Skeletal Muscle Mechanics Joseph Feher, Ph.D. LECTURE OUTLINE:

I. Introduction

A. Muscles either shorten or produce force.

B. Muscles perform diverse functions.

C. Muscles can be classified according to fine structure, neural control and anatomy.

II. Isometric Force is measured while keeping muscle length constant.

A. Experimental Set-up requires a rigid device for measuring force.

B. The muscle twitch depends on the kind of muscle and is longer than the action potential.

1. Slow twitch fibers

2. Fast twitch fibers

3. The action potential is a trigger.

C. Muscle force is determined by the number of motor units that are recruited.

D. Muscle force is determined by the frequency of activation.

E. Muscle force is determined by the length of the muscle.

1. Passive force

2. Active force

III. Isotonic Force is measured while keeping muscle force constant.

A. Experimental Set-up requires an afterload.

B. The twitch here consists of an isometric and isotonic part.

C. The velocity of muscle contraction varies inversely with the force.

D. Muscle power varies with the speed of contraction, load, and muscle type.

1. Power is force x velocity

2. Muscle power peaks at about one-third maximum force

3. Muscle power is 2-3 times greater in fast twitch fibers

4. Muscle power peaks at about one-third maximum velocity

E. Muscles can lengthen during contraction when loaded.

1. Lengthening is a negative velocity: eccentric and concentric contractions

2. Eccentric contractions exert more force

3. Concentric and eccentric contractions have different functions

IV. Muscle architecture influences force and velocity of the whole muscle

A. Muscle force is usually proportional to muscle cross-sectional area

B. Muscle fibers can be oriented at an angle to the direction of force

C. Pinnation increases muscle force but decreases muscle velocity

V. Fatigue is the decrease in force upon repeated stimulation of muscle.

A. Fatigue is produced within a few seconds of maximal stimulation

B. Fatigue of slowly twitch muscles takes longer

C. Muscles can be classified according to their contractile properties

D. Most muscles are heterogeneous mixtures of different muscle fiber types

OBJECTIVES:

1. Distinguish between isometric and isotonic force

2. Recall the approximate twitch times of skeletal muscle and distinguish between fast and slow twitch muscles

3. Define the term “motor unit”

4. Describe what is meant by “recruitment”

5. Describe the size principle

6. Calculate the lowest frequency at which skeletal muscle begins to show summation

7. Distinguish between active force and passive force when muscles are stretched

8. List three ways of grading force and describe their physiological role

9. Describe the relation between force and velocity

10. Describe the force and velocity at which maximum power output occurs

11. Distinguish between concentric, isometric and eccentric contractions

12. Describe the relation between muscle size and force

13. Describe the effect of pinnation on muscle force and velocity

14. Define fatigue

15. Distinguish muscle types on the basis of contractile properties

Suggested Reading: Berne and Levy, pp.242-245; 236-237

I. INTRODUCTION

A. Muscles either shorten or produce force The primary action of a muscle is to contract. The usual use of this word means to shorten, but physiologists often use it to mean to activate the muscle. Activation of the muscles can produce force without actually shortening, as you might do when holding something really heavy. Also, activation of muscles is used to decelerate motion, and under these circumstances muscles can actually lengthen.

B. Muscles perform diverse functions

1. Muscles that are connected to the skeleton (skeletal muscles) move one bone relative to another. These muscles allow us to lift weights and to move ourselves from place to place. These muscles also include the tongue, the muscles that move the eyeballs, and the upper third of the esophagus.

2. Muscles surrounding hollow organs. (heart, urinary bladder, gall bladder, uterus) develop tension in the walls that produces pressure within the organ according to LaPlace’s Law. Pressure propels material out of the organ.

3. Muscles in long hollow tubes ( the GI tract, the arterioles, the ureters and the airways) set the diameter or the length and may propel material by peristalsis. These are generally smooth muscle.

4. Muscles produce heat when activated. This is the reason for shivering thermogenesis.

C. Muscles can be classified according to fine structure, neural control, and anatomical arrangement.

1. Muscles are striated or smooth

2. Anatomic classification includes skeletal, cardiac and visceral muscles

3. Neural control is voluntary or involuntary.

CLASSIFICATION OF MUSCLE

Figure 1. Classification of muscle can be based on control properties, anatomical properties, or the fine structure observed histologically. The preferred classification is that highlighted in the figure, which is a mixture of several classification schemes.

