Human Power

Purpose:

The purpose of Human Power was simply to determine how much power is used when a person walks up a flight of stairs.

Introduction:

Power is defined to be the rate at which work is done:

Power = (∆PE) / (∆t)

Where ∆PE = change in potential energy, and ∆t = time to climb

In this experiment, we will climb up two flights of stairs, and time the trip up. In measuring the height of the stairs, and measuring our mass (kg), the change in gravitational potential energy can be evaluated:

∆PE = mgh

Where ∆PE = change in potential energy, m = mass, g = acceleration of gravity, and h = vertical height climbed

Procedure:

1)      Determine your mass by weighing yourself on the bathroom scale. The scale read in Newtons and read 636 N, so the mass had to be solved for:

F_w = 636 N

636 N = ma  à where a = g

636 N/ 9.8 m/s² = m

m = 64.9 Kg

2)      Next, the height of the stairwell that we were to climb needed to be measured. Two measuring sticks (each 2 m in length) were taken to the stairwell and placed directly on top of each other. The stairwell was measured to be 4.29 m. In fig 1, the method of measurement is pictured:

fig 1

3)      This is when the actual trials for every one take place. At the command of the timer, one person waits to begin their short trip up the stairs, and then the timer stops the watch once they reach the top of the stairs.

4)      The trial runs for every person are repeated, as we can have two separate times to do calculations with.

5)      From the two trials runs up the stairs, the individual times were t₁ = 6.13 s and t₂ = 6.68 s. Calculate the personal power output.

Taking the first time, the change in potential energy is evaluated as follows:

∆PE = mgh

∆PE = (64.9 kg)*(9.8 m/s²)*(4.29 m )

∆PE = 2728.5 Nm

Power (W) = (∆PE)/( ∆t)

Power (W) = 2728.5 Nm / 6.13 s

Power (W) = 445.1 W

hp = 445.1W (0.00134102209 hp / 1 W)

= 0.60 hp

Pictured in fig 2 is the data collected from the trial runs. The average power output for the two trials was calculated to be 0.57 hp.

fig 2

6) The average power output of the entire class was then evaluated in one excel spreadsheet. Pictured in fig 3 is the data collected from the entire class.

fig 3

Conclusion:

In performing the lab, one was able to determine the average power output of a person walking or running up the stairs based on the person's mass and how far they had climbed in what time. I learned that although the process and way in which energy is utilized to move up a flight of stairs can be complex, a simpler model of the energy expended can be obtained if we take the motion to be vertical only. The sources of error in the human power lab included the following:
1) The motion was not exactly vertical, we had to run horizontally as well as vertically in order to get up the stairs.
2) There was a roundabout in the middle of the staircase that needed to be swung around.

Questions:
1)      Is it okay to use your hands and arms on the handrail to assist you in your climb up the stairs?

Yes, although you are using multiple limbs in order to make your way up the stairs, there is still work being expended to get to the top. More energy is exerted in pulling yourself up for a faster time.

2)      Discuss some of the problems with the accuracy of this experiment.

-          -Actual times of travel may be rough estimates as we could not see the timer before we started.

-         - We were not just traversing vertically, we were also propelling our bodies horizontally, which we did not account for.

-         - There was a turn that had to be swung around in the middle of the stairwell.

Human Power Follow-Up Questions:
1)      Since the change in potential energy is the same for both people, the person who completes the journey in the fastest time will expend the most energy. Since power output is change in potential energy over change in time, we can see the smaller the time, the greater the power output.

2)      mg = 1000 N

h = 20 m

t = 10 s

Power (W) = (∆PE)/( ∆t)

Power(W) = (1000 N * 20 m ) / (10 s)

Power (W) = 2000W, or 2 KW

  3)      Brynhildur climbs up a ladder to a height of 5.0 m, if she is 64 kg:

a)      What work does she do?
The work that Brynhildur does climbing up the stairs is lifting her 64 kg mass up to a height of 5 meters.

b)      What is the increase in gravitational potential energy of the person at this height?

∆PE = mgh

∆PE = 64 kg * 9.8 m/s² * 5.0 m

∆PE = 3136 N m

c)      Where does the energy come from to cause this increase in PE?

The energy required to lift her up the ladder comes from her muscles both pulling and pushing her way up the ladder.

4)      Which requires more work: lifting a 50 kg box vertically for 2 m, or lifting a 25 kg box 4 m?

  They require the same amount of work, although the 25 kg mass is being lifted to twice the height, the 50 kg mass is being lifted to a height half the amount, meaning it takes the same amount of work.