Chapter 5 The Muscular System 169
time. The tension may be constant (for example,
when a gymnast holds a motionless handstand),
or it may vary cyclically (for example, during
running, cycling, or rowing). Generally, the
longer the physical activity is maintained,
the greater the required muscular endurance.
Because the force and speed requirements of
different movements can vary signifi cantly, the
Figure 5.13 Calculating Muscle Force
Fm (muscle force)
W (weight)
dW
dF
Joint center of rotation
Do you know how much force
your muscle must generate to hold
a fi ve-pound weight in the position
shown in the illustration? Let’s see
if we can calculate the amount of
force needed.
To hold the weight in this
position, the torque at the elbow
joint generated by the muscle
(muscle torque) must balance the
torque produced by the weight
(weight torque) at the elbow.
As you know from reading
this lesson, muscle torque is the
product of muscle force and the
perpendicular distance of that
force from the center of rotation
at the joint. We can state this in a
formula as
Tm = Fm × dF
where Tm = muscle torque, Fm =
muscle force, and dF = the
perpendicular distance.
Weight torque is the product of
the weight and the perpendicular
distance of that weight from the
center of rotation at the joint. This
formula can be stated as
TW = W × dW
where TW = weight torque, W =
weight, and dW = the perpendicular
distance.
Let’s suppose that the weight
in the illustration is 5 pounds, and
that it is being held at a distance
(dW) of 12 inches from the center
of the joint. The distance of the
muscle attachment from the joint
center (d
F
) is 1 inch. How much
force must the muscle produce to
support the weight?
Tm = TW
F
m
× d
F
= W × d
W
F
m
× 1″ = 5 lb × 12″
F
m
= 60 lb
Are you surprised? To support
just 5 pounds in the hand, the
muscle must generate 60 pounds
of force. What can we learn from
this? Because muscles attach
so closely to joints, the human
musculoskeletal system is designed
more for movement speed than for
strength.
Now you try: Suppose that the
weight (W) in this picture is 10
pounds, the dW is 15 inches, and
the dF is 1 inch. What is the Fm?