II. ISOMETRIC FORCE is measured while keeping muscle length constant

A. The experimental set-up requires a rigid device for measuring force

Figure 2. In this set-up, action potentials on the nerve are initiated by an external stimulator. The muscle is tied at one end to a stiff force transducer. Because the shortening of the muscle is very small, this contraction is called an isometric contraction. A single stimulation causes a single action potential in the nerve, then in the muscle, and then a single contraction of the muscle, called a muscle twitch.

B. The time of the muscle twitches depends on the kind of muscle and is longer than the action potential

1. A very brief (5 ms) stimulus causes a single muscle contraction called a muscle twitch. Force rises and then falls without the muscle shortening. The time for the force to rise is shorter than the time it takes to fall. When a gastrocnemius muscle of a rat is used, the twitch time is about 50 milliseconds. When the soleus muscle is used, the twitch time is over 150 ms. Thus, muscles can be distinguished because of their contractile properties, including their twitch times. The gastrocnemius is an example of a fast-twitch muscle; the soleus is a slow-twitch muscle.

2. The recording in Fig. 2 also shows that the action potential on the muscle lasts only a few ms, whereas the twitch lasts much longer. The action potential is a trigger for the muscle contraction.

C. Muscle force depends on the number of motor units that are activated

1. When the strength of the stimulus is gradually increased, the force of the twitch also increases until the force reaches a plateau, as shown in Fig. 3. Two questions: why does it take volts to stimulate the muscle and why does force increase with increasing strength of stimulation?

Figure 3. Increase in the muscle twitch with increased recruitment of motor fibers by increasing the strength of the external stimulus.

2. The motor nerve supplying the muscle is a bundle of motor neurons. The extracellular stimulus depolarizes the axons by passing an inward current across their membranes, but most of the current from the extracellular electrode does not go across the axon membrane. Thus, higher voltages are necessary to depolarize all of the axons in the bundle. This is why volts are necessary for the external stimulus, when only a few millivolts of membrane depolarization is needed to initiate an action potential.

3. Each motor nerve branches and connects to a set of muscle fibers, making a neuromuscular junction with each of them. The motor neuron and all of the muscle fibers it innervates make up a motor unit. The entire muscle consists of a large number (many thousands) of muscle fibers that are each enclosed in a plasma membrane called the sarcolemma. These are generally large, multinucleated cells. The

cells are typically 20-100 μm in diameter and can be many cm long. Each muscle fiber is typically innervated by a single motor neuron, typically in the middle of the fiber. However, motor neurons typically innervate more than one muscle fiber.

Figure 4. The motor unit consists of a motor neuron and all of the muscle fibers innervated by it. Here motor neuron 1 innervates fibers A, B, and C; motor neuron 2 innervates fibers D and E. When only motor neuron 2 fires an action potential, only fibers D and E contribute to the force developed by the muscle. When only motor neuron 1 fires an action potential, only fibers A, B and C contribute to the force. When both motor neurons fire an action potential, all of the muscle fibers contribute to the force. Thus, the force is greater when more motor units are recruited.

Figure 5. Intact nerve and extracellular electrode that stimulates it. As the strength of the stimulus increases, more axons are activated until, eventually, all axons fire action potentials. Since each axon innervates a set of muscle fibers, called its motor unit, progressive activation of axons causes progressive increases in the number of activated muscle fibers, and progressive increases in the total force produced by the muscle.

4. The increase in force with increasing number of motor units is called recruitment.

a. People can grade muscle force by recruiting motor units. We can vary the force a muscle produces more or less continuously from small to large forces. This means that muscle force is not all-or-none; it is graded. This variation is brought about by recruiting progressively more and more motor units until all of the motor units are activated. Although the gradation is fine, it is not really continuous because muscle fibers are activated in a discrete (as opposed to continuous) way. Because there are so many muscle fibers, the force appears to vary nearly continuously.

b. The motor units are recruited in order of their size. This is called the size principle. Large motor units are innervated by large motor neurons, and smaller motor units are innervated by smaller motor neurons. The small motor neurons are more excitable, so these are recruited first. This makes subjective sense. Delicate movements that require dexterity but little force are accomplished by recruiting small numbers of muscle fibers. Gross motor movements that involve a lot of force use large increments of force by recruiting successively larger motor units.

