Electric Fields and Protons: Solving for Time, Velocity, and Distance

[Knightycloud]

Homework Statement

Two protons that has a 'm' mass and '+q' charge appears suddenly at the time t=0 as the picture shows. The distance from A to B is 'd₀'. They start there motion from 0 velocity and move towards B.
1. What are the t₁ and t₂ times that are taken by the two masses to get to the plate B?
2. What are the v₁ and v₂ velocities that are taken by the two masses when they get to the plate B?
3. Then they leave the plate B and get to a distance 'S' at the same time. Area BS is field-less. Find 'S' using v₁, v₂, t₁ and t₂

Homework Equations

W = Vq = 1/2mv²
F = Eq
F = ma
E = V/d
S = ut + 1/2at²

The Attempt at a Solution

1. Vq/d<sub>0 = ma
S = 1/2at² → t = $\sqrt{2S/a}$

2. 1/2mv² = Vd1χq/d0</sub>

 

[Simon Bridge]

Just writing down a bunch of equations does not help us to help you - tell us about the physics, tell us about how you arrived at these answers: what was your reasoning?

We can only help you with your understanding - you have to do your homework
Of course, it also helps to ask a question.

From what I can tell, you think there is some acceleration in the region between B and S and that S has something to do with Q1.
I don't know why you used a chi in Q2.
But if you don't talk about it - how do I know what you are thinking?

 

[Knightycloud]

There is no acceleration in that B to S region. Plus I thought "χ" as the multiplication sign :D
Those two masses leave B at the velocities v1 and v2. Never mind that B to S part thingy. Did I get that t1, t2, v1 and v2 parts correctly? :D

 

[Simon Bridge]

Ah, that S in part (1) does not refer to the BS region (which is aptly named btw because it is magically free of any fields :) )

So, you are making me guess your reasoning then? OK...

For part (1) it looks like you are using F=ma, then you want to put that "a" into a kinematic equation? If S is supposed to stand for d_x where x = {1,2} then that one will work.

For part (2) it looks like you are using conservation of energy? Good call - you can also do it from kinematic equations.

I won't fault this approach - but your core problem is that you shouldn't need reassuring. The main reason students get nervous about their work at this stage is because they are applying equations instead of understanding the physics. One way of reassuring yourself is to use some method that helps you visualize things. eg.

You should draw v-t graphs for the entire motion - bearing in mind they start and end at the same time, and have the same acceleration in the first stage, but q2 accelerates for a shorter time.

Use the displacement = area and acceleration = slope.
The graphs are triangles and rectangles: easy geometry!

This is a very powerful tool, means you don't need to memorize the kinematic equations, and you avoid those niggly doubts.

 

[Knightycloud]

Thanks!

 

[Simon Bridge]

Cool - have fun.