Linea Bartel
Nelson Kilmer
PHYS 203
2 October 2007
Physics and Body Mechanics
The human body is an amazing and intricate example of how physics manifests itself in
our everyday lives. Our skeletal muscles and joints are a complicated system of levers which
allow us to move our bodies. Without them, we would simply be shapeless balls of fat rolling
around on the ground. Movement of our bodies is not something that we generally think about in
a critical manner.
In order to better understand the way that physics ties in with the movement of our
bodies, we will examine basic muscle physiology, Newton’s laws of movement, the concept of
torque, how joints and levers work and finally explore some new technology dealing with
artificial muscles.
There are three types of muscle in
the human body: Skeletal muscle, cardiac
muscle and smooth muscle. The physics of
movement in the body only concerns
skeletal muscle. A skeletal muscle consists
of many muscle fibers, each of which are
muscles in their own right. Muscle cells
are long and cylindrical cells that can
contract when stimulated by nerve signals.
Each muscle consists of bundles which
have smaller fibers contained within them.
This is illustrated in Figure 1. Skeletal
muscles are attached to the bones by
connective tissue called tendons. When
muscles contract, this allows them to move
the bones (Campbell 1066).
Myofibrils are the smallest muscle fiber. Each muscle is made up of bundles of
myofibrils which are tightly packed together in a parallel fashion. They consist of proteins called
actin and myosin. When a muscle fiber is relaxed, these proteins do not overlap each other.
However, when a muscle fiber is stimulated, the muscle contracts by pulling these proteins next
to each other. Because this occurs in every myofibril, the entire muscle will shorten, allowing it
to move the bones to which it is attached (1067-1068).
The human body’s system of bones and skeletal muscles is not only a means of
movement. It must be able to support weight even when it is not moving. If we think of the
human body as a mechanical structure, we can define the ways that the body supports its own
weight. Weight can be supported by sitting or resting on something, by hanging from something
or by being braced in place (Garfield 27).
In physics, the most basic rules when it comes to movement are Newton’s laws of
motion. Newton’s first law is also called the law of inertia. It states that an object at rest tends
to stay at rest and an object in motion tends to stay in motion with the same speed and in the
same direction unless acted upon by an unbalanced force (Physics Classroom). In other words,
an object will keep doing what it is doing until acted on by another force to do otherwise.
Inertia is the tendency for an object to resist changes in its pattern of motion. In
rotational motion, an object rotates around a fixed axis and remains stationary in space.
Therefore there is no kinetic energy associated with translational motion. This doesn’t seem to
make sense, but if we adopt the idea that each object is made up of an infinite number of
particles, we can see that each of these particles are in fact moving through space. Since we
know that the angular speed is the same for each of these particles, we can define inertia as:
I = Σ mi ri. Therefore, we can say that the total kinetic energy of a rotating object (such as the
forearm from the axis of the elbow) can be expressed using this equation: KE = ½ I ω². This is
important, because it enables us to see that kinetic energy of an object is directly proportional to
its inertia (Serway 300).
Sir Isaac Newton promoted the idea of this law in a time where other theories were much
more popular. In fact, the theory that was most commonly taught was the idea that objects
would tend to come to rest rather than stay in motion. Galileo was the first scientist to describe
inertia as a tendency of movement. Newton expanded on Galileo’s theory, stating that if an
object is placed in motion, such as a book sliding across a table; it is not the lack of force that
stops the book from moving, but rather the force due to friction that stops the book (Physics
Classroom).
Newton’s second law states that the rate of
change of momentum in an object is proportional to
the force acting on it and is in the direction of the
force. The third law states that for every action, there
is an equal and opposite reaction. When we look at
both of these laws together, we can get a better idea of
why the body moves in the way that it does.
Muscle contraction creates force on the bones
to which it is connected. In any kind of movement,
muscles do work. This means that not only are
muscles the means by which bones move, but they are
able to control the movement as well. We can see
Newton’s third law present in our movement with
respect to the earth. When we move, jump or run, the
force with which we push down on the ground is met
equally and in the opposite direction by the earth. It is
obvious that when we jump, we don’t change the
location of the earth (Garfield 28-29).
