# Is there such a thing as a work meter to measure work?

I know there are devices to measure power (e.g., dynamometers) but I can't think of any example of a device that measures work directly. Is there such a thing?

## 5 Answers

Several things that we don't normally think about as "work meters" effectively measure work.

For instance, if you marked a spring scale with energies instead of forces, you would have a device that measures work done to it.

An old method to measure mechanical work is the Prony brake. One measures with a spring balance the torque $T_p$ exerted by an immovable lever with an adjustable brake on a rotating axis (e.g. of a motor) and then counts the number of turns of the axis. The torque already has the dimension of work. The work performed by $n$ turns of the axis is given by $$W=2\pi n T_p$$ In this method, the mechanical work is transformed into heat generated by the friction of the brake.

If you've ever lifted an object on a pulley, the height of the object functions as a 'work meter'.

Another way to measure work is to convert the energy to heat and measure a temperature rise, which is the principle behind calorimeters.

A third method is to indirectly use chemistry. You can calculate the total energy released by a battery given the energy released in each individual reaction. Similarly, you can loosely estimate how much work a human is doing by seeing how much $\text{CO}_2$ they exhale.

I'm having trouble thinking of many things that measure "directly" in general.

The best examples I can think of would be length measurements; but even that is a convoluted physical process involving the comparison of light reflections that humans just happen to be really good at.

I'd say a dynamometer isn't very direct either. They usually measure torque and RPM, or some other variables that can be converted to work.

Basically, measurement is giving mathematical value to something physical. It's hard (impossible?) to make any measurement without a medium.

Note that to know work, you must measure a flow variable, an effort variable, and a time variable. I know of no measurement device that can capture all three "directly" i.e., in a single measurement.

But in the electrical realm, a work meter is called a watt-hour meter and there's one sitting on the outside of your house, which furnishes the basis for your monthly power bill.

And in the mechanical realm (specifically, steam power) there is a device called an indicator in which the stroke displacement of a piston in a steam engine is drawn onto the x-axis of a piece of chart paper while the steam pressure above the piston is drawn onto the y-axis. the area under the curve is an analog representation of the work done per stroke.