# Problem converting joules to dynes

1. Oct 29, 2014

### Tom Hardy

I have this question:

1. The problem
Convert 200 Btu to (a) BG (British gravitational), (b) SI and (c) cgs

3. The attempt at a solution
(a) and (b) are fine I got 155600ftlb and 200kJ but the answer the sheet gives for cgs is 211x10^10 dyne but surely the answer is 211x10^10 erg?! I can correctly convert to erg but I have no idea how to convert energy (joules) into a force (dynes).

My working was since joule is kg.m^2/s^2 to turn it into cgs units I would times by 1000 to account for kg --> cm and times by 10,000 to account for m^2-->cm^2 and I get an answer of 211x10^10 but the units is what's bothering me. Surely the units should be 'erg'? But the answer sheet is showing 'dyne', is there a way to to convert energy (joule) to force (dyne) or is there an error on the answer sheet?

Many thanks

2. Oct 29, 2014

### SteamKing

Staff Emeritus
The sheet appears to be using incorrect units. The dyne is a unit of force in the CGS system. 1 dyne = 1 g-cm/s2 = 10-5 N

This is why I dislike the metric system. There are too many units to keep track of.

3. Oct 29, 2014

### Staff: Mentor

Do you know the definition of an erg?

4. Oct 29, 2014

### Tom Hardy

Well, as I understand it, it has the same relationship with a dyne as newton does with newtom metres. So basically the amount of work that is done when a force of one dyne is exerted for one centimetre, something like that at least.

5. Oct 29, 2014

### Staff: Mentor

Right you are. So 1 erg = 1 dyne - cm. They must have left out the cm part in the answer.

Chet

6. Oct 29, 2014

### Tom Hardy

Ah, that must be it. Thank you for your help!