Adding time into the discussion

So far, we have defined the amount of effort as work and said nothing about the time to complete the work. In this sense, work is like the effort’s mortgage. It is a fixed value.

As with a mortgage, once you decide to assume it, you need to decide how quickly you will pay it back. In mechanics, this takes us into a discussion of power. The faster you complete a task, the more power you will need to expend per unit time. Whereas work is a property of the task, power parameterizes your time based options for implementing the task.

Cyclists and Power Plants

Power is what enables us to do tasks. Without our power plants, we would not have the electricity we need to go about our daily business. Similarly, you can think of a cyclist as a power plant, able to produce work by pushing on pedals for some period of time. This ability is fundamental to quantifying a rider’s training level.

Work and Power

Work is the total effort to move an object a certain distance against a given force. But something has been left out. How do you factor in how quickly the job was done? This is where power comes in.  Power is the averaged rate of doing work over a given time. The units for power are work per unit time. Power is defined in Watts which is short for nwts*kgs/sec or Joules/Sec.

What stays the same is the amount of work needed to do the job. But if the job is done quickly, the work must be done more quickly than for a longer time interval.

Whatever is doing the job must be able to work harder over that shorter time interval. Said differently, they must be more powerful, able to work harder to accomplish the job in the time interval.

Using Power in Making Purchases

You are shopping and want to buy a more powerful blender. Kitchen appliances are rated in terms of their power capabilities, particularly blenders.  Blenders are capable of producing anywhere from 300 – 1000 Watts. This tells you the work the blender can be expected to produce and therefore how powerful it is.

Computing Power for the Weightlifting Task

Assume our weightlifting exercise is a contest to see who can lift the weight the fastest. You would say the winner was the most powerful of the competitors. Assume first place was one second, second was 3 seconds, and third  10 seconds.

The individual power expenditures would be measured by dividing the total required effort by the time to complete.

Lifter1 = 338.954 Joules/Sec = 338.954 Watts

Lifter2 = 338.954 /3 = 112.985 Watts

Lifter3 = 33.8954 Watts

Now suppose you have a friend who has completed challenges with a power expenditure of 400 Watts. Could they have won the weightlifter contest if they were entered? Since it was won with an effort of 338 Watts, you would conclude they would. This is actually a calculation we will be making when we discuss cycling scenarios.

Cyclist Power

For cycling, power is an important parameter, routinely measured in  labs as well as attached devices. It measures a cyclist’s training level, as well as quantify required cyclist’s performance level to ride a given scenario such as climbing the Alpe d’Huze in under an hour.

Cyclist are not mechanical machines where power estimates can be directly made. However, sports scientists have been measuring power generation of athletes in the lab and produced a representative table of various training levels. These have been included in the Power Expenditure discussions.

Next Topic:   Energized Cycles