# Homework Help: Charged ball exiting a box....

1. Jul 19, 2015

### nmsurobert

1. The problem statement, all variables and given/known data
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.

2. Relevant equations
ΔE = E - E0

ΔE = q(V)

E = 1/2mv2

3. The attempt at a solution

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.

Last edited: Jul 19, 2015
2. Jul 19, 2015

### haruspex

Has it gained or lost electrostatic energy?

3. Jul 19, 2015

### haruspex

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

4. Jul 19, 2015

### 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.

5. Jul 19, 2015

### nmsurobert

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

6. Jul 19, 2015

### nmsurobert

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

7. Jul 19, 2015

### haruspex

Quite so. So what is the new KE?

8. Jul 19, 2015

### nmsurobert

Should it have been 4.55 and not 9.44?

9. Jul 20, 2015

### haruspex

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.

10. Jul 20, 2015

### nmsurobert

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

11. Jul 20, 2015

### haruspex

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?

12. Jul 20, 2015

### nmsurobert

-4.552J?

13. Jul 20, 2015

### haruspex

Right. What does that tell you?

14. Jul 20, 2015

### nmsurobert

Does that mean that the ball stopped?

15. Jul 20, 2015

### haruspex

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

16. Jul 20, 2015

### nmsurobert

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

17. Jul 21, 2015

### haruspex

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