Lesson: Balancing Act
Field Museum Extensions
a. Related Exhibitions.
1. Inside Ancient Egypt--Life along the Nile: the Shaduf. Students have the
opportunity to take measurements on, analyze, and operate a model of an
ancient Egyptian shaduf. The shaduf is an application of Archimedes law
of levers and is a model of the simple machine--the lever. Students will
investigate the construction of the shaduf. If they have used the Harris
Loan Life along the Nile Experience Box as described below, they can
compare their ideal hypothetical shaduf with the model at the museum.
Have students bring a measuring tape with them to measure (or to help
estimate) the lever arms in this exhibit. Then students can calculate how
this machine multiplies the force of the counterweight to lift a very heavy
container of water. If they have not used the Experience Box, students can
now propose ways in which the shaduf could be improved to meet other
needs of the Egyptians, such as large-scale irrigation.
Archimedes law of levers states that masses along a lever will be in
balance when their distances from a fulcrum are in inverse proportion to
their weights.
In other words, if the mass on the left in the diagram above has a weight of
“∆” and the mass on the right has a weight of “”, then the masses will be
balanced when
 BE

 AE
Referring to the diagram above, a shaduf would have a water container at
point A and a counterweight holding sand or clay at point B. A large
 from a river with very little effort by using a
water weight could be lifted
heavy counterweight and adjusting the lever arms. After the water is
emptied into an irrigation ditch or drinking water containers, the shaduf
operator would pull the water container down to the river to refill it. The
force required to pull it down would be the force at B (the counterweight)
times the fraction
BE
AE
So, the effort to lift the heavy counterweight is reduced by using the lever.
Students should also note that the distance that the operator would move
his end of the lever is greater than the distance that the counterweight
moves by the fraction 
AE
BE
This distance the operator moves his end of the lever is shown in the
diagram as the lever arm end movement from A to H. The distance the
counterweight moves is shown in the diagram as the distance from B to K.
 with an equal but opposite distance change.
The effort change is matched
Thus, the law of conservation of energy holds here. The energy change, or
work done, is force times distance, W = Fd. As the force, F, increases, so
the distance, d, decreases, and vice versa.
Improvements on the shaduf might be based on whether more water needs
to be lifted with each effort. If so, then the lever arm, AE, should be
longer. This would require a sturdier beam and fulcrum and would require
that the fulcrum be higher from the ground to allow for a greater A to H
movement.
Students might note that there is a limit to the efficiency of the shaduf, and
therefore may propose a more consistent means of moving water, using a
water wheel or animal driven pump.
2. Sue’s skeleton. Sue is an amazing fossil and one of the museum’s most
popular attractions. The skeleton provides a fascinating look into the
anatomy of this fearsome dinosaur and gives clues about its habits and
about its Cretaceous environment. Yet, it also gives students a unique
opportunity to look at the body as a series of levers and as a balancing act.
Can students find the various lever systems? Can they classify these
levers? Students will come to understand the speed and power of this
animal (and of themselves) as a combination of muscle force and bone
levers.
This activity presents an opportunity to show a connection between
physics and anatomy and physiology. All three classes of levers are
exemplified in the motion of Sue’s limbs. Students can find these classes
by noting the pivot point (fulcrum), the attachment of the muscles (this
would be the effort force, FE), and the location along the limb of the object
to be lifted or moved (this would be the load, FL). In other words, lever
class is assigned based on the relative location of fulcrum, as well as FE
and FL. The following diagrams show the possibilities for these positions.
In a 1st class lever, the fulcrum lies between the load and the effort force.
By Archimedes law of the lever, proper positioning of the fulcrum
magnifies the effort force.
In a 2nd class lever, the load lies between the fulcrum and the effort force.
This lever also magnifies the effort force.
In a 3rd class lever, the effort force lies between the fulcrum and the load.
Here, the effort force must be greater than the load. The benefit of this
lever is that it magnifies the speed of the load over the speed of the effort
force. So, this lever magnifies speed while at the expense of reducing
force.
While observing Sue, students should find a 1st class lever around the
attachment point of head and backbone. Muscle attachment on the back of
the skull and the center of mass of the head are on opposite sides of the
pivot point, which is where the skull and backbone meet.
Students should find a 3rd class lever at the hip. The fulcrum is at the hip
socket and the muscles (FE) are attached at a point lower on the bone. The
load is the ground when the animal is pushing off to walk or run. Because
this is a third-class lever, the speed of the muscle contraction is magnified.
Students might propose a 2nd class lever at the back of the foot, where a
tendon similar to the human’s Achilles tendon is attached. The pivot point
is at the bottom of the lower leg bone, and the load is then centered
between the tendon and the pivot.
More examples of these levers can be found and students can propose
whether the effect is to maximize the speed of the limb or to maximize
force.
b. Harris Educational Loan Center.
1. Ancient Egypt: Life along the Nile Experience Box. Construct a shaduf
and analyze it as an example of a simple balance. How is Archimedes’
Law of the Lever applied here? Measure the lever arms and determine the
ratio of the two masses at each end of the lever arm. Have students
generate ideas about how the ancient Egyptians might have constructed
the shaduf. What would have been the material used for the weight of the
short lever arm? What would have been a reasonable maximum weight
for this arm and why? How much water could have been raised with this
maximum weighted arm? What were the advantages to using this simple
machine? In other words, why not just draw the water from the source
using containers? Use this Experience Box as a precursor to a field trip to
Ancient Egypt at the Field.
