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The Physics of Body Mechanics

The Physics of Body Mechanics

by:  Linea Bartel

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.

Basic Muscle Physiology

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).  

Newton's Laws of Motion

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 ri².  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

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).

Joints & Levers

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 (Machines). 

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 (Machines).

As we have seen, there are many examples of levers present in the human body.  Also, 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 left.  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.

Artificial Muscles

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).

Conclusion

In closing, 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.


Works Cited

Ashley, Steven.  "Artificial Muscles."  Scientific American Oct. 2003:  53-59.

Baker, Martin J.  "Physics - Jointed Structures."  Euclideanspace.  2007.  1 Oct. 2007

    <http://www.euclideanspace.com/physics/kinematics/joints/jointstructures/index.htm>.

Campbell, Neil A., and Jane B. Reece.  Biology.  7th ed.  San Francisco: Pearson, 2005.  1066-1068.

Garfield, Sally, comp.  Sabbatical Paper:  the Impulse and Physics of Movement.  Drake University.  1 Oct.

    2007.

"Lesson 1:  Newton's First Law of Motion."  The Physics Classroom.  2004.  Mathsoft.  1 Oct. 2007

    <http://www.physicsclassroom.com/class/newtlaws.u211b.html>.

"Levers."  1 Oct. 2007 <http://www.brianmac.co.uk/levers.htm>.

Serway, Raymond A., and Jewett W. John.  Physics for Scientists and Engineers.  6th ed.  Belmont:

    Thompson, 2004.  300-301.

"Machines."  1 Oct. 2007 <http://www.tpub.com/machines/1.htm>.

"What is Torque?"  1 Oct. 2007 <http://www.physics.uoguelph.ca/tutorials/torque/Q.torque.intro.html>.


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LAB 11 - Muscle Physiology

 

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Muscles are the "engine" that your body uses to propel itself. they turn energy into motion. It would be impossible for you to do anything without your muscles. Absolutely everything that you conceive of with your brain is expressed as muscular motion.

Skeletal Muscle Tissue
Muscle is a very specialized tissue that has both the ability to contract and the ability to conduct electrical impulses. Muscles are classified both functionally as either voluntary or involuntary and structurally as either striated or smooth. From this, there emerges three types of muscles: smooth muscle, skeletal muscle and cardiac muscle.

Skeletal Muscle


Elongated cells
Multiple peripheral nuclei
Visible striations
Voluntary

Cardiac Muscle


Branching cell
Single central nucleus
Visible striations
Involuntary

Smooth Muscle


Spindle shaped cell
Single central nucleus
Lack visible striations
Involuntary

Neuromuscular Junction
Skeletal muscle cells contract as a result of impulses from motor neurons. The place where a motor neuron stimulates a muscle cell is called a neuromuscular junction. In order for skeletal muscle cells to contract each cell must be stimulated by a process of a motor neuron.

Sliding Filament Theory
The theory of how muscle contracts is the sliding filament theory. The contraction of a muscle occurs as the thin filament slide past the thick filaments. The sliding filament theory involves five different molecules plus calcium ions. The five molecules are: myosin, actin, tropomyosin, troponin, and ATP.

The myosin molecules are bundled together to form the thick filament. The head (cross bridge) of the myosin molecule has the ability to move back and forth. The flexing movement of the head provides the power stroke for muscle contraction. The hinge portion of linear tail allows vertical movement so that the cross bridge can bind to actin on the thin filament. The cross bridge has two important binding sites. One site specifically binds ATP, a high energy molecule.

This binding of ATP transfers energy to the myosin cross bridge as ATP is hydrolyzed into ADP and inorganic phosphate. The second binding site on the myosin cross bridge binds to actin.

Actin is the major component of the thin filament. Tropomyosin entwines around the actin and covers the binding sites on the actin subunits and prevents myosin cross bridge binding.

