696406A
Investigating the Interactions of
Muscles and Bones
INSTRUCTION
MANUAL
CARmunA
World-Class Support for Science & Math
Investigating the Interactions of Muscles and Bones
Instruction Manual
Overview
,
,
Objectives
,
,
'
,
3
3
Background
3
Materials
8
Assembly Instructions
8
Teacher Tips
8
Sample Data Tables and Graph
Answers to Questions
9
10
Photocopy Masters
Activity Instructions
S-l
Data Sheet
S-4
Questions
S-5
©2010 Carolina Biological Supply Company
Printed in USA
Investigating the Interactions of Muscles and Bones
Overview
The model used in this kit incorporates physiology and physics to demonstrate the
functional design of the human arm. Using this kit, students or teacher demonstrators
illustrate the action of antagonistic muscles using rubber bands to represent the triceps
and biceps. They also investigate the third-class lever design of the human arm. They
explore how the location of the biceps insertion (effort force) in relation to the elbow
(fulcrum) affects the amount of effort needed to raise a stack of weights (resistance
force). Effort force is measured using a spring scale, and the mechanical advantage
provided by the arm (lever) at three different insertion points is calculated and
compared. The arm model is also used to illustrate the relationship between effort force
provided by the biceps muscle and range of motion in the human arm to move the hand.
Objectives
•
Understand the action of antagonistic muscles
•
Understand the design of a third-class lever and how it relates to the human arm
•
Understand how the relationship between mechanical advantage and range of
motion explains the lever design of the human arm
Background
Biology of the Human Arm
Muscle Types
Humans are large and complex organisms that require muscular and skeletal systems
for support and locomotion. Muscles enable motion, cause the heart to beat, maintain
posture, manage blood pressure, move food through the digestive tract, absorb shock,
and help regulate body temperature.
There are three types of muscle tissue in the human body: cardiac, smooth, and
skeletal. Cardiac muscle is striated (striped) in appearance, due to the alternating
light and dark bands within the muscle fibers; it is present only in the walls of the
heart. Cardiac muscle is under involuntary control by the autonomic nervous system.
Smooth muscle is found in internal organs. It lines the walls of the digestive tract
and is found in blood vessels, the urinary bladder, the uterus, and other organs. Like
cardiac muscle, smooth muscle is under involuntary control, but it is not striated
in appearance.
Skeletal muscle is attached to the bones of the skeleton. Contraction of skeletal
muscles enables the movement of bones. Skeletal muscle is under voluntary control
by the somatic nervous system, meaning that there is conscious control over muscle
contraction and relaxation. Skeletal muscle is striated in appearance and is the most
abundant tissue in the human body. There are more than 400 skeletal muscles in the
body and they make up 40-45% of a person's total body weight.
Interaction of Skeletal Muscles and Bones
The skeletal system and skeletal muscles together make up the musculoskeletal
system. The skeletal system is comprised of bones and joints. Where two bones meet,
a joint is formed. Bones are connected at joints by tissues called ligaments. Skeletal
muscles are attached by connective tissues called tendons to at least two different
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bones across a joint. Muscles are necessary to move the bones. The attachment point
of the muscle nearer the center of the body is called the origin. The origin is on the
more stationary or fixed bone. The attachment point of the muscle further from the
center of the body and on the more mobile bone is called the insertion.
The biceps muscle of the upper arm is
attached by two origins (and therefore
has two heads) to the scapula bone in the
shoulder (shoulder blade). The biceps
runs the length of the humerus bone in
the upper arm and is attached to the
radius bone of the forearm (lower arm) at
its insertion (see Fig. 1). The forearm is
comprised of two bones, the radius and
the ulna.
The triceps muscle of the upper arm is
attached by three origins (and therefore
has three heads), one to the scapula and
two to the humerus. The triceps runs the
length of the humerus bone on the
underside of the upper arm and attaches
to the ulna bone of the forearm at its
insertion.
i
Biceps
origins
Biceps
muscle
Biceps
insertion
Figure 1. Origins and Insertions of
Biceps and Triceps Muscles
When skeletal muscles contract, the
(*Third triceps origin not shown.)
insertion is pulled toward the stationary
origin, causing bones to move at a joint.