This simple machine was used to move water from a river or pond or well
into irrigation ditches, where it would flow to agricultural fields. Students
might conjecture that the short lever arm was weighted with sand bags or
clay. These types of materials have densities between 1.5 to 2.0 times
greater than the density of water. And so, each liter of the counterweight
would have a mass between 1.5 and 2.0 kg (or, each gallon would weigh
between 12 and 16 pounds). A large container of sand or clay (about 20 to
30 gallons, or 80 to 120 L) might weigh as much as 300 or more pounds.
If the ratio of the lever arms was 5:1, then by Archimedes Law of the
Lever, the shaduf would be balanced with 1500 pounds of water (about
700 kg). Students might realize that this type of weight at each end would
break an average sized shaduf. Therefore, consideration of the strength of
the fulcrum and lever arms was an important part of planning the
dimensions and use of the shaduf.
Students should also realize that lifting and transferring water required
someone moving the lever. Where they stood determined how much
effort would be required to bring an empty bucket down to be refilled.
Students should measure the length of the lever arms of the model and
determine how many times the counterweight could be magnified
(therefore determining how much water could be lifted for a certain
counterweight).
c. Field Museum Science/Website Resources.
1. Dinosaurs: Ancient Fossils, New Discoveries Website:
http://www.fieldmuseum.org/dinosaurs/allabout.asp
In a scene from the movie Jurassic Park, an angry T. rex is in hot pursuit
of a potential human dinner. The fast moving dinosaur closes the gap on
the humans, who manage to keep the T. rex in their rear view mirror only
after putting the jeep into high gear. Still, the speedy dinosaur manages to
make the chase exciting for quite a while. But is this predator-prey
scenario realistic? Could a T. rex outrun a human, or keep up with a car?
Scientists continue to debate the maximum speed of this dinosaur.
In the web pages, Theropod Mechanics, students will read about this
debate. Some scientists claim that this large carnivore could reach speeds
of 45 miles per hour, while others believe the animal was much slower,
attaining a maximum speed of only 10 miles per hour. Students should
question whether either of these conclusions are reasonable. Does 45
miles per hour seem possible, even if the animal were not so massive?
Have students model the leg motion of the dinosaur as a rigid lever arm
attached at a pivot point, with the other end of the leg moving in an arc.
Use the information from the website to compare the arc speed of the T.
rex leg to a human’s leg. Do the speeds for human and T. rex match up?
And why do some scientists assume that the T. rex was so slow that some
humans might be able to outsprint the ferocious dinosaur? Also, if the T.
rex was as slow as a human, but not as agile and with supposedly poor
vision, what problems might this carnivore encounter?
Here, students will play the role of biophysicists as well as animal
behavior specialists. They should come to understand how some
knowledge of all disciplines in science is important to the specialized
work of a modern scientist. In other words, they might be able to explain
why paleontologists need to take physics classes.
A very simple model of a limb in motion is the swinging lever. The point
of attachment to the joint is the pivot point. The opposite end of the limb
then swings in an arc when muscles contract. The point of muscle
attachment (the point of FE) moves at a slower speed than the other end of
the limb, usually the point where the load exists (FL).
In the diagram above, the end of the limb moves thru arc AB at the
approximate speed of the animal. In the case of T. rex, this would be
either 45 mph or 10 mph. The point of muscle attachment would move
through arc CD. The ratio of the speeds is equal to the ratio of the arc
radii, which is the distance from the fulcrum, or pivot point, X. The speed
of the limb end differs from the speed of the point of muscle attachment
by a factor of
XA
XC
This idea can be extended to compare the speed of the limbs of a human
and a T. rex. Information from the website has the height of the T. rex at
about 12 feet, or, “at the hip, this adult T. rex is three times the height of
 This puts the length of the extended back leg
an average seven-year old”.
at around 10-12 feet. The lower leg of an adult human is approximately 3
feet, or about one-fourth the length of the T. rex leg. This means that the
dinosaur should be able to move the end of his leg (all other aspects of the
human and dinosaur remaining proportional) about 4 times faster than the
human. With the information given that a human can run about 10 mph,
this puts the T. rex speed at about 40 mph, which is close to the higher
speed. Again, this assumes that the dinosaur muscle can contract many
times faster than the human’s.
However, students should notice that dinosaur and human are far from
being proportional in many ways. The mass of the T. rex, at about 15 000
pounds, is 100 times more massive than the human. The muscle strength
needed to move this mass (increased load), as well as contract many times
faster than the human leg muscle to hit 45 mph, should make the argument
that this was a slow dinosaur believable.
On the other hand, if T. rex was a near-sighted animal that had trouble
detecting objects unless they were in motion, catching prey might be a
formidable task. So, a faster moving dinosaur might have a better
adaptation for survival.
2. Sue at the Field Museum Website:
http://www.fieldmuseum.org/sue/index.html
To prepare for an investigation of Sue as a system of levers and to analyze
the speed of T. rex using the Theropod Mechanics information, visit this
collection of pictures of Sue’s skeleton and Sue’s vital statistics.
Information about mass and height (13 meters at the hip) can be used to
add to the debate about T. rex speed. The image gallery includes pictures
of Sue that can be projected to the class for a pre-trip discussion of limbs
and levers.