Troponin is attached and spaced periodically along the tropomyosin strand. After an action potential calcium ions are released from the terminal cisternae and bind to troponin. This causes a conformational change in the tropomyosin-troponin complex, "dragging" the tropomyosin strands off the binding site.

The five organic molecules and the calcium ions all work together in a coordinated maneuver to cause the thin filament to slide past the thick filament, and are illustrated here.

Muscle Metabolism

The energy necessary for muscle contraction is provided by ATP. ATP energizes the power stroke of the myosin cross bridge, disconnects the myosin cross bridge from the binding site on actin at the conclusion of a power stroke, and energizes the calcium ion pump. In order to make ATP, the muscle does the following: breaks down creatine phosphate, adding the phosphate to ADP to create ATP, carries out anaerobic respiration by which glucose is broken down to lactic acid and ATP is formed, and carries out aerobic respiration by which glucose, glycogen, fats and amino acids are broken down in the presence of oxygen to produce ATP.

Fun Fact - After death, calcium levels inside the muscle cells rise and the body's level of ATP drops. Inside the muscles, myosin binds to actin and the muscles contract. However, with no ATP to reset the cross bridges and release the myosin, all of the muscles remain contracted and stiff. This state is called rigor mortis.

Contraction of Motor Units

The contraction of a skeletal muscle is the result of the activity of groups of muscle cells called motor units. In skeletal muscle, the cells never contract individually. Rather they contract as groups of muscle cells that are collectively connected to a motor nerve originating in the spinal cord. The combination of the motor nerve cell (neuron) and the muscle cells it innervates is known as the motor unit. The size of the motor units determines the precision of movement that a particular muscle can produce.

 

ZOOLOGY 310 GUIDE TO MUSCLE PHYSIOLOGY

 The arrival of an action potential in the T-tubule activates the voltage sensitive dihydropyridine receptors (Ca2+ channels) in the membrane.  These in turn, induce transient opening of the ryanodine sensitive Ca2+ channels in the SR causing Ca2+ to be dumped from the terminal cisternae into the cytosol, and raising the concentration from <10-7 M to >10-4 M.  The Ca2+ combines with TnC and causes exposure of the strong binding sites on the actin filament, initiating contraction.  As the action potential passes, the ryanodine channels close.  The released Ca2+ is soon bound to the calbindin (parvalbumin) in the cytosol, which has a higher affinity for Ca2+  than does TnC, but which combines with Ca2+  more slowly since the Mg2+ to which it is bound, must first be displaced.  The Ca2+ is then transferred to the Ca2+-Mg2+-ATPase in the SR and pumped back into the lumen of the cisternae.  Calcium ion concentration then, rises and falls as a brief pulse in response to the arrival of an AP in the muscle fibre.

This single pulse of Ca2+ released by a single action potential causes a brief contraction then relaxation, known as a twitch. The duration of this twitch varies in different muscle types, and in different types of skeletal muscle fibres.

 

A motor unit is a motor neuron plus all the muscle fibres which it innervates.  When an AP travels down the axon it reaches all the fibres in the motor unit, and all will normally be activated.  The neuron and all its fibres thus act as a unit.  Failure at the mammalian nerve-muscle junction is rare.

The fibres belonging to a motor unit are not normally clumped together, but are interspersed among those from other motor units.  The nature of the motor neuron and its firing pattern influences the characteristics of the muscle fibres in the motor unit.

 

 

 

Muscle twitch in mammalian skeletal muscle

In skeletal muscle the range of contraction times (time to peak) is from 7.5 ms for fast (extraocular muscle: IR- internal rectus); 40 ms for intermediate (G - gastrocnemius); to 90 ms for slow (S - soleus) muscle fibres. Most skeletal muscles have a mixture of different types of fibres: slow; fast oxidative glycolytic (rare); or fast glycolytic. However, all fibres in a given motor unit are of the same type - the type being determined to some extent, by the nature of the motoneurone. Small tonically active motoneurones prompt development of slow fibre types; large, phasic motoneurones favour fast glycolytic fibres.

 

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