Newtons Laws-Force with respect to time

[mikee]

Homework Statement

An electron is oriented between two charged plates (oriented vertically). The electron experiences a constant force perpendicular to the plates. It has a mass of 9.0 x 10^-31 kg, is moving vertically with a velocity of 2.0 x 10^6m/s and enters the region between the two plates. The region has a height of 1cm and while in it the electron experiences a force of 3.0 x 10^-18N. How long does the electron stay in the region, and what is the horizontal component of velocity as soon as the electron passes through the region

Homework Equations

The Attempt at a Solution

Ok here's how i started it, i figured out the acceleration of the particle by F= ma , a= 3.0 x 10^-18/9.0 x 10^-31 and therefore now that i have the acceleration and the x which = 0.001m i can use those to figure out the time and the velocity, so i figured out the velocity by using the equation Vo^2 + 2(a)(d)= V^2
and i used 2.6 x 10^6 for Vo^2 and solved for V and once i found that i used V to solve for the time and i used V= a(t) + Vo is this method correct or am i totally off, would i have to incorporate gravity into it, and also since it says the force is perpendicular to the plates would i have to take the force in the x direction instead of the y direction like i did and if so is it going left or right, those are some details i just wasnt to sure on, if anyone could help thanks alot

 

[nasu]

The electron is moving upward initially (let's call this y direction).
The acceleration is horizontal (x direction).
1 cm is the height of the plates. There is no acceleration along this direction.
The motion has two components:
- uniform motion along y, with given speed
- accelerated motion along x, with zero initial velocity

 

[baba89]

Your approach is correct. Since the electron is experiencing a constant force perpendicular to the plates, we can ignore the force in the x direction and focus on the motion in the y direction. The force of 3.0 x 10^-18N is the net force acting on the electron, which is equal to the mass (9.0 x 10^-31 kg) multiplied by the acceleration. So, using the equation F=ma, we can find the acceleration to be 3.3 x 10^13 m/s^2.

Next, we can use the equation v^2 = u^2 + 2as to find the final velocity of the electron after it has passed through the region between the plates. We know the initial velocity (2.0 x 10^6 m/s) and the acceleration (3.3 x 10^13 m/s^2), so we can solve for the final velocity to be 2.0 x 10^6 m/s.

To find the time the electron stays in the region, we can use the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. Plugging in our values, we get t = (2.0 x 10^6 m/s - 2.0 x 10^6 m/s) / (3.3 x 10^13 m/s^2) = 0 seconds. This means that the electron passes through the region instantaneously and does not stay in the region at all.

As for the horizontal component of velocity, since the force is perpendicular to the plates, there is no change in the horizontal component of velocity. The electron will continue to move with a horizontal velocity of 2.0 x 10^6 m/s after passing through the region between the plates.