Torque is a measure of how much a force acting on an object causes that object to rotate.
Since muscles and joints act in a hinge or lever, the force acting on the bones by the muscles can
be described as angular movement. Torque is a vector quantity. In fact, torque is defined as the
vector cross product between the displacement vector (or radius) and the angular force vector
applied to the radius. The direction of torque is very important when using it in calculations. To
find the direction of torque, we can use the right hand rule. The right hand rule states that if we
put our fingers in the direction of r, and curl them to the direction of F, then the thumb points in
the direction of the torque vector (Torque).
The equation for torque (expressed as the Greek letter tau, τ) is defined as the following:
τ = rFsinφ. Where r is the radius of the object, F is the applied force and φ is the angle at which
that force is applied. Torque can also be found using the equation τ = Fd where F is the applied
force and d is the perpendicular distance from the pivot point to the line of action, F. These
equations help us see that torque is a product of a force vector and a displacement vector. It is
important to realize that torque is not the same as force or work. It is measured in Newton ·
meters, a unit of force times length (Serway 306).
Examples of places where torque may
occur are present in all joints in the human
body. The most common and perhaps the
easiest example to understand is the human
arm. If we define the elbow joint (labeled F),
then torque can occur in both the upper arm
and the lower arm. Let’s concentrate on the
lower arm for this example. The radius would
be defined as the distance from the axis (the
elbow) to the end of the hand. Let’s say a
force is applied in such a way that would
cause the angle of the elbow to increase, for
example, the weight of a ball being held in the
hand. This would cause torque on the system
because a force is being applied to cause the
object to rotate about a fixed axis.
Let us then say that a force is applied to the upper arm. For example, the bicep muscle
contracts, causing the angle of the elbow to decrease. This would cause another torque on the
system of the arm. The torque of the entire system can be found by adding together the torques
of all of the different forces of the object. It is important to consider the direction of torque when
magnitudes of different torques are added together. The direction of torque can be found using
the right hand rule. If you take your right hand and wrap it around a rotational axis with your
fingers pointing in the direction of the force, then the direction of torque will be in the same
direction as your thumb. This is a useful tool when trying to conceptualize the idea of the
direction of torque (Torque).
A lever is a type of machine. A machine is any device that helps us to do work. We use
machines to transform energy, or to transfer it from one place to another. Machines can be used
to multiply force, multiply speed and change direction of force. There are six different kinds of
simple machines: a lever, a block, a wheel and axle, the inclined plane, the screw and the gear.
In physics, the only two basic principles in machines are those of the lever and the inclined plane
(Levers).
A lever is made up of three basic parts. These are the fulcrum, a force (also called an
effort) and a resistance (also called the load). The fulcrum is the pivotal point of a lever, the
effort is the force that is applied to one part of the lever and the resistance is at the other end
working against the force of the effort. Perhaps one of the simplest examples of a lever is a
seesaw.
There are three defined classes of levers. A first class
lever is the simplest. It has the fulcrum lying between the
effort and the resistance (load). In a first class lever, the
amount of weight and the distance from the fulcrum can be
varied to comply with what is needed. An example of a first
class lever in the human body is the triceps muscle of the arm.
In this example of a first class lever, the elbow is defined as
the fulcrum and the hand as the load. The effort is then made
by the triceps muscle as seen in the first picture.
A second class lever is one in which the fulcrum lies at one
end with the effort at the other end. The load then lies in the middle
of the effort and the fulcrum. An example in every day life of a
second class lever is a wheelbarrow. In the human body, an example
could be the ankle joint. The fulcrum would then be defined as the
foot, with the effort being the contraction of the calf muscle. The
load then would be the weight of the person. This can be seen in the
second picture to the right.