D. Muscle force can be graded by the frequency of motor neuron firing.

1. The action potential is short compared to the muscle twitch. The action potential on the motor neuron is very short, 1-2 ms. Similarly, the action potential on the muscle cell membrane is also short, on the order of 3-5 ms. The muscle twitches are long by comparison, some 30 -200 ms, depending on the muscle type. Therefore, we can stimulate the muscle with another action potential before the muscle has relaxed. Indeed, we can stimulate a muscle again before it reaches its peak tension. What happens when we do this? Fig.6 shows the results of varying the frequency of stimulation at maximum recruitment.

Figure 6. Gradation of muscle force by the frequency of stimulation. 2. Repetitive stimulation of muscle results in summation of force.

Fig. 6 shows that when a muscle is stimulated before it has completely relaxed, there is a new twitch that begins force where the first twitch left off, resulting in a greater force. Thus, muscle force summates with repetitive stimulation. When the frequency of stimulation is great enough, the muscle produces a single forceful contraction during the period of stimulation, with no waviness in the force. This condition is called tetanus.

3. The tetanic frequency varies with muscle type. The frequency required to reach tetanus depends on how fast the muscle contracts and relaxes. If the muscle twitch is 100 ms long, then summation will just begin when the next stimulation arrives at the end

of relaxation. Since there are 10 100 ms intervals in a second, summation for such a fiber should begin at a stimulation frequency of about 10 Hz. (Hz is a Hertz, meaning a cycle per second; 10 Hz is therefore 10 cycles or events per second). Typically most muscles in the human tetanize between 20 and 100 Hz. The lowest frequency that shows summation is the inverse of the twitch time: f = 1/p, where f is the frequency and p is the period, or duration, or the twitch.

4. People can grade muscle force by the frequency of motor neuron firing. In addition to recruitment, summation is one of the main ways we have of grading muscle force. We grade the force of a muscular contraction by altering the frequency of motor neuron firing.

5. Tetanic force is much greater than the twitch force. As you can see from Fig. 6, the tetanic force is much greater than the twitch force. In general, tetanic force is about 5 times larger than the twitch force, but the tetanus/twitch force ratio varies from about 2 to 10 in different muscles.

E. Muscle force also depends on the length of the muscle

1. Stretching a muscle produces a passive force. The device shown in Figs. 2, 3 and 6 can be adjusted to vary the length of the muscle. When muscles are relaxed, they exert no force. However, when they are stretched without activation they produce a passive force. This is due to elastic properties of the muscle material itself and not to the development of force that depends on activation of the muscle. This passive force increases steeply with increases in length. The dependence of the passive force on the length of the muscle is curvilinear.

2. The active tension rises and then falls with stretch of the muscle. When the muscle is stimulated tetanically, it produces a force in addition to the passive force. This force is called the active tension because it depends on activation of the muscle by the stimulus. The additional active force produced by stimulation depends on the length of the muscle. The active force added by stimulation increases to a maximum and then declines with further increases in muscle length.

The relation between active force and muscle length is the length-tension curve.

Figure 7. The length-tension relationship in muscle. 3. Physiologically, muscles operate near the maximum of their length-

tension curve. Muscles have a resting length, L0, that is typically at the top of the active length-tension curve, and close to the zero point of the passive length-tension curve. This means that antagonist muscles pairs do not fight against each other. Because muscles are attached to the skeleton, their shortening is defined by the movement of the bones and the origins and insertions of the muscles. Most muscles do not shorten or lengthen by more than about 30% of their rest length. For this reason, length is not an important variable in determining muscle strength compared to recruitment and frequency of stimulation.

4. There are three ways to vary muscle force: recruit muscle fibers, vary the frequency of activation, and vary the length. Of these, recruitment and varying the frequency of activation are physiologically most important.

III. ISOTONIC FORCE is measured when the muscle exerts a constant force.

A. The experimental set-up requires an afterload. The afterload is a weight supported by a shelf prior to activation of the muscle. Thus, the muscle does not feel the afterload until after the muscle has begun to contract.

Figure 8. Experimental set-up for measuring the force and velocity of isotonic contractions. B. The twitch in an afterloaded muscle is divided into two parts: an isometric

part and an isotonic part. When the muscle is stimulated, it cannot shorten until it produces a force equal to the afterload. It takes some time for the muscle to develop this force, and during this time it doesn’t shorten - the contraction is isometric. After the muscle develops a force equal to the afterload, it lifts the afterload and continues to shorten, keeping an approximately constant force while it shortens. Because the force is constant during this interval, the contraction is called an isotonic contraction.

