Chapter 1

The branch of physics called mechanics deals with forces on the motion of bodies.

It was the first branch of physics to be successfully applied to living systems.
The study of mechanics began a long time ago.
It can be traced back to the Greek philosophers.
The first to apply physical principles to animal movements were the early Greeks.
The animal that moves makes a change of position by pressing against something beneath it.
The search for general principles in nature by the Greek philosophers marked the beginning of scientific thought.

After the decline of ancient Greece, the pursuit of all scientific work entered a lull that lasted until the Renaissance.

Leonardo da Vinci made detailed observations of animal motions.
Hundreds of people have contributed to our understanding of animal motion since da Vinci.
Improved analytic techniques and the development of instruments have aided their studies.

The development of artificial limbs and mechanical hearts is an active area of research.

Every other subject in science starts with a certain number of basic concepts and then supplies the rules by which they are interrelated.

The basic concepts in mechanics are summarized in Appendix A.

We will look at static forces that act on the human body.

We will discuss stability and equilibrium of the human body, and then we will calculate the forces exerted by the skeletal muscles on various parts of the body.

Every small element of mass in the object is attracted by the Earth, which exerts an attractive force on the mass of the object.

The total weight of the body is the sum of these forces.
The center of mass or center of gravity is where this weight can be considered a force.
A body is in static equilibrium if both the forces and the Torques on the body are zero.
The body is not in equilibrium if it is not supported.
In order for a body to be stable, it must be supported.

The center of mass with respect to the base of support deters mines if the body is not stable.

If the center of mass is directly over the base of support, the body is in stable equilibrium.
The force of gravity and the Torque produced by it are canceled out by the reaction force at the base of support.
If the center of mass is outside the base, the weight will cause the body to topple.

The more stable the base on which the body rests, the harder it is to topple it.

The same amount of displacement of a narrow-based body will cause it to topple.
If the center of gravity is closer to the base, a body is more stable.

Maintaining the center of gravity above the feet is required for balancing.

A person falls when his center of gravity moves beyond his feet.

The body tends to compensate by bending and extending the limbs so as to shift the center of gravity back over the feet.

The constant bending of the torso can cause a permanent distortion of the spine for people who have lost an arm.

It is recommended that amputees wear an artificial arm if they can't use it.

The downward force of weight may not be the only force that the body is subject to.

We can calculate the force applied to the shoulder that will topple a person.

A person is carrying something.

Assuming he doesn't slide.

A force was applied to a person.

A person can resist a much greater sideways force by bending the torso in the opposite direction to the applied force.

There is a side-pushing force.

There are many thousands of parallel fibers wrapped in a flexible sheath that narrows at the ends of the muscles.

The muscles are made of strong tissue and grow into the bone.
The majority of muscles have a single tendon.
The muscles are attached to a bone.
The two bones attached by muscles are free to move at the joints where they contact each other.

Leonardo da Vinci wrote, "The muscles always begin and end in the bones that touch one another, and they never begin and end on the same bone."

Spreading the legs increases stability.

Da Vinci's observation about the pulling by muscles is correct.

The nerve endings in the muscle contract when they receive an electrical signal.
This results in a shortening of the muscle and a pulling force on the bones that hold it in place.

The pulling force that a given muscle can apply is variable.

The force of contraction is determined by the number of individual fibers in the muscle.

When a fiber gets an electrical stimulation, it contracts to its full ability.
A larger number of fibers are stimulated to contract if a stronger pulling force is required.

Experiments have shown that a muscle's cross section affects its maximum force.

It has been estimated that a muscle can exert a force of about 7 x 106 dyn/ cm2 of its area.

A drawing of a muscle.

The various joints in the body can be analyzed in terms of levers.

Some assumptions are simplified by a representation like this.
We will assume that the bones are connected to the tendons at well-defined points.

In the real world, simplifications are needed to calculate the behavior of systems.

Even when the system is known, consideration of all the details is not necessary.

It is assumed that a model is a good representation of the real situation in a calculation.

Load lifting and movement from one point to another can be accomplished with lyres.

The fulcrum is between the applied force and the load in a Class 1 lever.

A Class 1 lever is an example of a crowbar.
In a Class 2 lever, the force is applied to the other end and the load is in between.

A wheelbarrow is an example of a lever.

A Class 3 lever has a load at one end and a load at the other.
The force is applied to both ends.
Class 3 levers are used for many of the limb movements of animals.

The force needed to balance a load is smaller than the load.

The mechanical advantage of a Class 1 lever can be larger or smaller depending on the distance from the fulcrum.

A large mechanical advantage can be obtained with a Class 1 lever.
The mechanical advantage of a Class 2 lever is greater.
The situation is different in a lever.
The mechanical advantage is always less than one.

