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EXSS 323
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EXSS 323
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During this lab, we will focus on the concepts of work, energy, and power as applied to human movement. In doing so, we first need to define (review) some concepts.
Work is defined as a force applied through a displacement in the direction of the force. Mathematically, work is represented by:
W = F * (cos q) * d
If the force is in the direction of the displacement, the angle of application is 0°, and the equation reduces to:
W = F * d
The units of work are: Force in Newtons * displacement in meters = Newton-meters (Nm); however, in order to distinguish work from torque, work is assigned a special unit called the Joule (J); 1 Nm = 1 J
Closely related to work is the concept of power. Power is defined as the work done per unit time, or the rate of doing work. Mathematically, power is represented by:
P = W / Dt
Substituting the expression for work into the power equation, we arrive at an alternative expression for power:
P = F * d / Dt = F * v
The units of power are: Work in Joules / time in seconds = Joules/second (J/s). Again, a special unit is defined to take the place of J/s; the unit of power is the Watt.
Energy is defined as the capacity to do work. There are many types of energy, but the type of concern in biomechanics is Mechanical Energy. There are four types of mechanical energy; we will only be concerned with two in this lab - kinetic energy and potential energy.
Kinetic energy is the capacity to do work by virtue of the velocity of an object. It is expressed as:
KE = ½mv2
From the expression, it can be seen that KE can never be negative, as mass is never negative. The units for kinetic energy are: mass in kilograms * (velocity in meters per second)2 = kg·m2/s2 = Nm = J
Potential energy is the capacity to do work by virtue of the position above or below a reference position. It is mathematically expressed as:
PE = mgh
From the definition, PE can be either positive or negative, depending upon
position. The units for potential energy are:
mass in kilograms * gravitational acceleration in meters per second2 * height
in meters = kg·m2/s2 = Nm = J
While these concepts are easily defined, difficulties arise when trying to apply these concepts to human motion. Calculating the work and power of human movement is problematic for several reasons. First, it is often difficult to determine the forces that are acting. In such a case, an alternative means of calculating work (and thus power) must be utilized. Based on the definition of energy, the common units of work and energy, and the principle of Conservation of Energy (energy can neither be created nor destroyed, only altered in form), one can equate the work done in a situation to the energy expended (converted to another form). In this respect, we can rewrite the formula for work as follows:
W = DE = DKE + DPE = ½m(vf2 - vi2) + mgDh
One might suppose that, with this relationship, calculating the work in a giving situation might then be very easy. Herein lies a second difficulty in calculating work. Consider, for example, the case of a runner at a constant velocity over level ground. Since velocity is constant, DKE = 0; since the height (altitude, elevation, etc) of the activity is constant, DPE = 0 as well. Therefore, an individual running at constant speed over level ground does no work!
A variety of procedures for addressing this seemingly impossible problem have been developed; they are, however, beyond the scope of this course. What we will be doing in lab today is utilizing a different method, borrowed from Exercise Physiology, to determine work and power. This method was proposed by Rodolfo Margaria1 in 1966 and has gained wide acceptance as a means of determining anaerobic power, both due to its simplicity and repeatability. We will be using Margaria's method to determine the work and power at several different running speeds.
Margaria's method involves running up a staircase at maximum speed for a short time duration. "When one runs up a staircase at top speed, provided that the effort is maximal, a constant speed is attained in about 1-2 sec, which is constant up to the 5th sec, then declines. This exercise is a very convenient ergometric procedure as it appears2 that the energy requirement for speed maintenance in running a given distance is independent of speed. Provided that the effort is maximal, for a given incline of the steps, the energy requirement depends only on the mechanical work as calculated from the body lift."1
Based on the work-energy equivalence, if we know the energy change, we can calculate the work and, ultimately, the power. In the case of Margaria's method, the energy change is due solely to the change in height. Therefore, the work done is calculated by the change in potential energy. Power is then calculated by dividing the work by the time expended.
W = DPE = mgDh
and
P = W / Dt = mgDh / Dt
While this method was originally developed to measure anaerobic power (maximum effort, short duration), it is sufficient for measuring power at any speed, as long as the speed is constant.
Two photocells will control an electronic timer that will display the time it takes for the vertical displacement between them. They will be set up on the eighth and twelfth steps of a standard staircase. When you run the stairs two-at-a-time, the cells will determine the time between your fourth and sixth footfalls. The procedure used is as follows:
Based on your personal data briefly summarize the methodology and results of this experiment. Discuss potential sources of error, as well as what could be done to minimize errors. Attach your graphs to the printout and return these to your lab instructor at the beginning of the next lab meeting.
References
1. Margaria R, Aghemo P, & Rovelli E (1966). Measurement of muscular power (anaerobic) in man. Journal of Applied Physiology 21(5): 1662-1664.
2. Margaria R, Aghemo P, & Rovelli E (1965). Indirect determination of maximal O2 consumption in man. Journal of Applied Physiology 20: 1070-1073.