# Units of acceleration [f/s^2] vs [g]

1. Nov 20, 2014

### jahmookcity

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

2. Relevant equations
F=ma

3. The attempt at a solution

Hi

I am having a hard time understanding the units of acceleration. Normally I am used to distance/time^2 being the standard unit [ m/s^2 , ft/s^2 ]

Now I am seeing this gravity unit [g] being thrown around. Here are 2 examples of simple calculations that use this unit (note highlighted regions of text)
http://imgur.com/S14dnYS,oB56WXS
http://imgur.com/S14dnYS,oB56WXS#1

**The problem I have is:**
If g represents gravity, shouldn't 1.5g = 1.5*32.2[ft/s^2] or 1.5*9.8[m/s^2]. I like doing all my calculations using consistent units and this [g] unit is throwing me off.

For example:
If you look at yellow highlighted text in the 2nd link above, you will see some person claiming that from F=ma:
F = 600lbm x 1.5g = 900lbf

...I feel like this person is incorrect and the F=ma equation should be:

F = 600lbm x 1.5 x 32.2 ft/s2 = 28,980lbf.

2. Nov 20, 2014

### Staff: Mentor

Hi Jamookcity. Welcome to Physics Forums.

The problem you are encountering with the calculations you refer to is that they are using "English units." A unit of mass in this system is the lbm, and the unit of force is lbf. The lbm is defined such that it has has a weight of 1 lbf at the surface of the earth, where the acceleration of gravity is 32.2 ft/sec2. So you can see that, in these units, F is not equal to ma. In these units F = ma/32.2. The dilemma of using lbm is overcome in one of two ways. One of these is to properly define the mass such that F does equal to ma. This is done by defining the unit of mass as the Slug M, which is equal to the mass in lbm divided by 32.2: M = m/32.2. So, F = Ma. The other way of overcoming this is to include a constant in the F = ma equation, called gc. gc = 32.2 (lbfft)/(lbmsec2). Then F = ma/gc.

I know that all this sounds crazy to someone who has never worked with it. But it all goes back to the historical development in the English system of units. Back in the old days, when the metric system was not used as extensively in the US, we were taught to work with the English system, and we eventually got used to it.

Chet

3. Nov 20, 2014

### Bystander

Good here.

"Pound mass," and "pound force." Remember back in high school, or whenever, that for English units, a mass of one slug at earth's surface exerted a force of 32 pounds? Therefore, the "pound mass" is 1/32 of a slug.

... and Chet beat me to it.

4. Nov 20, 2014

### jahmookcity

Ok, thank you both for your responses. I understand this now. Also, I agree with both of you that SI is easier to understand and work with.

5. Nov 21, 2014

### Orodruin

Staff Emeritus
I never liked arguments like this. I think it is more physical to always have F = ma, which is a relation for dimensionful quantities and thus includes the units. In the end you will be left with a new dimensionful quantity with units depending on what units you put in. This may not be the units you desired and in that case you have to do unit conversion, which is just a matter of changing units, not fundamentally changing the physical relationship.

6. Nov 21, 2014

### Staff: Mentor

Later in the post I explained the gc (i.e., the 32.2) has units of $\frac{lb_m}{lb_f}\frac{ft}{sce^2}$. It all goes back historically to the use of the lbm unit in the English system. In the extensive scientific and engineering literature in which the English system is used, gc appears abundantly, and it is important for the Starter to be aware of this if he encounters it. His unawareness of it was what led him to get the wrong answer.

Chet

7. Nov 21, 2014

### Orodruin

Staff Emeritus
The only thing I am saying is that I do not want the OP to think that the physics depends on the units used to describe it. Thus, to be picky, the 32.2 comes with a unit (lbm ft / lbf s2) with which it essentially evaluates to 1, just as when converting from m to cm, you would multiply by 1 = 100 cm/m.

8. Nov 21, 2014

### lep11

I personally prefer the metric system over imperial units. inches, feet, gallons, miles and pounds are just stupid.

9. Nov 21, 2014

### Staff: Mentor

Just as an aside, this sort of question is fine in the discussion forums e.g. General Physics, even if it arises from school coursework.

The homework forums are intended for help with working through textbook-type exercises, whether they are part of schoolwork or not.

10. Nov 21, 2014

### Staff: Mentor

I personally prefer computers and calculators over slide rules and abacus. Slide rules and abacus are just stupid. (lol)

But seriously, there is still tons of equipment out there that was designed using the imperial system. In the US, flow rates and production rates are still often expressed in lbm/hr. Equipment sizes and product sizes are still in imperial units. Economically, it's very expensive to make the conversion to metric, particularly in such a huge economy.

Chet