It is important to note that muscles act by exerting a pulling force, never a pushing
force. Contracted muscles are shorter and thicker than when they are relaxed. When
the biceps contracts, the arm bends at the elbow joint as the insertion on the forearm
is pulled toward the origin on the shoulder blade. The biceps muscle is called a flexor
because it flexes, or bends, the elbow joint. The triceps muscle works in opposition to
the biceps. When the triceps contracts, the insertion is pulled toward the origin,
causing the arm to straighten, or extend, at the elbow. The triceps is therefore an
extensor muscle.
The biceps and triceps flank the upper arm and work as an antagonistic muscle pair
across the elbow joint. That is, when one muscle contracts, the other relaxes.
Movement produced by contraction of the biceps muscle and relaxation of the
triceps can be reversed by contraction of the triceps muscle and relaxation of the
biceps. When the biceps flexes the forearm, it acts as an agonist. The triceps working
in opposition to the biceps is an antagonist. Other movable bones of the skeleton are
also flanked by antagonistic skeletal muscles, or muscle groups, to control body
movements across joints.
Physics of the Human Arm
The Human Arm is a Lever
A simple machine is a device that multiplies or redirects a force to make tasks easier.
A lever is a type of simple machine that consists of (1) a rigid bar, (2) a fixed point
or fulcrum upon which the bar pivots, (3) an object or weight to be moved, and
(4) a force supplied to move the weight. The resistance force is the force exerted by
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the load (object to be moved) while the effort force is the force applied to move the
load. There are three types, or classes, of levers; each class is defined by where these
forces are applied to the lever in relation to the stationary fulcrum.
In first-class levers, the effort and resistance forces are on opposing ends of the lever
arm, with the fulcrum between the two forces (see Figure 2a). A common example of
a first-class lever is a seesaw. The board of the seesaw is the rigid bar across the pivot
point (fulcrum). One person on the seesaw supplies the effort force to move the
weight of the other person (the resistance force). In second-class levers, the fulcrum
is at one end of the lever arm, the effort force is at the other end of the lever arm,
and the resistance force is between the two (see Figure 2b). A common example of
a second-class lever is a wheelbarrow. The wheel acts as the fulcrum, and the load in
the container supplies the resistance force. The effort force is applied to the handles
to lift the load.
a. first, class lever
b. second, class lever
c. third, class lever
Figure 2. Types of Levers
(R = resistance force, E = effort force, F = fulcrum)
In third-class levers, the fulcrum is at one end of the lever arm, the resistance force is
at the other end of the arm, and the effort force is between the two (see Figure 2c).
Contraction of the biceps to raise the human forearm is an example of a biological
third-class lever. The forearm bones comprise the rigid bar of the lever. The elbow
joint is the fulcrum, the pull of the biceps insertion on the forearm provides the effort
force, and the weight of the forearm and hand (including objects held in the hand) is
the resistance to be lifted (see Figure 3).
Figure 3. The Human Arm is a Third-Class Lever
(R = resistance, E = effort, F = fulcrum)
The human arm is most commonly thought of as a third-class lever when it bends at
the elbow to raise the forearm. However, straightening the arm at the elbow to lower
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the forearm actually represents a first-class lever. In this case, the effort force is
provided by the pull of the triceps insertion on the forearm. The insertion of the
triceps is located behind the elbow. Therefore, the fulcrum (elbow) is located
between the effort and the resistance. This classifies the lowering of the forearm by
the triceps as a first-class lever. The human body utilizes all three types of levers for
different adaptive purposes.
Mechanical Advantage
The three classes of levers differ in how they magnify or redirect the applied effort
force. The relative amount of effort force necessary to overcome a counteracting
resistance force varies among the classes of levers. The required effort force depends
on the distance the effort and resistance forces acting on the lever are from the
fulcrum of the lever.
