# pound force and pound mass

I have a question about work measured in foot-pound.

Let's say we have a 10 pound-mass ($$10$$ $$\text{lb}_m$$) object. Then since that 10 pound-mass ($$10$$ $$\text{lb}_m$$) object gives 10 pound-force ($$10$$ $$\text{lb}_f$$) due to gravity, if we raise that object 2 feet, the work is 20 foot-pound ($$20$$ $$\text{ft}\cdot\text{lb}_f$$).

I was wondering if I am right.

• For me the main problem is that I've seen many times $lbf$ and $lb$ used interchangeably. That also happens with mass and weight but not as much lately.
– NMech
Feb 16, 2021 at 15:00
• Go metric, man. Go metric. 5 kg x 9.81 m/s² = 50 N approx. No confusion and understandable by an international audience. How are things in the colonies? Feb 16, 2021 at 16:24
• @Transistor metric should be simple, but the times I've seen graduate students trying to convert 1$[mm^2 ]$ to meters and come up with an answer of 1000$[m^2]$ disproves that.
– NMech
Feb 16, 2021 at 16:35

You are correct.

$$F = \left( \text{mass} \right) \cdot \left( \text{acceleration} \right)$$, therefore, $$\text{weight} = \left( \text{mass} \right) \cdot \left( \text{acceleration} \right)$$ due to gravity

Weight of a $$10 \text{ lb}_m$$ object = $$\left( 10 \text{ lb}_m \right) \cdot \left( 32.2 \frac{\text{ft}}{\text{s}^2} \right)$$ (approximate acceleration due to gravity on Earth)

Weight of a $$10 \text{ lb}_m$$ object = $$322 \frac{\text{lb}_m \cdot \text{ft}}{\text{s}^2}$$.

Since $$1 \text{ lb}_{\text{f}}$$ = $$32.2 \frac{\text{lb}_m \cdot \text{ft}}{\text{s}^2}$$, you are correct that its weight is $$10 \text{ lb}_{\text{f}}$$

$${Work} = \left( \text{force} \right) \cdot \left( \text{distance} \right) = \left( 10 \text{ lb}_{\text{f}} \right) \cdot \left( 2 \text{ feet} \right) = 20 \text{ ft} \cdot \text{lb}_f$$

The conversion 1 lb$$_m$$ = 1 lb$$_f$$ only works on earth. When the gravitation constant is different (e.g. on the moon), the direct conversion is not valid. Here are some points of reference.

• by definition: $$1$$ lb$$_m = 0.453592387$$ kg

• standard gravity on earth $$g = 32.174$$ ft/s$$^2 = 9.80665$$ m/s$$^2$$

• by definition: $$1$$ lb$$_f$$ $$= 32.174$$ ft/s$$^2$$

By example, an object with a mass of 5 lb$$_m$$ has a mass of 2.2680 kg regardless of where it sits (e.g. what planet). But this mass

• exerts 5 lb$$_f$$ as its weight on earth
• exerts 0.827 lb$$_f$$ as its weight on the moon with gravitation 5.32 ft/s$$^2$$

By inversion, an object that exerts 5 lb$$_f$$ as its weight on the moon has a mass of 30.2 lb$$_m$$.