To determine the power output of a person.
Equipment
Two meter sticks, stopwatch, force plate or kilogram bathroom scale.
Introduction
Power is defined to be the rate at which work is done or equivalently, the rate at which energy is converted from one form to another. In this experiment, you will do some work by climbing from the first floor of the science building to the second floor. By measuring the vertical height climbed and knowing your mass, the change in your gravitational potential energy can be found:
Δ PE = mgΔh
Where m is the mass in kg, g is the acceleration of gravity in m/s/s, and h is the vertical height gained. Your output power can be determined by:
Power = Δ PE / Δt
Where Δt is the time it takes to climb the vertical height h.
Procedure
1. Determine your mass by weighing on the kilogram bathroom scale or force plate. Record your mass in kg or your force due to gravity in N.
- Since Potential Energy requires mass, acceleration due to gravity, and a vertical height, mass and gravity can be combined to get the force of gravity on the person by using the formula Fg = mg.
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 sticks held end to end in the stairwell.
-This was done using the two meter sticks end to end and stacking them from the floor of the ground floor to the floor of the second floor.
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 trips up the stairs. Obtain the average power output from the two trials.
-Fg = 770 N -
-Δh = 4.26 m -T2 = 6.19 s -1 hp = 746 watts
Power = (mg)Δh/Δt = (770 N)(4.26 m)/(6.01 s) = 545.79 watts
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.
-Average power of class = 0.7 hp
7. Determine your average power output in units of horsepower.
-545.79 watts = 0.7316 hp
Questions
1. Is it okay to use your hands and arms on the railing to assist you in your climb up the stairs? Explain why or why not.
-It is okay to use your hands and arms to assist in climbing the stairs because it shortens the time taken to climb the stairs. Since mass, gravity, and height don't change when calculating the power, time is all that's left that could change the power output. When time is shortened, power is increased. When you use the handrail to aid you in climbing, you are exerting additional power to climb, and therefore shorten the time. Walking up will take longer thereby decreasing the power output.
2. Discuss some of the problems with the accuracy of this experiment.
-Some problems in the accuracy of the experiment may include: inconsistent climbing style for the class (running vs. walking, stepping on individual steps vs. skipping steps), human error in measurement (height, time)