C. The velocity of muscle contraction varies inversely with the afterload. Everyday experience shows that the speed of muscle contraction depends on the load that must be moved. We know that we can move a light load quickly, whereas we move a heavy load slowly. The force-velocity curve is produced by measuring the initial velocity and plotting it against the

afterload. The initial velocity can be measured using a device such as that shown in Fig. 8, where the afterload is varied. The force-velocity curve is shown in Fig. 9. A.V. Hill first described this as a hyperbolic relationship. More recent studies suggests that at the high force side it deviates from a single hyperbolic relation. These force-velocity curves vary with muscle length.

Figure 9. The force-velocity curve for an intact fast twitch or slow twitch muscle.

D. Muscle power varies with the speed of contraction, the load and the muscle type.

1. Power is the force times the velocity. Power is defined in physics as the rate of energy production or consumption. Thus, power has the units of energy per unit time. In mechanical terms, energy is work. Work is further defined in mechanics as force x distance. Thus, we have the following: Power = Energy / time (1) Energy = Work (2) Work = Force x distance (3) Inserting eq. (3) into eq. (2) and then into eq. (1), we get: Power = Force x distance / time (4) From the definition of velocity, Velocity = distance / time (5) We get: Power = Force x velocity (6)

Figure 10. Power-force curve for slow-twitch and fast-twitch muscles.

2. Muscle power peaks at about one-third maximal force. The force-velocity curve is displayed in Fig. 10. We can obtain the power-force curve by multiplying force and velocity at every point on the force-velocity curve. This power is the instantaneous power produced during the initial shortening of the muscle. Power is usually expressed in units of watts, or N-m s-1, per unit weight of muscle.

3. Muscle power is about 2-3 times greater in fast twitch fibers than in slow twitch fibers.

The results of Fig.10 show that the maximum force is not different for slow and fast twitch muscles, but the power is about 2-3 times greater in fast twitch fibers because of their greater speed of contraction.

4. Muscle power varies with speed of contraction and muscle type.

The muscle power can be plotted against the load, as in Fig. 10, or against the speed of contraction, as in Fig. 11 below. The two curves come to very different conclusions. The conclusion of Fig. 11 is that the contribution of slow twitch fibers to the power of a contracting muscle depends on its speed. During rapid contractions, the slow twitch fibers make almost no contribution to the power, whereas at slow contractions it makes a large contribution. Power output peaks at about one-third maximum velocity.

Figure 11. Power vs. velocity curve. The dashed lines represent the force-velocity curve and the solid lines are the power plotted against the velocity. Power peaks at about one-third maximum velocity and is about 2-3 times greater in fast twitch fibers than in slow-twitch fibers. In a mixed muscle consisting of both fast and slow twitch fibers, the contribution each fiber type to the power of the muscle depends on the velocity. At rapid contractions, all of the power derives from the fast-twitch fibers. At slow contractions, the slow-twitch contributes much of the power.

E. Muscles contraction can involve a lengthening of a muscle.

1. The force-velocity curve can be extended to negative velocities. According to the way in which we measured velocity, a positive velocity corresponds to a shortening of the muscle. If the support for a very large afterload in Fig. 8 is removed, the large afterload will cause the muscle to lengthen during contraction. This lengthening is a negative velocity of the muscle. Contraction of the muscle during a lengthening is called an eccentric contraction. Contraction of a muscle that causes a shortening is called a concentric contraction.

2. Muscles can exert more force in an eccentric contraction As seen in Fig. 12, muscles can exert about 40% more force in an eccentric contraction compared to the maximal isometric force measured at zero velocity.

Figure 12. Concentric and eccentric contractions. Concentric contractions involve a shortening of the muscle. Eccentric contractions involve a lengthening of the muscle. Isometric contractions occur when the muscle length does not change, and occurs at zero velocity.

3. Concentric and Eccentric contractions have different functions. Table 1 below lists the three types of contractions, their functions for movement and the work performed.

Table 1. Types of Contractions Type of Contraction Distance Change Function Work

Concentric shortening (+D) Acceleration (upstairs)

positive W = F x (+D)

Isometric no change (0 D) Fixation zero

Eccentric lengthening (-D) Deceleration (downstairs)

negative W = F x (-D)

IV. MUSCLE ARCHITECTURE influences force and velocity of the whole muscle

A. Muscle force is usually proportional to muscle cross-sectional area Muscle force is proportional to the size of the muscle, and size is generally taken to be the cross-sectional area at the widest part of the muscle. However, muscles are oddly shaped – they are not regular geometric shapes. Also, muscles generate greatly different forces when the cross-sectional area is the gross muscle area. The angle the muscle fibers make with the tendons contributes to this variability in the gross muscle force.

