# Problem converting joules to dynes

I have this question:

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

## 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

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SteamKing
Staff Emeritus
Homework Helper
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.

Chestermiller
Mentor
Do you know the definition of an erg?

Do you know the definition of an erg?
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.

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

Chet

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

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