Human Power

Purpose: To determine the power output of a person
Equipment: two meter meter sticks, stopwatch, kilogram bathroom scale
Introduction: This lab includes an experiment involved that allows people to run or walk up stairs and get timed. After they were timed, the person would come back and calculate the horsepower that they outputted. The way to do this is by measuring the vertical height climbed, and knowing your mass, the change in potential energy can be found. This is given by the equation:

(change in PE) = mgh
where m is the mass, g is the acceleration of gravity, and h is the vertical height gained. Power output can be determined by the equation:

Power = (change in PE) / (change in time)
where change in time is the time it takes to climb the vertical height.

Procedure: 

1. Determine your mass by weighing on the kilogram bathroom scale. Record your mass in kg..
2. Measure the vertical distance between the ground floor and the second floor for the science building. This can most easily be done by using two meter long metersticks held end to end in the stairwell at the west end of the building. Make a careful sketch of the stairwell area that explains the method used to determine this height.

3. Designate a record keeper and a timer for the class. At the command of the timing person, run or walk (whatever you feel comfortable doing) up the stairs from the ground floor to the second floor. Be sure that your name and time are recorded by the record keeper.
4. After everyone in the class has completed one trip up the stairs, repeat for one more trial.
5. Return to class and calculate your personal power output in watts using the data collected from each of your climbing trip up the stairs. Obtain the average power output from the two trials.
6. Put your average power on the board and then calculate the average power for the entire class once everyone has reported their numbers on the board.
7. Determine your average power output in units of horsepower.

Data:

 h: 4.29m
mg: 855N

△t = 4.10s

Power = mgh / △t = 855N × 4.29m / 4.10s = 864.62 J/s =864.62 W = 1.1997 HP

Questions:

1. Is it okay to use your hands and arms on the hand railing to assist you in your climb up the stairs? Explain why or why not.
- No because horse power is mainly described by force from the legs and when you are being assisted by the hand rails, you are pulling yourself up, consequently your legs are working less than normal and it is not calculating true horsepower.

2. Discuss some of the problems with the accuracy of this experiment.
- Some errors could have been the time keepers watch could have been off by a couple of milliseconds, depending on the reactions of the timekeeper. Also, another source of error could be the measurement of the height of the staircase could be off by a couple of centimeters.

Follow up questions:
1. Two people of the same mass climb the same flight of stairs. Hinrik climbs the stairs in 25 seconds. Valdis takes 35 seconds. Which person does the most work? Which person expands the most power? Explain your answers.
- They both did the same amount of work but Hinrik expanded the most power because it took him a shorter time to climb the same height.


2. A box that weights 1000 Newtons is lifted a distance of 20.0 meters straight up by a rope and pulley system. The work is done in 10.0 seconds. What is the power developed in watts and kilowatts.
- (1000N*20) / 10s = 2000 watts = 2 kilowatts

3. Brynhildur climbs up a ladder to a height of 5.0 meters. If she is 64 kg:
 a) What work dose she do?
64*(9.8)^2 * 5 = 3136J

b) What is the increase in the gravitational potential energy of the person at this height?
-It would have a 3136J change because PE and work are found by the same equation.

c) Where does the energy come from to cause this increase in P.E.?
-You must use kinetic energy to climb the height of the stairs and the more you climb, the more PE you gain.

4. Which requires more work: lifting a 50 kg box vertically for distance of 2m , or lifting a 25kg box vertically for a distance of 4 meters?
-They require the same amount.
25 * 4 * 9.8^2
50 * 2 * 9.8^2

Conclusion:
 This lab was really fun and educational. It taught us the definition of power and potential energy. By measuring height, mass, and time, we were able to determine horse power. Some source of error was the height measurement, time, and as a result, the power would not be accurate.