B. Muscle fibers can be oriented at an angle to the direction of force There are three major orientations of the muscle fibers within muscles: parallel fibers, fusiform and pinnate. The parallel fiber arrangement is present in muscles shaped like a strap, or in parts of flat-shaped muscles. In fusiform muscles, the muscle fibers are parallel to the longitudinal axis of the muscle. In pinnate muscles, the fibers are oriented at an angle to the tendon or aponeurosis. Because of their resemblance to a feather, these are called pinnate or pennate. Both spellings are used. See Fig. 13.

Figure 13. Different arrangement of muscle fibers. Parallel fibers are oriented longitudinally in the direction of the muscle action. Fusiform fibers are tapered. Pinnate fibers are parallel but oriented at an angle to the action of the muscle.

C. Pinnation increases muscle force but decreases muscle velocity The consequence of orienting the muscle fibers at an angle with respect to the tendon is to increase the effective cross-sectional area of the muscle while reducing the distance the muscle can contract along the lines of the tendons. To see this, I have calculated the force and velocity of two different muscles: a strap muscle with parallel fibers having a volume of 300 cm3 and a length of 36.8 cm and a second muscle with pinnate architecture with fibers 12 cm long and an overall length of 36.8 cm, with the same volume as the strap muscle. The pinnate muscle has fibers oriented at 15° to the line of action. The geometry of these two is shown in Fig. 14. Strap muscles such as the sartorius are composed of muscle fibers that do not span the distance from tendon to tendon. The longest muscle fibers are

about 12 cm. Such strap muscles are divided into compartments by fibrous bands called inscriptions. The sartorius muscle has three inscriptions, giving four compartments; the semitendinosus has three compartments, and the biceps femoris and gracilis have two compartments each. Without belaboring the calculations, the results are summarized in the boxes in Fig. 14: the strap muscle has a high velocity but low force compared to the pinnate muscle. The pinnate muscle allows more muscle fibers to get into the act of producing force, while being constrained to its anatomic location and volume. It pays for this force by being slower.

The effect of the pinnate architecture, then, is to increase muscle strength at the expense of muscle speed.

Figure 14. Comparison of a strap muscle, such as the sartorius, with a pinnate muscle. Both muscles are 36.8 cm long and both have a volume of 300 cm3. Because of the orientation of the muscle fibers, the pinnate muscle generates more force at slower velocities than the comparably sized parallel-fibered strap muscle.

V. FATIGUE is the decrease in force upon repeated stimulation of a muscle.

A. Fatigue is produced within a few seconds of maximal stimulation Everyday experience shows us that maximal effort can be sustained only briefly. The more intense the effort, the faster one fatigues. From our earlier sections it should be clear that intense efforts rely predominately on fast twitch fibers. These are more easily fatigued than the slow twitch fibers.

Figure 15. Fatigue of a maximally stimulated muscle (complete recruitment and tetanus) during prolonged stimulation.

B. Fatigue of slowly contracting muscles takes longer to produce Fatigue also occurs when muscles are repetitively used in less powerful movements. This fatigue, however, takes longer to produce, and longer to recover.

C. Muscles can be classified according to their contractile properties. Burke’s system of classification recognizes four types of muscle fibers, based on their contractile properties, include resistance to fatigue:

1. S = slow twitch fibers

2. FR = fast, fatigue-resistant

3. FI = fast, intermediate fatigue resistant

4. FF = fast, fatiguable

D. Most muscles are heterogeneous mixtures of the different muscle types

Most muscles consist of thousands of muscle fibers. In general, muscles contain all of the different fiber types, but differ in the percentage. For example, the soleus muscle in the human consists predominately of slow twitch fibers, whereas the gastrocnemius consists of predominately fast-twitch fibers. Neither are entirely one type or another, however. There is considerable individual variation in the percentages of different muscle fibers that comprise any particular muscle.

