- #1
Abu
Homework Statement
This is an example problem I found on khan academy and it didn't have an official problem statement... So I am going to have to make up my own problem statement from what was given. I can link the video if any of you want to see it.
A positive charge 4uC and a negative charge 2uC, both with a mass of 1kg, are placed 12 cm apart from each other. Find their final speeds when they are 3 cm apart from each other
Homework Equations
w = v * q
f = K q1*q2/r^2
v = K q/r
F = ma
Vf^2 = Vi^2 + 2ad
The Attempt at a Solution
I know the real solution to this problem as it was shown in the video that I watched to get this example. But my question is how come my solution does not work.
What I attempted to do was:
F = K q1*q2/r^2
F = 9*10^9 (4*10^-6) (2*10^-6)/0.12^2
F = 5 N
This is the force of attraction between the two charges
F = ma
5 = 1a
a = 5m/s^2 since the mass of each charge was 1kg in the problem (I realize 1kg is an absurd mass)
Vf^2 = Vi^2 + 2ad
Vf^2 = 0 + 2(5)(0.045) I did 0.045 because if they are 0.03m apart then that means they each traveled 0.045 m
Vf = 0.67 m/s
Now this answer is incorrect. I can post the link to the video I got the problem from. It is the second/final problem in the video. Their solution uses conservation of energy. It starts at 10:30, and their final solution was 1.3 m/s
Here is why I think my solution is wrong: The acceleration is not constant, because as their charges move closer together, the force of attraction is stronger and thus their acceleration increases.
Is there any way I can correct my answer by still using the force of attraction method? Can I do the change in force from their initial positions to when they are 3 cm apart - or is the conservation of energy method the only way?
If you would like me to clarify anything please let me know. Thank you.