# Special Relativity -- Dynamics -- Energy

1. Dec 8, 2015

### Barry Melby

1. The problem statement, all variables and given/known data
Antihydrogen is the only antimatter element that has been produced in the laboratory, albeit just a few atoms at a time. Each antihydrogen atom consists of a positron in orbit around an antiproton and has the same atomic mass as hydrogen. If an antihydrogen atom collides with a hydrogen atom, they annihilate each other and create gamma radiation.

If this energy could be harnessed in a matter-antimatter automobile engine, how far could a car travel on 10 mg each of antihydrogen and hydrogen? At highway speeds, a typical automobile expends about 2.5×10^3 J per meter.

2. Relevant equations
E = mc^2

3. The attempt at a solution
I know the answer is 9.00 * 10^8 m, but I haven't been able to work out an answer that is even close to this.

I've solved the minimum amount of energy that is released in this process (3.01 * 10^-10 J). I'm not sure if this is relevant, but I solved it if necessary.

Last edited: Dec 8, 2015
2. Dec 8, 2015

### Buzz Bloom

Hi Barry:

I think you omitted an important equation: E = mc2.

Hope this helps.

Regards,
Buzz

3. Dec 8, 2015

### Barry Melby

Okay, so if i use E = mc^2 with m = 10 mg then i get 9 * 10^12 J. Where do I go from here?

4. Dec 8, 2015

### Buzz Bloom

Hi Barry:

Look at the end of 1. Problem Statement. Also be careful about your units.

Regards,
Buzz

5. Dec 8, 2015

### Barry Melby

I realize that you should be able to take E / 2.5 * 10^3 J/m , but this is incorrect.

6. Dec 8, 2015

### Buzz Bloom

Hi Barry:

What units are you using for c and m?

Regards,
Buzz

7. Dec 8, 2015

c: m/s
m: kg

8. Dec 8, 2015

### Buzz Bloom

Hi Barry:

What values are you using for c and m?

Regards,
Buzz

9. Dec 8, 2015

### Barry Melby

c: 3.00 * 10^8 m/s
m: 10 * 10^-5 kg

10. Dec 8, 2015

### Buzz Bloom

Hi Barry:

How are you converting 10 mg into kgs?

Regards,
Buzz

11. Dec 8, 2015

### Buzz Bloom

Hi Barry:

Also, what is the TOTAL input mass, hydrogen and anti-hydrogen?

Regards,
Buzz

12. Dec 8, 2015

### Barry Melby

This is exactly what I'm doing:

[(20 * 10^-6)(3 * 10^8)^2] / (2.5 * 10^3) = 720000000

which is incorrect.

13. Dec 8, 2015

### Barry Melby

i figured it out. thank you.

14. Dec 8, 2015

### Buzz Bloom

Hi Barry:

OK. You get the same answer I do, which is not the same as the answer you say you know is correct: 9.00 * 10^8 m. Where did this "correct" answer come from?

Regards,
Buzz

15. Dec 8, 2015

### Buzz Bloom

Hi Barry:

Glad to have been of some help.

Regards,
Buzz