MECHANICAL WORK, ENERGY, AND POWER - Biomechanics and Motor Control of Human Movement - page 146

0.1 s, the mechanical work done is 10 J. This means that 10 J of mechanical
energy has been transferred from the muscle to the limb segments. As the
example in Figure 6.6 shows, power is continuously changing with time.
Thus, the mechanical work done must be calculated from the time integral
of the power curve. The work done by a muscle during a period t 1 to t 2 is:

t 2

W m = P m dt J (6.2)

t 1

In the example described, the work done from t 1 to t 2 is positive, from t 2
to t 3 it is negative, from t 3 to t 4 it is positive again, and during t 4 to t 5 it is
negative. If the forearm returns to the starting position, the net mechanical
work done by the muscles is zero, meaning that the time integral of P m from
t 1 to t 5 is zero. It is therefore critical to know the exact times when P m
is reversing polarities in order to calculate the total negative and the total
positive work done during the event.

6.0.8 Mechanical Work Done on an External Load
When any part of the body exerts a force on an adjacent segment or on an
external body, it can only do work if there is movement. In this case, work
is defined as the product of the force acting on a body and the displacement
of the body in the direction of the applied force. The work, dW , done when
a force causes an infinitesimal displacement, ds ,is:

dW = Fds (6.3)

Or the work done when F acts over a distance S 1 is:

S 1

W = Fds = FS 1 (6.4)

0

If the force is not constant (which is most often the case), then we have
two variables that change with time. Therefore, it is necessary to calculate
the power as a function of time and integrate the power curve with respect
to time to yield the work done. Power is the rate of doing work, or dW/dt .

dW
dt

F ds
dt

P = =

= F · V (6.5)

= instantaneous power, watts

where: P

=

F force, newtons

V = velocity, m/s