a final velocity of +2.21 * 10^6 m/s while traveling a distance of 0.040 m. The electron's acceleration is due to two electric forces parallel to the x axis: 1 = +6.75 * 10^-17 N, and 2, which points in the -x direction. Find the magnitudes of the net force acting on the electron and the electric force 2.
I have been trying to do this problem for close to an hour and still cannot make any headway on it. Can someone please show me the steps to solving this problem? Thank you so much!
First of all,calculate acceleration.then use the acceleration the net force.then subtract the net force from F1.
A sailboat race course consists of four legs, defined by the displacement vectors , , , and , as the drawing indicates. The magnitudes of the first three vectors are A = 3.60 km, B = 5.30 km, and C = 4.70 km.
To solve this problem, we need to use Newton's second law of motion which states that the net force acting on an object is equal to its mass multiplied by its acceleration (F_net = m * a).
Step 1: Find the acceleration of the electron.
The initial velocity is given as +5.31 * 10^5 m/s, and the final velocity is given as +2.21 * 10^6 m/s. The distance traveled is 0.040 m. We can use the equation of motion to find the acceleration (a):
v^2 = u^2 + 2as
Here, v is the final velocity, u is the initial velocity, a is the acceleration, and s is the distance traveled. Rearranging the equation, we have:
a = (v^2 - u^2) / (2s)
Substituting the given values:
a = ((2.21 * 10^6)^2 - (5.31 * 10^5)^2) / (2 * 0.040)
a ≈ 1.92 * 10^14 m/s^2
Step 2: Calculate the net force.
We can now use Newton's second law to find the net force acting on the electron. The mass of the electron (m) is given as 9.11 * 10^-31 kg. Substituting the values into the formula:
F_net = m * a
F_net = (9.11 * 10^-31) * (1.92 * 10^14)
F_net ≈ 1.75 * 10^-16 N
The magnitude of the net force acting on the electron is approximately 1.75 * 10^-16 N.
Step 3: Find the magnitude of electric force 2.
To find the magnitude of electric force 2 (F2), we need to consider that F_net is the vector sum of F1 and F2. Since F2 acts in the opposite direction to the x-axis, it will have a negative sign. Therefore, we have:
F_net = F1 - F2
Substituting the known value of F1 (+6.75 * 10^-17 N), we can rearrange the equation to solve for F2:
F2 = F1 - F_net
F2 = +6.75 * 10^-17 - (+1.75 * 10^-16)
F2 ≈ -1.07 * 10^-16 N
The magnitude of electric force 2 is approximately 1.07 * 10^-16 N.
Note: The negative sign indicates that the force is in the opposite direction to the positive x-axis.