An electron is accelerated by a uniform electric field (1000 V/m) pointing vertically upward. use newton's laws to determine the electron's velocity after it moves .10 cm
To determine the electron's velocity after it moves a distance of 0.10 cm (or 0.001 m) under the influence of a uniform electric field, we need to use Newton's laws of motion. Here's how you can approach the problem:
1. Convert the distance from centimeters to meters:
0.10 cm = 0.001 m
2. Identify the relevant forces acting on the electron:
Since the electron is accelerated by a uniform electric field, the only force acting on it is the electric force (F = qE), where q is the charge of the electron and E is the electric field strength.
3. Determine the acceleration of the electron:
The acceleration of an object is given by Newton's second law of motion (F = ma).
Therefore, the acceleration of the electron (a) is equal to F (electric force) divided by the mass of the electron (m).
4. Calculate the electric force:
The electric force on the electron is equal to the product of its charge (e) and the electric field strength (E).
F = qE = eE
5. Determine the mass of the electron:
The mass of an electron is a well-known value, approximately equal to 9.11 x 10^-31 kilograms (kg).
6. Substitute the values into the equation for acceleration:
a = F/m = (eE)/m
7. Calculate the acceleration:
Substitute the known values for e, E, and m into the acceleration equation to find the acceleration of the electron.
8. Use the kinematic equation to determine the final velocity:
Since the electron's initial velocity is not given, we can assume it started from rest (u = 0). The kinematic equation for calculating final velocity (v) given an initial velocity (u), acceleration (a), and displacement (s) is:
v^2 = u^2 + 2as
Rearranging the equation to solve for v:
v = √(u^2 + 2as)
Substitute the known values for u, a, and s, and calculate the final velocity of the electron.
By following these steps, you should be able to determine the velocity of the electron after it moves a distance of 0.10 cm under the influence of the uniform electric field.
To determine the electron's velocity after it moves a distance of 0.10 cm in an upward-pointing uniform electric field, we will use Newton's second law of motion and the equation of motion for constant acceleration.
Newton's second law of motion states that the force acting on an object is equal to the mass of the object multiplied by its acceleration:
F = m * a
In this case, the force acting on the electron is due to the electric field and can be calculated using the equation:
F = q * E
where:
F is the force,
q is the charge of the electron (1.6 x 10^-19 C),
E is the electric field strength (1000 V/m).
Since the force is acting vertically upward, the acceleration experienced by the electron will also be in the same direction.
Now, let's calculate the force:
F = (1.6 x 10^-19 C) * (1000 V/m)
F = 1.6 x 10^-16 N
We can now use the equation of motion for constant acceleration:
v^2 = u^2 + 2 * a * s
where:
v is the final velocity,
u is the initial velocity (assumed to be zero since the electron starts from rest),
a is the acceleration,
s is the distance traveled.
Rearranging the equation:
v^2 = 2 * a * s
v = sqrt(2 * a * s)
Now, let's calculate the final velocity:
v = sqrt(2 * (F/m) * s)
v = sqrt(2 * (1.6 x 10^-16 N) / (9.11 x 10^-31 kg) * (0.10 cm)
v ≈ 5.37 x 10^6 m/s
Therefore, the electron's velocity after it moves 0.10 cm in the upward-pointing uniform electric field is approximately 5.37 x 10^6 m/s.