Download Applied Science in Palaeontology: Physics

DISTANCE LEARNING PROGRAM
PROGRAM OVERVIEW
TOPIC: Discover how physics can be applied to the fascinating field of palaeontology.
THEME: What was the bite force of a T. rex? How can we calculate the speed of a dinosaur from its footprints? How
much energy was released by the impact of an asteroid that killed off the dinosaurs 65 million years ago? Find out the
answers to these questions and much more in this challenging program that uses High School Physics to tackle the
ancient mysteries of the Mesozoic Era.
PROGRAM DESCRIPTION: There are three modules in the program:
1. BITE FORCE: Students will calculate the bite force of Tyrannosaurus rex.
2. VELOCITY: Students will calculate the velocity of Tyrannosaurus rex from a trace fossil.
3. IMPACT: Students will calculate the amount of kinetic energy released from the asteroid impact 65 million years ago.
The students will be working in teams of 2–3. If not already pre-divided, the Science Educator will divide the
students into small teams (there can be up to 10 teams). The Science Educator will introduce the game concept
and explain that the students will be competing against each other. Using scientific calculators, the students
work together to supply answers using the provided “Calculation Sheet.” Answers must be calculated to two
decimal points, and units count!
AUDIENCE: Grades 10 – 12
DURATION: 45-minutes
ALBERTA CURRICULUM CONNECTIONS:
Grade 10
Science 10: Energy Flow in Technological Systems
Science 14: Understanding Energy Transfer Technologies
Grade 11
Science 20: Changes in Motion
Physics 20: Kinematics; Dynamics; Circular Motion; Work and Energy
PACKAGE CONTENTS:
Detailed Program Breakdown
page 2
Formulas Sheet
page 4
Activities
Dino Balancing Act
page 5
Planet Smashers: Meteor Impact Experiment
page 7
Heavy Hitters
page 12
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DETAILED PROGRAM BREAKDOWN
1. BITE FORCE
This module is based on the research of Dr. François Therrien, Curator of Dinosaur Palaeoecology.
Jaws can be simplified into simple beam lever mechanisms. Use Dr. Therrien’s formulas to calculate the relative
strength of a T. rex lower jaw (mandible).
Students will:
· Learn about Beam Theory
· Calculate the Bending Strength of the mandible
· Calculate Bite Force (a proxy value since T. rex is extinct)
The resulting value for force is in centimetres squared. This is a comparative value. For example,
Dr. Therrien has calculated the proxy bite force on the American alligator (the mean of a variety of
specimens) as 0.16 cm2. That means that T. rex had a bite force about 16 times that of a Nile crocodile.
· Solve two questions and will submit their answers for points on the scoreboard.
2. VELOCITY
Based on the research of Dr. Donald M. Henderson, Curator of Dinosaurs.
Students will:
· Calculate the hip height of T. rex
· Understand Stride Length: the distance between two successive placements of the same foot.
· Learn about William Froude and the “Froude Number.” Froude was a naval engineer who developed a way to scale
model ships to their full-sized versions. It is a dimensionless number that has no units and is used for comparison and
scaling.
· Transpose the Froude Number Formula to solve for velocity.
· Learn about Robert McNeill Alexander. He is a palaeontologist that uses Froude numbers to calculate the speed of
dinosaurs.
· Calculate the Relative Stride Length of T. rex
· Calculate the velocity of T. rex
Only one single Tyrannosaurus rex footprint has been discovered. Since trackways (a series
of footprints) have yet to be found, there are many unanswered questions about exactly how fast
it could have moved. Our calculations in this program are made under the assumption that T. rex was
walking when it made the track.
· The students will solve four questions and will submit their answers for points on the scoreboard.
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3. IMPACT
There are objects that can collide with the Earth.
N.E.O or “Near Earth Object”: any object (comet or asteroid) with an orbital distance that is less than
1.3 AU (astronomical units). An astronomical unit is the mean distance between the Earth and the Sun
or about 150,000,000 km N.E.A or “Near Earth Asteroid.” Any solid object 50m ~ 32km in diameter
~ 6244 known, comprised of dense, heavy metal such as iron.
Students will:
· Calculate the mass by multiplying the volume by the density
The formula for determining the volume is: V = π 4/3 radius cubed.
The radius of the asteroid is 5000 metres.
The density of the meteor is estimated to be 4.5 grams per cubic centimetre (density for iron)
· Calculate the mass of the meteor by multiplying the volume by the density.
· Calculate the kinetic energy (KE) of the asteroid
The velocity of the asteroid is estimated to be 11,000 metres per second. (KE= ½ mv 2 )
The asteroid that created the Chicxulub crater at the end of the Mesozoic Era would have released two
million times more energy than the largest nuclear bomb ever detonated—the emperor bomb, created
by the Soviet Union, which was 50 megatons!
How much energy is that? The largest atomic bomb ever created was the “Tsar Bomba”
at 50 megatons and when detonated released approximately 2.1 x 1017 J. That means the energy
released from the asteroid impact would have been equivalent to about 681,000 Tsar Bombas
detonating!
CONCLUSION
Palaeontologists make use of basic science principles and physics in their studies of ancient life.
REFERENCES
Students are encouraged to look into dinosaur biomechanics and the application of physics in areas of interest to
them.
Alexander, R. McN. 1991. How Dinosaurs Ran. Scientific American, April:130–136.
