Lab 8 - Human Power

Purpose:  To determine the power output of the students in the class, and to create an average for them.

Procedure:
Step 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

Step 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.

Step 3: 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.

 

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

 

Step 5:   From the two trials runs up the stairs, the average time was t = 4.62 s. Calculate the personal power output.

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

∆PE = mgh

∆PE = (105.0 kg)*(9.8 m/s²)*(4.29 m )

∆PE = 44414.41 Nm

Power (W) = (∆PE)/( ∆t)

Power (W) = 4414.41 Nm / 4.62 s

Power (W) = 955.5 W

hp = 955.5W (0.00134102209 hp / 1 W)

= 1.28 hp

 

 Step 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.

Data Sheet for the entire class with average watts and HP.

Possible Sources of Error:  There are several factors for the errors in this lab.  The largest one is the time keeping.  If the timer and the person going up the steps were not in sync, then the time would be off a great deal.  Other factors might include the health of the person.  It is possible that there might have been a physical defect that would prevent them from doing this lab to their full potential.

 

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 experiement.

This was covered in the PSOE section above.

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.