Electric field, charged balls, conservation of energy, velocity

[thermocleanse]

Homework Statement

near the surface of the Earth there is an electric field of about 150 V/m which points downward.

2 identical balls with mass 0.540 kg are dropped from a height of 2.0 m, but one of the balls is positively charged with q1 = +650 uC and q2 = -650 uC.
use conservation of energy to find difference in speed of 2 balls when they hit ground (neglect air resistance).

Homework Equations

please c attached

The Attempt at a Solution

please c attached

 

[collinsmark]

Here's a hint.

You don't want to use kinematics for this, so forget about the
y = y₀ + v₀t +(1/2)at²
from your list of relevant equations. Instead use conservation of energy to solve this.

There are three aspects of energy that relate to each ball (and not necessarily the same way for each ball).

Gravitational potential energy. This can be expressed as mgh.

Kinetic energy. This can be expressed as (1/2)mv².

Work done by the electric field. I'm going to let you form this equation yourself. But it's related to
W = Fs
where W is the work done by a constant force F, over a distance s.

 

[thermocleanse]

i worked out the 3 aspects of energy related to each ball, but i get two ways to get the velocity. one way is via use of KE equation, whereas the other way is via conservation of energy. i don't even see how it can be 2 different velocities!

anyway, please c attached.

 

[collinsmark]

i worked out the 3 aspects of energy related to each ball, but i get two ways to get the velocity. one way is via use of KE equation, whereas the other way is via conservation of energy. i don't even see how it can be 2 different velocities!

anyway, please c attached.

You're going to have to redo the part of the work done by the electric field. The work done specifically by the electric field has nothing to do with the ball's mass or gravity.

Also, in your equations, you are using E = kQ/r². This equation is only applicable when calculating the electric field created by a point chage, or at least a spherically symmetric charge. But it doesn't apply here.

According to the problem statement, the electric field is already given to you. It is a constant 150 V/m, pointing downward. It is independent of r.

Given a constant electric field E, what is the force that it places on a charge q, within the constant electric field? What is the work done if that charge is moved a distance z, given that constant electrical force? (hint: the constant electrical force is in one direction for one ball, and the opposite direction for the other ball).