Physics 1AL
EQUILIBRIUM & CENTER OF GRAVITY
Winter 2009
Introduction
In this lab you will use a model of the lower arm to investigate the force that the bicep muscle
needs to exert for you to be able to lift and hold your lower arm and hand at various angles, and
for you to be able to support masses in your hand when the lower arm is horizontal. You should
review sections 8.1 to 8.4 of your text before coming to the lab. You will need to use the
concepts of center of gravity, torque, and rotational equilibrium.
The figure shows a diagram of an arm
bent at about 90°. The upper arm is
vertical and there is a mass supported
by the hand. We will assume that the
bicep muscle pulls vertically upwards
on the upper bone (the radius) of the
lower arm. For this experiment we will
work with conditions in which the
tricep muscle is relaxed and not
exerting a force. The lower arm rotates
about a pivot point close to the base of
the humerus (the bone in the upper
arm).
Our model of this system is simple but
contains all the important features. The
lower arm and hand are represented by
a length of wood supported at the
elbow end by a rod passing through a
hole. The force of the rod on the wood
is the same as the force of the humerus
on the ulna and radius. A mass can be
attached to the end of the wood at the
hand end. The bicep is represented by a
string pulling upwards with the tension
measured by the force sensor. The
mass of the wood itself represents the
mass of the lower arm and hand. The
protractor and plumb line allow
measurement of the angle of the
“forearm”.
T biceps
mghand
mgCOG forearm
pivot and
support point
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Physics 1AL
EQUILIBRIUM & CENTER OF GRAVITY
Pre-lab Questions
1. On the seesaw shown to the right, mass A
is 30 kg, mass B is 15 kg, and mass C is
5.0 kg. Mass A is 0.50 m from the pivot.
Mass C is 1.5 m from the pivot. The
seesaw is at an angle of 30 degrees from
the horizontal. Calculate the torques of
mass A and mass C about the pivot. Where
you should place mass B in relation to the
pivot for the system to be in rotational
equilibrium (i.e. there is no net torque on the system)?
2. Calculate the center of mass of the object
to the right. Assume the mass is
uniformly distributed.
3. As part of a physical therapy program
following a knee operation, a 3.5 kg object is
attached to an ankle and leg lifts are done as
sketched in the figure. Calculate the torque
about the knee due to this weight for the four
positions shown.
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Winter 2009
Physics 1AL
EQUILIBRIUM & CENTER OF GRAVITY
Winter 2009
Group Activity:
• You will find a metal L bracket on your lab bench. Measure its dimensions and calculate
the position of its center of mass (CoM).
• Devise a practical method to measure the position of the CoM. Your TA will help you.
Use this method to find the CoM experimentally. Measure and note your results.
• Compare your experimental result with your calculation. Do they agree? Should they
agree?
Experiment A
Examine the model of the human forearm. Record the masses and lengths for your apparatus.
This section of the experiment will measure the force of the bicep muscle as a function of the
mass supported by the hand when the forearm is horizontal. Make sure the “bicep” string is
vertical.
A1. Start with no extra mass in the hand and set the force sensor to the 50N scale. With
reference to the pivot point, calculate and record the torque of the weight of the forearm,
and the torque of the tension of the bicep muscle. With reference to your diagram of the
setup, which torques are clockwise and which are counter clockwise? Do the CW and
CCW torques balance?
A2. Repeat the measurement of bicep tension when the hand supports 0.2 kg, 0.4 kg and 0.6
kg masses. Make a table showing your data and the calculated torques. Do the torques
continue to balance?
A3. What are the sources of uncertainty in your calculation of the torque? What are the
values of these uncertainties?
Experiment B
In this part of the lab, you will investigate if you need a greater bicep tension when your lower
arm is horizontal, or when it is at an angle (always keeping the upper arm vertical). Before you
start this part of the lab pick up a 1 kg mass in your hand and try the experiment on your own
arm. Compare the lower arm horizontal with it at 45o above and below the horizontal. Record
your best (subjective) evaluation of the relative bicep forces at these angles.
For the experiment, use a 0.2 kg mass in the “hand” throughout.