The distance of the applied effort to the fulcrum is called the effort distance (or
effort arm) and the distance of the counteracting resistance to the fulcrum is called
the resistance distance (or resistance arm). The length of these arms helps determine
how much effort force is needed to overcome the resistance force. When the effort
arm is longer than the resistance arm (as in a second-class lever), a smaller amount
of effort force is needed to overcome a larger resistance force. When the resistance
distance is longer than the effort distance (as in a third-class lever), the effort force
necessary to move the load is greater than the resistance force.
The ratio of effort distance (dE) to resistance distance (dR) determines the ideal
mechanical advantage (IMA) of the lever (IMA = dE/dR).Ideal mechanical
advantage represents the advantage the lever provides in a frictionless environment.
Since friction is inevitable in the real world, mechanical advantage is calculated as
a ratio of the resistance force (FR) to the effort force (FE) as represented by the
equation MA = FR/FE'As a result, mechanical advantage can be either less than
or greater than one. If the effort force needed to overcome the resistance (move
the load) is greater than the force supplied by the load (resistance force), the
mechanical advantage will be less than one. The most effective levers require an
input of effort force that is less than the counteracting resistance force to move the
load. These levers magnify the effort force and have a mechanical advantage that is
greater than one.
The mechanical advantage of third-class levers is always less than one. This is
because the effort force is between the fulcrum and the resistance, causing the effort
distance to always be less than the resistance distance. In the human arm example,
the effort arm is the distance from the elbow to the biceps insertion. The resistance
arm is the distance from the elbow to the hand (see Figure 4). A greater amount of
effort force provided by the biceps than resistance force applied by the load is
required to raise the forearm.
Range of Motion
In terms of mechanical advantage, the third-class lever design of the human arm
actually operates at a disadvantage. However, there are adaptive reasons for such
a biological lever. The third-class lever design of the human arm gains in speed and
displacement of the moving end of the lever arm at the expense of effort force. A
lever that multiplies the effort force and increases mechanical advantage sacrifices
the distance the resistance can move.
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Although third-class levers always require more effort force than counteracting
resistance force, moving the effort closer to the resistance can reduce the required
effort. In the human arm, if the biceps insertion were closer to the hand, or if the
forearm were shorter, mechanical advantage would improve. Moving the biceps
insertion would increase the length of the effort arm. Shortening the forearm would
decrease the length of the resistance arm. The closer the effort force is to the
resistance force, the less effort needed to counteract it.
However, having the biceps insertion closer to the hand, or shortening the forearm
would greatly restrict the range of motion in the arm to move the hand, and any
objects in it. When the forearm is held perpendicular to the body (with the arm bent)
and a weight is placed in the hand, effort must be applied by the biceps to keep the
weight perpendicular to the body. However, without adding any effort, the weight can
be displaced a great distance. If the biceps insertion were located closer to the hand,
or the forearm were shorter, no additional effort would be necessary to keep the
weight in the hand perpendicular to the body, but the range of motion in the arm
would be limited.
In the human body, maximized range of motion of the forearm is more important to
function than decreased input of effort force by the biceps muscle. The design of the
human arm fits the function of the body by allowing for a wide variety of movements.
Figure 4. Resistance and Effort Distances in the Human Arm
(R
Materials
=
resistance, E
=
effort, F = fulcrum,
dE = effort distance, dR
=
resistance distance)
The materials in this kit are designed for teacher demonstration or for a small group
of students working cooperatively.
Included in the kit:
arm model (3 parts prior to assembly)
package of rubber bands
mass hanger
7 10-g weights
roll of string
spring scale
tape measure
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Needed, but not supplied:
scissors
Assembly
Instructions
Before beginning the activities, assemble the model according to the following
instructions:
1. Place the rectangular base of the model on a flat surface.
2.
Insert the length of pipe that has no attachments into the hole in the base. Press
the pipe into the hole to create a secure fit.
3.
Place the pipe with the attached arm model on top of the pipe secured to the
base. Orient the arm model so that the forearm is in line with the base.
