HPP A17.v2
How Strong Are Your Muscles?
How Strong Are Your Muscles?

You should be working with new lab partners starting with this lab.
Exploration: Thinking about forces and torques…
Your lab instructor will lead the class through three separate demonstrations, which we
will refer to as (a) the baton demo, (b) the meterstick demo, and (c) the doorknob demo.
Invention Discussion #1
During the Invention, your laboratory instructor will lead a discussion of the results for
the previous activities as well as to introduce some important terms.
Helpful concepts:

Torque: The tendency of a force to produce motion around a pivot point is called torque.

Center of Mass: To apply these concepts to the various parts of the body it is useful to use
the concept of the center of mass. Any extending object can be treated as a point mass with
all of its mass at that point. This imaginary point is called the center of mass.
Answer the following questions after this invention discussion.
1.
What can you say about the torques on the meter stick when it is balanced? Explain, using
a force vector diagram to aid your explanation.
2.
What makes the baton easier or more difficult to turn? Is the weight of the mass different
for each example? If not, then what is different?
3.
Record your answers to the following questions about the doorknob demo. Include a
sketch of the door and hinges to make your answers clear.
 Which doorknob was easiest and hardest to use to open the door? Why?
 Where on an ordinary door is the doorknob located in relation to the hinges? Why?
 What if two people push from opposite sides at different locations?
Application Activities #1-3: Balancing Your Arms
During the following Application Activities, you will apply the concept of torque to
determine the forces that must be exerted by various muscles of your body to keep you
balanced and to support additional weights.
 Humanized Physics Project
2004 - UNL
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How Strong Are Your Muscles?
As you complete each of the activities, one person in your group will be the subject of
study and each person needs to be the subject at least once. At this time you should decide who
will be the subject for each of the following: study of the lower arm (bicep muscle - #1A-B), the
upper arm (tricep muscle - #2), and the shoulder (deltoid muscle - #3).
Many of the activities in this lab will require you to make calculations based on your
weight. It doesn't matter if you are completely honest about your weight value, but it is
important that you pick a value and use it consistently throughout the lab.
4.
Choose your "ideal" body weight to use for all calculations in this lab. Write it in your
logbook both in units of lbs and N.
During this lab, you can use the following chart to estimate the weight of various parts
of your body.
Method to Estimate the Weight of Various Body Segments
Based on the Body Weight
Segmental weight
ratios from a 1969 cadaver study
Body weight
(Sample size = 13)
Head
7.3 %
Trunk
50.7 %
Upper arm
2.6 %
Forearm
1.6 %
Hand
0.7 %
Total Arm
4.9 %
Forearm and hand
2.3 %
Thigh
10.3 %
Calf
4.3 %
Foot
1.5 %
Total leg
Calf and foot
16.1 %
5.8 %
 Humanized Physics Project
2004 - UNL
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
The following activities will ask for the "maximum" weight that you
can hold. However, keep in mind that this is physics, not weight
lifting!! Be careful not to overdo. It should be the maximum weight
you can comfortably hold, not the absolute maximum weight.
 Humanized Physics Project
2004 - UNL
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Application #1A-B: Forearm and Biceps – Subject #1
Identify the name of the subject and which of his/her arms will be studied (left or right).
During activities 1A-1B you will estimate the forces applied by the biceps.
Assume that the center of mass of your forearm and hand is halfway between your
elbow joint and the middle of your closed fist.
Application #1A: Level Arm – No Extra Weight: (Bicep calculation)
In this application, you will complete the described procedure to answer the following
question:
 What is the force exerted by the biceps to keep the lower part of your arm
level with your upper arm perpendicular to the lower arm?
Procedure:
 Locate the pivot point for the subject's lower arm and where the biceps connect to the
lower arm.
 Estimate the relevant distances from the pivot for this person's arm (such as the distance
to the place where the muscles connect and the distance to the center of mass)
 Estimate and record the weight of the subject's lower arm (using the chart).
F
Joint
F
Biceps
F
Lower arm weight
5.
(a)
Carefully sketch a vector force diagram representing the lower arm system,
including all relevant forces (arm weight, bicep force, and force on the elbow joint)
on this diagram.
(b)
Record all distance and weight measurements on this drawing. Show any necessary
calculations.
(c)
Using what you know about the torques in this situation, determine the force (in N
and lbs) exerted by the subject's biceps to keep the arm level. Show all of your work
in completing the necessary calculations.
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2004 - UNL
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(d)
Using what you know about the forces in this situation, determine the x and y
components of the force acting on the pivot point (elbow joint) and determine the
magnitude of this joint force.
(e)
Calculate the value of the bicep force and the joint force in units of the subject's body
weight.
 Humanized Physics Project
2004 - UNL
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Invention Discussion #2
Application #1B: Level Arm – Holding Extra Weight (Bicep calculation)
In this application, you will complete the described procedure to answer the question:

What is the maximum weight you can hold in your hand if you keep the
lower part of your arm level and your upper arm perpendicular to the lower
arm (that is, a 90 bend at the elbow)?
Procedure:



Position your arm as shown in the diagram (90 bend at the elbow).
Hold an empty cloth bag in your hand.
Have a lab partner carefully put as much weight in the bags as you can hold (keeping
your arm level). Keep your arm bent at 90 and do not overdo!
Record the total weight held by the subject.

