Human Power

Introduction

Power can be described as the rate at which work is done which can also be translated as the rate at which energy is converted from one from to another. To show this we look at the equation:

Change in PE = mgh

PE=potential energy

M=mass

G=gravity

H=height

We can use this equation to find the change in potential energy which we need because the equation for  power output is:

Power = (change in PE) / (change in time)

Unit Analysis

Potential Energy= mgh

PE=kg(m/s^2)(M)

PE=(kg(m^2))/s^2=J

Power= PE/t

Power= J/s

Watt=J/s

1 watt= 0.00134102209 horsepower

In this lab we had to run up a flight of stairs that was 4.29 m high and record the time it took to make it from the bottom of the stairs to the top of the stairs.

Power Output

Trial	Weight Force (N)	Height of Stairs (m)	Change in Potential Energy (J)
1	888.86	4.29	3813.21
2	888.86	4.29	3813.21
Trial	Change in Time (s)	Power Output (watts)	Average Power Output (watts)
1	13.6	280.38	399.95
2	7.34	519.51

Then to find my horsepower out I did the following:

399.95 watts*(0.00134102209 hp/1 watt)= 0.54 hp

Discussion

To find my percent difference in relation to the class average I did the following. 

% Difference= [(Measured Value of Class - My value)/ 0.5(class+me)]*100

Watts [(634.98-399.5)/0.5(634.98+399.95)]*100

[.45419]*100

45.4 % difference

Horsepower.... [(.85-.54)/0.5(.85+.54)]*100

[.44604]*100

44.6 % difference

The values that I obtained let me know that I had less power out put than the class The percent difference for watts was 45.4% and the percent difference for horsepower was 44.6%.  I put out roughly less then 50% of what the class put out. 

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

It is okay to use your arms to assist in the climb up the stairs because the force that is exerted on the hand rail is to push you up. That force comes from your body so there is no difference in hand force and leg force they can both propel you upward and thus change your gravitational potential energy.

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

Some sources of inaccuracy in this experiment are measurement of the height of the stairs, Timing of the runs up the stairs, human reaction time, when the recorders decided to stop the timer, the moment it took to turn around in the stairs to head the other direction. Another is that we are not perfectly at sea level

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 expends the most power? Explain your answer.

Hinrick does the same amount of work as Valdis in less time, Hendrick has higher power output.

2. A box that weighs 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 (w) and kilowatts (kw)?

Work = ΔPE = 1000 (N) * 20 (m) * 9.8(m/s2)= 196000 (J)

Power = ΔPE/Δt = 20000 (J) / 10 (s) = 2000 (w) or 2 (kw)

3.  Brynhildur climbs up a ladder to a height of 5.0 meters. If she is 64 kg:

a. What work does she do?

The work she does is to  pull herself up and increase height.

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

W= ΔPE= mgh = 64 (kg) * 9.8 (m/s2)  * 20 (m) = 3136 (J)

c. Where does the energy come from to cause this increase in P.E.?

From her own arms and legs - she uses her arms to pull herself up and her legs to push herself up.

4. Which require more work: lifting a 50 kg box vertically for a distance of 2 m, or lifting a 25 kg box vertically for a distance of 4 meters?

Since work is defined as force x distance and both would result in the same amount,

50 kg * 9.8 (m/s2) * 2 (m) = 980 J

25 kg x 9.8 (m/s2) x 4 (m) = 980 J

Both of them do the same amount of work

Conclusions

In this lab I learned the that ∆ PE = mgh where m is mass g is gravity (9.8 m/s^2) and h is the height. To see how much power you put out when your height is changed you use Power  = ∆ PE/∆t , the change in potential energy is divided by the change in time. So power is put out by us climbing  the stairs but that power is not lost, the energy is converted from out kinetic energy running up the stairs to our change into our gravitational potential energy from now being at a different height. So our body used energy from our food to move us up (kinetic) and as we climbed the stairs we lost kinetic energy and gained Potential energy. So energy is conserved in every action, energy does not just disappear it is just transformed into a different type of energy.