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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.

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  • $\begingroup$ 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. $\endgroup$
    – NMech ♦
    Feb 16, 2021 at 15:00
  • $\begingroup$ 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? $\endgroup$
    – Transistor
    Feb 16, 2021 at 16:24
  • $\begingroup$ @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. $\endgroup$
    – NMech ♦
    Feb 16, 2021 at 16:35

2 Answers 2

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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 $10 \text{ lb}_{\text{f}}$

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

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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$_m$.

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