You will be instructed when to use the supporting materials with the model when
performing the included activities.
Teacher Tips
Sample Data
Tables and
Graph
8
Teacher's
Manual
•
When directed in the activity instructions, place the rubber bands, mass hanger,
and loop of string securely on the pegs, behind the caps.
•
Usage over time will cause the rubber bands to lose some elasticity. Although this
will slightly affect the data gathered in Activity 3, it will not alter the relationship
between insertion point and range of motion.
•
The arm model in this kit is a simplified representation of the human arm.
As such, there are deviations and omissions from the actual structure of the
human arm.
•
In Activity 1, rubber bands are used to represent the biceps and triceps muscles.
The multiple heads of these muscles are not reflected in the rubber band model.
•
The arm model focuses only on the biceps and triceps muscles of the arm, but it
is important to note that there are additional muscles in the arm that contribute
to movement.
•
The structure of the arm model outlines the shape of the human arm but does
not detail the internal bones. In reality, the biceps and triceps muscles are
attached directly to bone.
Sample Data Table for Activity 2: Mechanical Advantage
Biceps
Insertion
Effort Force (FE)
unit = N
Resistance Force
(FR)
unit = N
Mechanical
Advantage
(FR/FE)
Effort Distance
(dE)
unit = cm
B
13.5 N
1.71 N
0.13
5.3 cm
C
7.8N
1.71 N
0.22
7.5 cm
D
5.8N
1.71 N
0.29
10.1 cm
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Sample Graph for Activity 2: Mechanical Advantage
Mechanical Advantage
0.45
Ql
Cl
I
I I I
i
I I I
vs. Effort Distance
0.35
.el
c
co
>
"0
<t:
co
0.30
()
c
co
.s:::
()
Ql
~
0.25
0.20
0.15
0.10
5
4
6
7
9
8
11
10
Effort Distance (cm)
(
Sample Data Table for Activity 3: Range of Motion
Biceps Starting Distance Ending Distance
unit = cm
Insertion
unit = cm
Change in
Distance
unit = cm
B
54.5 cm
16.6 cm
37.9 cm
C
63.5 cm
36.2 cm
27.3 cm
D
64.7 cm
50.2 cm
14.5 cm
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Answers to
Questions
the
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1. The biceps and triceps muscles flank the humerus bone of the upper arm. How,
then, are these muscles able to raise and lower the forearm?
The biceps and triceps muscles flank the humerus bone of the upper arm but each is
connected to a bone of the lower arm at its insertion. The biceps insertion is on the
radius (upper bone) of the forearm and the triceps insertion is on the ulna (lower bone)
of the forearm. To raise the forearm, the biceps contracts, causing the insertion to pull
the forearm upward. To lower the forearm, the triceps contracts, causing the insertion to
pull the forearm downward. The triceps and biceps work as an antagonistic muscle pair.
When the biceps contracts, the triceps relaxes.
2. What does it mean to have a lever with a mechanical advantage greater than one
in terms of resistance force versus effort force?
A lever with a mechanical advantage greater than one means that the resistance force
acting on the lever can be overcome by an input of effort force that is less than the
counteracting resistance force. The lever magnifies the effort force such that less effort
force than resistance force is necessary to move the load.
3.
The action of raising the forearm represents a third-class lever. Third-class levers
always have a mechanical advantage less than one. Activity 2 showed that if the
biceps insertion were closer to the resistance, mechanical advantage would
improve. Describe another modified design of the human arm that would
improve mechanical advantage.
Mechanical advantage of the human arm would be improved if the length of the
forearm were shorter. This would bring the resistance closer to the effort and decrease
the length of the resistance arm. Although the effort arm would remain unchanged in
this scenario, shortening the resistance arm has the same effect as lengthening the effort
arm in terms of improving mechanical advantage.
4.
Sketch one possible way the human arm would look if it were designed to
maximize mechanical advantage.
Answers will vary, but may include a sketch of the arm with a short forearm, or
a sketch with the biceps insertion close to the hand.
