Lab 10: Human Power

Purpose: To determine the power output of a person

Equipment: Two meter metersticks, stopwatch, 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:

                                                                    △PE = mgh

Where m is the mass, g is the acceleration of gravity, and h is the verticle height gained.
Your power output can be determined by:
     
                            Power = △PE / △t     Where △t is the time to climb the vertical height h


Data:


The height of the stairs is 4.29m

 h: 4.29m
m: 61.02kg
mg: 598N

△t₁ = 8.84s
△t₂ = 9.03s

Power₁= mgh / △t₁= 598N × 4.29m / 8.84s = 290.21 J/s = 290.21 W = 0.39 Hp
Power₂= mgh / △t₂= 598N × 4.29m / 9.03s = 284.1 J/s = 284.1 W = 0.38 Hp

Power_avg =  (Power₁ + Power₂ ) / 2 = (0.39 Hp +0.38 Hp) / 2 = 0.385 Hp

Question:

1. Is it okay to use your hands and arms on the handrailing to assist you in your climb up the stairs? Explain why or why not.

     If we use our hands and arms on the handrailing to assist us, our calculated value of power won't change. Because when you put your hands on the handrailing, the handrailing will give you a normal force upward, but your weight doesn't change, which is still equal to mg. So, according to the formula △PE = mgh, the change of the gravitational potential energy will be the same.


2. Discuss some of the problems with the accuracy of this experiment.
 
    The height of the floor, the mass and the time are all measured values that are not really accurate, so our calculated values of power are also have error.


Followup 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.

     Because △PE = mgh, their mass and the height are the same, so they both did the same work.
     Hinrik expands more power. Because  Power = △PE / △t , △PE are the same, but Hinrik used less time, so he had a higher power.


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.
   
         Power = △PE / △t = (1000N× 20m) / 10s=  2000W= 2KW


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

    a) What work dose she do?
                 
        Work = mgh = 64kg × 9.8m/s^2 × 5m =3136J

    b) What is the increase in the gravitational potential energy of the person at this height?
 
        △PE = mgh = 64kg × 9.8m/s^2 × 5m =3136J
         Increase 3136J

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

         the force of gravity do the negative work on the person, so the gravitational potential energy will increase by the same amount. The energy the person gets to do the work come from this person's chemical energy. The consumption of chemical energy increases this person's gravitational potential energy.

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?

  Lifting a 50 kg box:
  Work = mgh = 50kg × 9.8m/s^2 × 2m = 980N
  Lifting a 25 kg box:
  Work = mgh = 25kg × 9.8m/s^2 × 4m = 980N
 
  So, they require the same work.


Conclusion:

     In this lab, we determined the power output when people climb the floors. We also learned the definition of the potential energy and power.
     Potential energy is energy stored in an object. This energy has the potential to do work. Gravity gives potential energy to an object. This potential energy is a result of gravity pulling downwards. The gravitational constant, g, is the acceleration of an object due to gravity. This acceleration is about 9.8 meters per second on earth. The formula for potential energy due to gravity is PE = mgh. As the object gets closer to the ground, its potential energy decreases while its kinetic energy increases. The difference in potential energy is equal to the difference in kinetic energy. After one second, if the potential energy of an object fell ten units than its kinetic energy has risen ten units. Potential energy units are joules.
    Power is the rate at which energy is transferred, used, or transformed. The unit of power is the joule per second (J/s), known as the watt. Energy transfer can be used to do work, so power is also the rate at which this work is performed. The same amount of work is done when carrying a load up a flight of stairs whether the person carrying it walks or runs, but more power is expended during the running because the work is done in a shorter amount of time.

Source of error:
    The height of the floor, the mass and the time are all measured values that are not really accurate, so our calculated values of power are also not accurate.