The load will be lifted by a force slightly greater than what is required.

The load's speed is 1 The relationships apply to all levers.

The mechanical advantage is related to the excursion and velocity of the load.

The biceps and the triceps are the most important muscles for elbow movement.

The opening of the elbow is caused by the contraction of the triceps and the closing of the elbow by the biceps.

We will only consider the action of the two muscles in the analysis of the elbow.

There are many other muscles that play a role in elbow movement.
As the elbow moves, some of them help the joints at the shoulder.

The arm is pulled downward by the weight.

The muscle force on the lower arm must be in the up direction.
The biceps is the most active muscle.
The upper arm is fixed by the shoulder muscles.

The answer will be provided by the calculations.

The equations alone aren't enough to determine the three unknown quantities.

The equation is obtained from the conditions for equilibrium.

The point for our Torque balance will be chosen for convenience.

The fulcrum's Torque must be zero.

The forces on the joint and muscle are large.

The force that the muscle exerts is much greater than the weight it holds.
This is the case with the muscles in the body.

They all use levers that have a mechanical advantage that is less than one.

The arrangement provides for greater speed of the limbs.
Nature likes speed to strength.
The speeds at the limbs are remarkable.
A skilled pitcher can throw a baseball at a high rate of speed.
This is the speed of his hand when he releases the ball.

The hip joint and simplified lever representation are typical of a male body.

The angle of this force with respect to the horizon is about 71.

The weight of the body is supported by this force.

The result is used in Eq.

The calculation shows that the force on the hip joint is more than the weight of the person.

The hip joint has a force of 1625 N.

Persons who have an injured hip limp by leaning toward the injured side as they step on that foot.

As a result, the center of gravity of the body shifts into a position more directly above the hip joint, decreasing the force on the injured area.
The forces applied during a one-legged stance have been reduced.

The spine pivots when the trunk is bent forward.

We will look at the forces involved when the trunk is bent at 60* from the vertical.

The effect of 1 can be seen by a weight suspended in the middle.

Two people are at the end of a lever arm.
The muscle has an angle between it and the spine.
320 N is 72 lbs and 160 N is 36 lbs.

The solution of the problem is an exercise.

A person is walking on an injured hip.

This example shows how large forces are exerted on the fifth lumbar vertebra.

It's not surprising that backaches are the most common at this point.
The recommended way of lifting a weight is not shown in the figure.

This lever is a Class 1 lever.

The balancing force is provided by the muscles on the heels.

The position of standing on tiptoe is strenuous.

The forces on the human body are static.

They are constant in time.
The human body is a dynamic system that responds to stimuli generated internally and by the external environment.

Because the center of gravity is less than the height of the soles of the feet, even a slight displacement can topple the body.

The simple act of standing upright requires the body to be in a constant back and forth, left and right swaying motion, keeping the center of gravity over the base of support.

In a typical experiment designed to study this aspect of posture, the person is instructed to stand, feet together, as still as possible, on a platform that records the forces applied by the soles of the feet.
To compensate for the shifting center of gravity, the center of pressure is constantly shifting over the area of the soles of the feet on a time scale of about half a second.
The ankle movements compensated for small back-and-forth perturbations of the center of mass.
Hip movements have to compensate for larger displacements.

As the support for the center of gravity shifts from one foot to the other, a series of compensating movements are needed to maintain balance.

Keeping the body upright is a very complex task for the nervous system.
The performance of this task is remarkable when we slip and the center of gravity is displaced.
An erect human body that looses its balance will hit the floor in about 1 second.
The whole muscular system is called into action by the "righting reflexes" to mobilize various parts of the body so as to shift the center of mass back over the base of support.
In the process of restoring balance, the body can perform amazing contortions.

The nervous system can get information from three sources: vision, the vestibular system and the somatosensory system.

An increasing number of injuries due to falls are caused by the decreasing efficiency of the functions required to keep a person upright.
The United States has a higher rate of accidental deaths due to falls for people over the age of 80 than it does for people under the age of 70.

The interconnectedness of the musculoskeletal system is one of the aspects of the body dynamics.

A change in muscle tension or limb position in one part of the body must be accompanied by a change in other parts of the body.
The system can be seen as a tentlike structure.
The tent poles and the muscles are the things that bring the ropes into and balance the body.
The proper functioning of this type of structure requires that the forces be distributed over all the bones and muscles.
The tent collapses if the tension in the back ropes is not increased.
The same thing happens with the musculoskeletal system.
The large muscles at the front of our legs tend to pull the torso forward.
The muscles in the back have to tighten to compensate for the forward pull.
Excess tension in one set of muscles may be seen as pain in another part of the body.

The person's weight is distributed on both feet if they don't slide.

The relationships were stated.

The lower part of the arm is no longer horizontal.

Information is provided in the text.