B1. Repeat A2 above (lower arm horizontal) with the 0.2 kg mass and confirm your results
are consistent.
B2. Now set the arm to 30o below the horizontal and repeat. Measure, calculate, and compare
your clockwise and counter-clockwise torques. Do they balance?
B3. Repeat B2 at 45o below horizontal, 30o above the horizontal, and 45o above horizontal. In
each case, check CW and CCW torques.
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Physics 1AL
EQUILIBRIUM & CENTER OF GRAVITY
Winter 2009
B4. From you data in B1, B2, and B3, how does the bicep force change as a function of
angle? From your data, assess how confident you can be with your result.
B5. Find a general expression for the tension in the bicep muscle in terms of the mass and
relative positions of the forearm and hand. How does the tension depend on the angle
above or below the horizontal? Calculate the tension you would predict at each angle you
used in parts B2 and B3.
B6. Do your predictions from B5 agree with your measurements?
Post Lab Activity
(Note: for Post Lab 8 you have two choices: 1) to complete the problem below or 2) complete a
survey, see the next page for instructions. No matter which choice you make, you will still need
to write-up a conclusion for Lab 8.)
The large quadricep muscles in the upper leg terminate at the lower end in a tendon attached to
the upper end of the tibia (See the figure below). The forces on the lower leg are modeled below,
where T is the tension in the tendon, w is the force of gravity acting on the lower leg, and F is
the weight of the foot. Find w when the tendon is at an angle of 20° with the tibia, assuming that
T = 450N, F = 15.0N, and the leg is extended at an angle of 45.0° with the vertical. Assume that
the center of gravity of the lower leg is at its center, and that the tendon attaches to the lower leg
at a point one sixth of the way down the leg. Include a diagram for this situation.
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Physics 1AL
EQUILIBRIUM & CENTER OF GRAVITY
Winter 2009
Invitation to participate in a survey on students in physics
The purpose of this announcement is to extend to you an invitation to participant in the survey
portion of a research study about the experiences, beliefs and perceptions of students enrolled in
physics lab classes. You have been asked to take part because you are currently enrolled in a
physics lab class (i.e., Physics 1AL, 1BL, 1CL, 2AL, 2BL, or 2CL). The principal research
investigator is Dr. Tricia Bertram Gallant.
The purpose of this study is to determine the services and education that UCSD can provide to
enhance student success and learning in physics labs. There will be approximately 2800
participants in this study and we will be conducting the study over the course of the 2008-2009
academic year. For each physics lab course you enroll in this year, you will receive an invitation
to complete the survey so you could complete the survey as many as three times, but
participation is completely voluntary.
If you volunteer to participate in this survey portion of the study, you can access the survey via
the link below. Completing the survey should take no longer than 15 minutes.
https://physics-apps.ucsd.edu/survey/phpQ/fillsurvey.php?sid=2
You may sense discomfort responding to questions about your academic experiences, but you
can refuse to answer any questions you wish and end the survey at any time. Participation in
research is entirely voluntary. You may refuse to participate or withdraw at any time without
jeopardy to you of any kind. If you complete the survey, please print off the confirmation page at
the end and submit it to your physics lab TA for academic credit (in lieu of completing the postlab 8 assignment). If you would rather not complete the survey, you can choose to complete the
post-lab 8 assignment as an alternative option for earning your academic credit.
Individual survey responses will be kept confidential and your responses anonymous; we will not
be tracking your individual responses in anyway, including to an IP address. Neither your course
instructor or your teaching assistant(s) will see your individual responses.
By clicking on the survey link, you indicate your agreement to participate in this research study.
Completing the survey should take less than 15 minutes. At the end of the survey, you will
receive a confirmation of completion; please print that out and submit it in your physics lab to
receive your academic credit.
If you have additional questions or need to report-research related problems, you may contact the
principal investigator at tbg@ucsd.edu or 858-822-2163. You may also call the Human Research
Protections Program at 858-455-5050 to inquire about your rights as a research subject or to
report research related problems.
Sincerely,
Tricia Bertram Gallant, Ph.D.
Principal Investigator
The UCSD Institutional Review Board has reviewed and approved this research involving
human subjects.
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