5.
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Teacher's
Manual
Explain why the human arm is not designed to maximize mechanical advantage.
Maximized mechanical advantage comes at a cost to range of motion. In the human
body, maximized range of motion of the forearm is more important to function than
decreased input of effort force by the biceps muscle.
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Activity Instructions
Activity 1: Antagonistic
Muscles
This activity illustrates the action of antagonistic muscles, using rubber bands to represent the triceps and biceps.
1. Stretch a rubber band between positions A and B on the arm model. This rubber band represents the biceps
muscle. Position A represents the origin of the biceps and position B represents the insertion of the biceps in
the human arm.
2.
Stretch another rubber band between positions E and F on the arm model. This rubber band represents the
triceps muscle, with the origin at E and the insertion at F.
3.
Slowly move the end of the forearm up and down. Observe how the triceps and biceps rubber bands change
in relation to each other as the arm moves. When the forearm is raised, the biceps rubber band is shorter than
the triceps rubber band. This represents contraction of the biceps and relaxation of the triceps to raise the
forearm. When the forearm is lowered, the triceps rubber band is shorter than the biceps rubber band. This
represents contraction of the triceps and relaxation of the biceps to lower the forearm. The biceps and triceps
muscles work antagonistically such that when one is contracted the other is relaxed, and vice versa.
4.
Predict how the arm model will move when the biceps contracts. To represent contraction without manually
moving the arm, add an additional rubber band between positions A and B and slowly let go of the model.
Observe how the arm model moves.
5. Predict what will happen to the arm model if the triceps now contracts to the same degree the biceps was
contracted. Add an additional rubber band between positions E and F. Observe how the arm model moves.
6.
Both the biceps and the triceps now have two rubber bands and are counterbalanced. Predict what will
happen to the arm model if a third rubber band is added to the triceps. Remember that addition of a rubber
band represents contraction of the muscle. Test your prediction by adding a third rubber band. Observe how
the arm model moves.
7.
Removal of a rubber band represents relaxation of the muscle. Predict what will happen to the arm model if
two of the rubber bands are removed from the triceps position. Test your prediction by removing two of the
rubber bands from the triceps position. Observe how the arm model moves.
8.
Experiment freely with the arm model by adding and removing rubber bands, in quantities of your choosing,
to and from the triceps (E and F) and biceps (A and B) positions. Observe how the relationship between
contraction and relaxation of the antagonistic muscle pair affects whether the arm is raised or lowered.
Activity 2: Mec~nical Advantage
This activity focuses on the third-class lever design of the human arm. It illustrates how the location of the effort
(biceps insertion) in relation to the fulcrum (elbow) affects the amount of effort force necessary to raise the
resistance (forearm, mass hanger, and weights). The mechanical advantage provided by the arm at three different
insertion points is calculated and compared.
1. Remove all rubber bands from the arm model. Hang the mass hanger with all seven lO-g weights from
position G on the end of the forearm.
2.
Cut a length of string 80 cm long. Tie a loop at each end of the string, large enough to fit over the cap on the
pegs on the model. Thread the string over the peg at position A.
3.
Loop one end of the string around the peg at position B on the model. Hang the spring scale by its hook from
the loop on the other end of the string, as shown in the figure on page S-2.
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Carolina
Biological
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Company
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Measure the effort force needed to lift the resistance by
pulling down on the metal loop of the spring scale until the
molded guidelines on the upper and lower arm come
together to form a straight, vertical line. Keep the spring
scale and string to the left of position F and parallel to the
pipe support of the model while pulling down on the scale.
Once the molded guidelines are aligned, read the force on
the spring scale in Newtons. Maintain a constant pressure
on the spring scale. Read the force measurement carefully,
as the spring scale will be upside down. The scale ranges
from 0 to 10 Newtons in 2-Newton increments. Record the
effort force at insertion B in the table on page SA.
5. Move the loop from position B to position C and repeat
Step 5 to measure the effort force required at this insertion
to raise the resistance. Record the effort force at insertion C
in the table on page S-4.