V. PRACTICE QUESTIONS

1. An ocular muscle has a twitch time of about 25 ms. Stimulation at maximum recruitment at 20 Hz ( I Hz = 1 cycle per second) for 0.5 s gives

A. An unfused or partial tetanus

B. Tetanus

C. A sequence of twitches separated by 50 ms

D. Slightly greater twitches separated by 20 ms

E. Fatigue

2. Passive tension

A. Is the increment in muscle force upon activation by its nerve

B. Varies linearly with muscle length

C. Increases to a maximum at L0 and then decreases

D. Increases less than linearly with muscle length

E. Is the force measured by stretching a muscle without activating its nerve

3. Muscle A has a cross-sectional area of 10 cm2 and a maximum velocity of 20 cm s-1. Muscle B has a cross-sectional area of 20 cm2 and a maximum velocity of 40 cm s-1. The ratio of their maximum power, PA / PB should be about

A. 0.25

B. 0.5

C. 1

D. 2

E. 4

4. After drinking (= alcohol) a little too much, your somewhat juvenile friend decides to challenge you to a test of strength. The winner is the one who can hold up the heaviest weight in the supine palm of the hand with the elbow at a right angle. The game proceeds by adding successive copies of Dr. Costanzo’s text, Physiology, 3rd edition. Remember, you’ve been drinking. The contraction here is classified as

A. Isometric

B. Concentric

C. Eccentric

D. Isotonic

E. Isovolumic

5. The ability to hold the additional copies of Dr. Costanzo’s text in the above question is achieved by

A. Increasing the frequency of activation of all motor units

B. Activating the large motor units first

C. Successively activating more and more motor units

D. Changing the length of the biceps brachii and brachialis muscle

E. Increasing the magnitude of the action potentials on all of the muscle fibers

6. Mr. Universe’s biceps brachii and brachialis muscles have a total cross sectional area of 160 cm2 whereas a representative puny medical student, “Amy” has a total cross sectional area of only 40 cm2. Mr Universe says he can flex his arm loaded with 25 Kg (!) faster than the student can flex his arm loaded with 10 Kg. A third medical student, “Bill” feels the competition is unfair and challenges them both when his load is 12.5 Kg. His muscles are 100 cm2 in area. Your friendly professor measures peak velocity of movement during a biceps curl. After the competition is over,

what is the order of the finishes? Assume that the length of the arms and positions of origin and insertions of the muscle are identical. (In short, ignore mechanical advantage and focus on the muscles)

A. Universe, Bill, Amy

B. Bill, Amy, Universe

C. Bill, Universe, Amy

D. Universe, Amy, Bill

E. Amy, Universe, Bill Answers:

1. C The twitch time is 25 ms = 0.025 s. This means that summation just begins at 1/0.025 s = 40 Hz. At a stimulation frequency of 20 Hz the twitches are separated by 50 ms, which occurs at baseline and therefore no summation occurs. There is no partial tetanus, no tetanus, and sequence of twitches is separated by 50 ms. tetanus).

2. E The passive tension is the tension developed without activation of the nerve. It varies progressively with distance, being near zero at rest length and increasing faster than linear with length.

3. A Muscle power is proportional to force times velocity. Maximum muscle power is proportional to maximum force, which is proportional to area., and the velocity at maximum power is proportional to the maximum velocity (it occurs at about one-third Vmax). Thus PA α AreaA VmaxA and PB α AreaB VmaxB so PA / PB =(10 cm2 x 20 cm s-1) / (20 cm2 x 40 cm s-1) = 2/8 = 0.25. This ratio is inexact, but it is closer than any other alternative answer.

4. A Isometric. The muscle is not moving when additional weight is placed on it. Isometric contractions keep muscle length constant; eccentric contractions lengthen the muscle; concentric contractions shortens it. Isotonic contractions shorten but keep force constant. Isovolumic contraction refer to the heart’s isometric contraction before the valves open.

5. C This is recruitment. Force is increased by activating more motor units. The smaller ones are activated first (the size principle). Of course, to keep the books held the muscles must be activated in trains of impulses.

6. C. The speed of contraction depends on the load. We can calculate the load per unit cross sectional area: Mr Universe is 25 Kg / 160 cm2 = 0.156 Kg cm-2; Amy’s is 10 Kg/40 cm2 = 0.25 Kg cm-2; Bill’s is 12.5 Kg /100 cm2 = 0.125 Kg cm-2. So the load is lightest with Bill, intermediate with Mr. Universe and heaviest for Amy. The fastest person should be Bill, followed by Mr. Universe and then Amy, because the speed is inversely proportional to load.