To determine how much work a person does to move himself or herself, we need to measure the force exerted and the distance traveled (Work = Force x Distance). An easy way to do this is to climb a flight of stairs. To climb stairs, a person must do work to overcome gravity. The work done is equal to her weight, which is the force she must exert to overcome gravity, multiplied by the height of the staircase. For example, the work done by a person weighing 550 Newtons* (N) and climbing a 3-meter-high staircase is:
Work (joules) = Force x Distance
= person’s weight x height of staircase
= 550 Newtons x 3 meters
= 1,650 joules
*NOTE: The Newton is the metric unit for weight, the gravitational force (9.8 m/s2) of an object’s mass (kg). 550 Newtons is equal to about 125 pounds (1 lb. = .45 kg). To figure out your weight in Newtons using a bathroom scale, multiply the weight in pounds by .45 kg and then by the force of gravity (9.8 m/s2).
Joules (j) is the unit used to measure work (how much an object is moved). Using the force of one Newton to push an object one meter results in one joule of work (work = force x distance; 1 joule = 1 Newton x 1 meter).
Does a person do more work if they walk or run up the stairs? No; the formula for work does not take into account the time to climb the stairs. Yet the two situations are different. When a person runs up the stairs, he does the same amount of work in less time than when he walks up the stairs. In other words, he works faster. The term that expresses this difference is power, which is defined as the work done per unit of time, or the rate of doing work.
The formula for power is:
Power (watts) = work done/time
For stair climbing (unit = watts)
Power = weight (Newtons) x height of stairs (meters) / time (seconds)
Power output of a person walking up the stairs
Power = (550 Newtons x 3 meters) / 10 seconds = 165 watts
Power output of a person running up a stairs
Power = (550 Newtons x 3 meters) / 2 seconds = 825 watts
One watt is equal to one joule of work done per second. Watts are a unit of power often associated with electrical equipment like light bulbs, hair dryers, and stereo amplifiers. Watts also describe the power output of engines and students running up stairs. The watt is a small unit of power. Therefore, multiples of the watt, such as the kilowatt (1000 watts) or the megawatt (one million watts), are often used (Taken from the KEEP Activity Guide ” People Power”).
Calculations to try:
1. What is your weight in Newtons (see above)?
2. What is the height of the staircase in meters?
3. Calculate the work performed in joules. Multiply your weight in Newtons X the height of the staircase in meters (Force X Distance) How much work did you do?
4. Calculate your power output. Time yourself both walking and running up the stairs. (Power (watts) = weight (Newtons) x height of stairs (meters) / time (seconds)). What was your power output in watts?
5. Suppose your power output in number 4 could be directly converted into electrical power. How many 100-watt light bulbs could you light by climbing the stairs slowly and rapidly? (Formula: Watts from #4/100)