What Is the Speed of a Charged Ball Exiting a Box?

[nmsurobert]

Homework Statement

A small ball has mass 3.4x10^-8 kg and charge of 2.0x10^-5 C. It enters a box with initial speed 1.2x10^4 m/s. The point where the charge leaves the box is at a voltage 350kV higher than the entry point. Find the speed of the ball as it leaves the box. [/B]

Homework Equations

ΔE = E - E₀

ΔE = q(V)

E = 1/2mv²

The Attempt at a Solution

[/B]
E = 1/2 (3.4x10^-8)(1.2x10⁴)² = 2.448 J
ΔE = (2.0x10^-5)(350000)= 7 J
7J = E - 2.448J

9.448J = 1/2(3.4x10^-8)v²

v = sqrt ((2(9.448))/(3.4x10^-8)

v = 23577 m/s

Does this look right? Apparently the ball doesn't leave the box. But that doesn't make any sense to me.

 

[haruspex]

ΔE = (2.0x10-5)(350000)= 7 J

Has it gained or lost electrostatic energy?

 

[haruspex]

E = 1/2 (3.4x10^-8)(2.0x10^-5)²

I assume the (2.0x10^-5) is a typo.

 

[nmsurobert]

It's lost energy because the charge is positive, right?

I don't believe it a typo. I'm helping someone with their homework. Their instructor said the ball doesn't leave the box. But that makes no sense to me.

 

[nmsurobert]

That is a typo. I just saw what I did wrong.

 

[nmsurobert]

But even with that 2.448 is correct. I put it in my calculator correctly but I typed it wrong.

 

[haruspex]

It's lost energy

Quite so. So what is the new KE?

 

[nmsurobert]

Should it have been 4.55 and not 9.44?

 

[haruspex]

It's lost energy

I'm sorry, I misremembered which way round I asked the question. I should have said that answer was wrong.
It is a positive charge which has moved to a point at a higher potential. It has gained electrostatic energy.

 

[nmsurobert]

Ok. That doesn't help me though. I'm confused about what you're trying to get at.

 

[haruspex]

Ok. That doesn't help me though. I'm confused about what you're trying to get at.

If it started with 2.448J KE and gained 7J PE with no work being done on it, how much KE does it now have?

 

[nmsurobert]

-4.552J?

 

[haruspex]

-4.552J?

Right. What does that tell you?

 

[nmsurobert]

Does that mean that the ball stopped?

 

[haruspex]

Does that mean that the ball stopped?

Is it possible for the ball to exit with negative KE?

 

[nmsurobert]

Wouldn't that mean the ball turned around. You can't have negative mass so it has to have negative direction.

 

[haruspex]

Wouldn't that mean the ball turned around. You can't have negative mass so it has to have negative direction.

Energy is a scalar. No matter which way it is moving it cannot have negative KE.