The final class of levers is called the third class lever. In this
kind of lever, the fulcrum is located at one end and the load is at the
other end of the lever arm. The effort then is located between the
fulcrum and the load. An example of a third class lever in the
human body is that of the biceps muscle in the arm. The third
class lever action is the primary reason why our arm is able to
flex so quickly and with so much force.
First and second class levers are often used to help
overcome a large resistance with an effort that is fairly small by
comparison. A third class lever will help speed up the
movement of resistance even though a large amount of effort
will still need to be used. However, third class levers are
generally used to do something quickly and not to do extremely heavy jobs (Levers).
As we have seen, there are many examples of levers present in the human body. As we
have seen, joints act in a centripetal motion. Perhaps to understand all of the forces present in a
joint, we should look at what forces are present in a hinge. A hinge is very similar to a joint in
the way that it is constructed. In fact, a joint is a type of hinge.
A jointed structure allows two nodes to be attached to each other in a flexible way so that
the forces in the plane of the joint will be transmitted through the joint, but forces perpendicular
to the plane of the joint will cause the joint to bend. Joints can be thought of as a set of
constraints on the dynamics of the individual masses which are joined together. The constraints
can be summarized by equations (Baker).
The forces present in
a joint are shown in the
figure to the right. Fa is the
external force acting on the
center mass of object A. Fb
is the external force acting
on the center mass of object
B. The torques present in
the system are Ta and Tb.
No other forces are acting on
the system. There is no
torque between the two
masses because a hinge is
used for that movement.
It’s fairly safe to say that not many huge scientific strides have been made very recently
when it comes to dealing with muscle physiology, Newton’s laws of motion, torque and levers.
However, within the past 5 years, some very interesting and very applicable discoveries have
been made in the production of artificial muscles. Not only could this be a new and interesting
way to look at the physics of the human body, but could also be widely used for patients of
physical therapists dealing with muscle wasting diseases or artificial limbs.
These artificial muscles are made from electroactive polymers (EAP’s). EAP’s move in
response to an electrical impulse, in the same way that a real muscle would contract. Polymers
that change their shape in response to an electrical impulse can be placed into two different
groups. The first group is ionic EAP’s. These work because of electrochemistry, which is the
way that charged ions move. They run off of batteries, but often need to be in a wet environment
in order to work properly. The second group is electronic EAP’s. These work because of
electric fields. They require fairly high voltages in order to work and because of this, can cause
an uncomfortable electric shock. They do not need a coating like ionic EAP’s, however, and can
deliver strong mechanical forces with a very quick reaction time (Ashley 54).
When insulating plastics are exposed to an electrical field, contract in the direction of the
field and expand in the direction perpendicular to the field. This is called Maxwell stress.
EAP’s are basically two charged plates that have an elastomer film contained in the middle of
them. When the electric impulse is turned on, the positive and negative charges in the opposite
electrodes attract each other and travel down the insulator. This expands the area of the plastic.
These elastomers can grow up to 400 percent their original size when activated (Ashley 55).
The uses for these devices can not only be found in the human body, but can also be
applied elsewhere. SRI International, a nonprofit research laboratory from Menlo Park, CA has
been at work developing various products using EAP’s. A few of the concepts include
loudspeakers, pumps, power generators as well as smart surfaces that might be able to conform
to the texture of a surface on demand (Ashley 58).
In conclusion, it is obvious that the physics of the human body has many components not
even touched by this research paper. Getting to know the physics of body mechanics through
discovering basic muscle physiology, Newton’s laws of motion, torque, forces within joints and
new strides in technology are all important when learning more about the subject.
So the next time you are in the weight room doing curls, think about the angular
momentum necessary to lift that weight. When you’re bored in class and you begin to kick your
feet back and forth, remember how Newton’s third law applies to the forward swing of your foot
by bringing it back again. The physics of body mechanics are present all of the time in our
everyday lives and isn’t something we normally think about. Keep it in mind. It will help you to
better understand your body and why it behaves in the way that it does.