Do not hold weights over your toes in
case the bag slips or breaks!!
6.
(a)
Carefully sketch a vector force diagram representing the lower arm/weights system,
including all relevant forces (weights, arm weight, bicep force, and force on the
elbow joint) on this diagram.
(b)
Record all distance and weight measurements on this drawing. Show any necessary
calculations.
(c)
Using what you know about the torques in this situation, determine the maximum
force (in N and lbs) exerted by the subject's biceps. Show all of your work in
completing the necessary calculations.
(d)
Using what you know about the forces in this situation, determine the x and y
components of the force acting on the pivot point (elbow joint) and determine the
magnitude of this joint force.
 Humanized Physics Project
2004 - UNL
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(e)
Calculate the value of the bicep force and the joint force in units of the subject's body
weight.
(f)
How do the values compare to those found with no additional weights being held?
 Humanized Physics Project
2004 - UNL
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Application #2: The Upper Arm and Triceps – Subject #2
Now it is time for the next subject. Identify the name of the subject in your logbook. In
this application, you will complete the procedure to answer the following question:

What is the maximum force that you can exert when pushing down with
your hand if you keep the lower part of your arm level and your upper arm
perpendicular to the lower arm?
Procedure:

Locate the pivot point for the subject's arm and where his/her tricep connects to the
lower arm.
Estimate the necessary distances and angles.
Push down on the scale with as much force as you can while keeping your forearm level.
No fair leaning on the scale!


7.
(a)
Carefully sketch a vector force diagram representing the lower arm/scale system,
including all relevant force and distance values. Show any necessary calculations.
(b)
Using what you know about the torques, determine the maximum force (in N and
lbs) exerted by the subject's triceps. Show all of your work in completing the
necessary calculations.
(c)
Using what you know about the forces, determine the x and y components of the
force acting on the pivot point (elbow joint) and determine the magnitude of this
joint force.
(d)
Calculate the value of the tricep force and the joint force for this situation in units of
the subject's body weight.
 Humanized Physics Project
2004 - UNL
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How Strong Are Your Muscles?
Application #3: The Upper Arm/Shoulder and Deltoids – Subject #3
Time for another subject. Gently loosen up your shoulder joint and muscles of your
strongest arm. Hold this arm straight out from your body, level with the floor, and with the
palm facing down (as shown in the image). You will have your lab partner put weights into a
bag hanging from your hand. How much weight can you hold up while keeping your arm
rigid and level?
In this application, you will answer the following question:

What is the maximum weight that you can hold if your whole arm is held out
rigid and horizontal at shoulder level?
Procedure:
 Locate the pivot point for this subject's upper arm and where his/her deltoid connects to
the upper arm.
 Feel and measure the angle that the deltoid muscle makes. Take half of that angle to be
the center of the muscle – where the resultant of the muscle force vector will be taken.
 Estimate any other necessary distances and angles.
 Keeping your arm straight, have weights added to the bag(s) until you reach your limit
or use all of the available weights. Keep your arm straight and do not over do!

Assume that the center of mass of your total arm is located at the center of your
arm/hand system.
Do not hold weights
over your toes in case
the bag slips or breaks!!
8.
(a)
Carefully sketch a vector force diagram representing the upper arm system,
including all relevant force and distance values. Be careful to accurately represent
any important angles. Show any necessary calculations.
(b)
Determine the x and y components of the deltoid muscle force (in N and lbs) exerted
by the subject. What is the magnitude of the deltoid force? Show your work.
(c)
Determine the x and y components of the force acting on the pivot point (shoulder
joint). Determine the magnitude of this joint force. (Hint: FJoint 
2
2
FJx  FJy )
 Humanized Physics Project
2004 - UNL
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(d)
Calculate the value of the deltoid force and the joint force for this situation in units of
the subject's body weight.
 Humanized Physics Project
2004 - UNL
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Summary Questions
9.
Which of the muscles that you investigated seems to be the strongest? Explain your
choice.
10.
(a)
Which joint experiences the largest force? The smallest force?
(b)
How are the sizes of the joint forces related to the size of the bone and joint?
11.
In words, describe what conditions are required to keep you in balance.
End of Lab Procedures

Return all weights and bags to the lab table.

Shut down the computer if for some reason it is turned on.
Want More Information?



Center of mass (see Walker, Section 9-7 and 11-4)
Torque (see Walker, Section 11-1)
Static equilibrium (see Walker, Section 11-3)

Some art work included in this lab was created by Hagen Schafer.
 Humanized Physics Project
2004 - UNL
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