6.
Move the loop from position C to position D and repeat
Step 5 to measure the effort force required at this insertion
to raise the resistance. Record the effort force at insertion D
in the table on page S-4.
7. Force (in Newtons) is equal to mass (in kg) x acceleration
due to gravity (in m/s2). Calculate the resistance force
acting on the arm by multiplying the mass of the forearm,
hanger, and weights (0.174 kg) by the acceleration due to
gravity (9.81 m/s2). Record this resistance force in the table
on page SA. In this activity, the resistance force at positions
B, C, and D is constant while the effort force required to lift
it varies.
8.
Using the effort forces and resistance force, calculate the mechanical advantage provided by the arm at each
biceps insertion point. Mechanical advantage is the ratio of resistance force to effort force (FWFE)' Record the
mechanical advantage in the table on page S-4.
9.
Remove the spring scaje, weights, and string from the arm model.
10. Using the tape measure, measure the distance in centimeters from each biceps insertion point (B, C, and D)
to the elbow joint (i.e., the center of the pivot disc, not peg F). This distance is called the effort distance (or
effort arm). Record each effort distance in the table on page SA.
11. To illustrate the relationship between effort distance and mechanical advantage, plot the mechanical
advantage (y-axis) versus effort distance (x-axis) for each insertion point on the graph on page S-4.
Activity 3: Range of Motion
This activity illustrates the relationship between effort force provided by the biceps and the range of motion
available to the forearm moving a load (mass hanger and weights).
1. Stretch a rubber band between positions A and B on the arm model to represent the biceps muscle. No other
rubber bands are needed.
2.
Using the tape measure, measure the distance in centimeters from the center of the cap at position G to the
top of the base. Record this as the starting distance for position B in the table on page S-4.
©2010
Carolina
Biological
Supply
Company
5-2
Investigating
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3.
Carefully hang the mass hanger with all seven 10-g weights from position G and watch the forearm of the
model move.
4.
Using the tape measure, measure the ending distance from the center of the cap at position G to the top of
the base (if necessary, estimate this distance). Keep the tape measure perpendicular to the base and as straight
as possible (the weights may slightly obstruct the line of measurement). Record this distance in the table on
page S-4.
5.
Calculate the change in distance for position B by subtracting the ending distance from the starting distance.
Record this distance (in centimeters) in the table on page S-4.
6.
Remove the weight and move the rubber band between positions A and C. Repeat steps 2-5 for position C.
7.
Remove the weight and move the rubber band between positions A and D. Repeat steps 2-5 for position D.
8.
Compare the "Change in Distance" data for each insertion, and discuss the significance of your findings.
©2010
Carolina
Biological
Supply
Company
5-3
Data Sheet
Name
696406A
Date
Investigating the Interactions of Muscles and Bones
Activity 2: Mechanical Advantage
Biceps
Insertion
Effort Force (FE)
unit = N
Resistance Force (FR)
unit = N
Mechanical
Advantage (FR/FE)
Effort Distance (dE)
unit = cm
B
C
D
Activity 3: Range of Motion
Starting Distance
unit = cm
Biceps Insertion
Ending Distance
unit = cm
Change in Distance
unit = cm
B
C
D
©2010
Carolina
Biological
Supply
Company
5-4
Questions
1.
The biceps and triceps muscles flank the humerus bone of the upper arm. How, then, are these muscles able
to raise and lower the forearm?
2.
What does it mean to have a lever with a mechanical advantage greater than one in terms of resistance force
versus effort force?
3.
The action of raising the forearm represents a third-class lever. Third-class levers always have a mechanical
advantage less than one. Activity 2 showed that if the biceps insertion were closer to the resistance,
mechanical advantage would improve. Describe another modified design of the human arm that would
improve mechanical advantage.
4.
Sketch one possible way the human arm would look if it were designed to maximize mechanical advantage.
5.
Explain why the human arm is not designed to maximize mechanical advantage.
©2010
Carolina
Biological
Supply
Company
5-5