My work as an **engineering expert** has often required that I perform calculations to quantify the *energy* consumed by electric motors and steam turbines, such as when they *work* together at power plants to generate electricity. Today we’ll see how *work* and *energy** ***share an interesting relationship** that is brought out by examining the units by which they are measured.
Last time we used de Coriolis’ formula to compute work to calculate the amount of *work* performed while pushing a loaded wheelbarrow a distance of 3 meters. We found that in order to move the wheelbarrow that distance, a gardener must exert a force equal to 534 *Newton** • meters* of *work*. That relationship is shown here,
*Work = *178 *Newtons* ×* *3 *meters = *534 *Newton** • meters* (1)
**de Coriolis’ Formula to Compute Work**
The *Newton, *as discussed previously in this blog series, is shorthand notation for metric units of force, and we’ll use those units today to demonstrate the special relationship between *work* and *energy*.
We’ll start by supposing that you’re unfamiliar with the Newton as a unit of measurement. In that case you’d have to employ longhand notation to quantify things, which means you’d be measuring units of force in terms of *kilogram • meters per second*^{2}.
Putting equation (1) in longhand notation terms, we arrive at,
*Work = *178 *kilogram • meters per second*^{2} ×* *3 *meters* (2)
*Work = *534 *kilogram • meters*^{2} per second^{2} (3)
If you’ve been following along in this blog series, you’ll recognize that the unit of measurement used to compute *work, *namely, *kilogram • meters*^{2} per second^{2}, is the same as was used previously to measure *energy. * That unit is the *Joule, *which is considerably less wordy.
Equations (2) and (3) bear out the *interesting relationship* between *work* and *energy — *they share the same unit of measure. This relationship would not be apparent if we only considered the units for *work* presented in equation (1).
So following standard engineering convention where *work* and *energy* are expressed in the same units, the *work* required to push the wheelbarrow is expressed as,
*Work = *534 *Joules*
Yes, *work* and *energy* are measured by the same unit, the *Joule*. But, *energy* isn’t the same as *work*. *Energy* is distinguished from *work* in that it’s the *measure of the ability to perform ***work**. Stated another way, *work* cannot be performed unless there is *energy* available to do it, just as when you eat it provides more than mere pleasure, it provides your body with the *energy* required to perform the *work *of pushing a wheelbarrow through the garden.
Next time we’ll see how *work* factors into the *Work Energy Theorem*, which mathematically relates *work* to *energy*.
Copyright 2015 – Philip J. O’Keefe, PE
Engineering Expert Witness Blog
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