Work and Energy Share an Interesting Relationship

 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 second2.      Putting equation (1) in longhand notation terms, we arrive at, Work = 178 kilogram • meters per second2 × 3 meters       (2) Work = 534 kilogram • meters2 per second2                    (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 • meters2 per second2, 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 ____________________________________