Analysis: Work and power

Power is thrilling. Supplying power or using it is what sets some engineers apart. Mechanical engineers deal with power, of course, and others do, too– such as solar, mechatronic, electrical, Naval architects, aerospace engineers. We’re going to build an intuitive understanding of mechanical power into your engineers’ eyes by exploring the power requirements of an electric car. Back in the 1860s, James Watt wanted to tell potential customers how much weight his steam engines could lift out of mines. He compared his engines to what a horse could do. He gave us the horsepower. It turns out that power is work done divided by the time taken to do it, so we need to understand work. Consider Watt’s engine lifting a weight from a mine.

The work done was the weight times the distance it was lifted, or w equals mg times h. And you can see that twice the weight means twice the work. Twice the distance means twice the work. Power is the rate of doing work. In symbols, it becomes p equals mg times h divided by t, where t is time. Watt decided on a standard value of power for a horse, and compared his engines to that. Let’s try some numbers.

If an engine lifted a load of 100 kilograms through a distance of 50 metres, then the work done by the engine was, in modern units, w equals 100 times 9.8 times 50 joules - a joule is the SI unit of work - or the work, w, equals 49,000 Joules, or 49 kilojoules. Now for power. If the engine lifted 100 kilograms through 50 metres in 5 minutes, the power was p equals 49,000 divided by 5 times 60. The 60 is to convert the time from minutes into seconds. That gives us power equals 163 watts. Another way of looking at this is to say that power is force times speed.

For this calculation, speed– which is distance divided by time– must be in metres per second. In our example, speed is v equals 50 divided by 5 times 60 metres per second, or 0.167 metres per second, and power is 100 times 9.8 times 0.167 watts. So, power is 163 watts, as before. Let’s finish by using our concept of work, energy, and rolling friction to understand the rolling test, where we let the weight hit the floor and the tractor kept rolling on. It goes like this. Everything is driven by the falling weight. Some work done by the weight is lost in friction at the table edge, but the rest accelerates the tractor and accelerates the weight itself.

When the weight hits the floor it stops, and its kinetic energy is lost. But the tractor continues, and its kinetic energy is gradually used up in overcoming the rolling resistance until the tractor finally comes to a stop. It’s possible to analyse this mathematically, but we don’t have the time. A tiny amount of the energy with the rolling tractor has stirred up the air and warmed it up as it creates drag. It matters more at high speeds. Now you can start your design exploration.