Alvarez, W. 1997. T.rex and the Crater of Doom, Princeton University Press, Princeton, New Jersey:
185 pp.
Henderson, D. M. 2003. Footprints, Trackways, and Hip Heights of Bipedal Dinosaurs – Testing Hip
Height Predictions with Computer Models. Ichnos, 10:1–16.
Therrien, F., Henderson, D.M., and Ruff, C.B. 2005. Bite me: Biomechanical models of theropod
mandibles and implications for feeding behavior. In K. Carpenter (ed.), The Carnivorous Dinosaurs,
Indiana University Press, Bloomington, pp. 179–237.
Thulborn, R.A. 1990. Dinosaur Tracks. Chapman and Hall, London: 410 pp.
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FORMULAS
1. BITE FORCE
Relative Bending Strength (cm3 )
Z= πab2
4
Bite Force (proxy value, cm2 )
Fp = Z
L
2. VELOCITY
Height of leg (m)
H= 4L
Froude Number (no units)
Fr= v2
λg
Relative Stride Length (no units)
R= λ
H
3. IMPACT
Mass (kg)
M= ρV
Volume of a sphere (m 3 )
Kinetic Energy (J)
V= π 4/3 r3
KE= ½ mv2
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DISTANCE LEARNING PROGRAM
grades 10–12
DINO BALANCING ACT
How do the principles of balance and load bearing relate to dinosaur
biomechanics? A bipedal dinosaur balances like a teeter totter with each end
acting as a lever. Using the lever theory, explore the fundamentals of balance
in this fun, hands-on experiment.
CONCEPTS
When balancing a lever such as the body of a bipedal dinosaur, the longer
the lever arm, the greater the mechanical advantage. Therefore, a small
weight over a long lever, such as a T. rex tail is able to counterbalance the
greater weight closer to the fulcrum in the head and chest of the dinosaur.
ACTIVITY 1: EXPLORING BALANCE
In this activity, we will explore the relationship between the length of lever arms and its affect on balance of the
whole lever.
MATERIALS:
· Metre sticks, one per group of four students.
· Plasticine or sticky tack, 500 grams per group of students.
· Scales for weighing plasticine.
METHOD:
1. Divide plasticine into equal pieces that weigh 250 grams each.
2. Stick a piece of plasticine at the tip of each end of the metre stick.
3. Label the half of the metre stick from 0 cm to 50 cm “Side A” and from 50 cm to 100 cm “Side B.”
4. Find the balancing point in the middle of the metre stick. Where can you support the metre stick with just one
finger and have it rest horizontally? That is the place we call the balancing point.
Balance point
cm mark
5. Try the following experiments with weights and lengths:
· Put all of the weight in the centre.
Balance point
cm mark
· Put 250 grams at the 25 cm mark on side (A) and 250 grams at the 100 cm mark on side (B).
Balance point
cm mark
· Put 250 grams at the 100 cm mark and 250 grams at the 50 cm mark in the middle.
Balance point
cm mark
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DINO BALANCING
ACT 5
ACTIVITY 2:
RECONSTRUCTING T. REX
T. rex had a massive head and very tiny front limbs, counterbalanced by a long tail. In this activity, we will make
a model of this dinosaur and explore how it was able to balance its massive body.
3m
+
1m
+
The center of mass in each half of the animal is marked
with a ‘plus’ sign.
The fulcrum between the two levers runs vertically through the
animal’s hips at the hip socket.
The lever of the tail end is three metres from the fulcrum to the
tail’s centre of mass. The lever of the torso is one metre from
the fulcrum to its centre of mass.
For this activity, we’ll call the torso lever the moment arm of load and the tail lever the moment arm of effort.
What mechanical advantage does this give to the tail? Use Archimedes’ formula:
Mechanical Advantage =
mechanical advantage =
load force = moment arm of effort
effort force
moment arm of load
To recreate the balance of a T. rex; use the metre stick and the plasticine.
1. Place the fulcrum under the metre stick at the point where side (a), the tail end has a mechanical advantage of
three to one over side (b), the torso end.
2. Place 300 grams of plasticine on the tip of the (b) end to represent the weight of the torso.
What weight of plasticine must be put onto the tip of the (a) end in order to achieve equilibrium at the
fulcrum point?
Weight
a
b
Once you have created your balance models, can you walk across the room with the metre stick balanced on
one finger at the balance point?
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DINO BALANCING
ACT 6
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DISTANCE LEARNING PROGRAM
PLANET SMASHERS: METEOR IMPACT EXPERIMENT
grades 10–12
Recreate the awesome power of a meteorite on a small scale. Calculate the velocity and kinetic energy
of various impactors. Extrapolate data based on observations and then make and test hypotheses about changes
in experimental outcomes.
CONCEPTS:
The kinetic energy of a falling object can be calculated using the known factors of gravitational acceleration
and object mass. Objects with the same density, but different mass, will have different kinetic energy.
Ancient craters formed by extraterrestrial impactors have been found all over the Earth. Using the principles
of physics, scientists are able to estimate the mass and velocity of ancient objects that no one has ever witnessed.
MATERIALS:
· Two graphs provided, per student or group
· A variety of pencil crayons
· Large tray or tub at least 30 cm deep
· Sand – enough to fill the tray approximately 20 cm deep
· White fl our – enough to create a layer 7 cm deep
· Cocoa powder, tempera paint, or glitter – enough to sprinkle uniformly on top of the fl our
(may want to use a sieve)
· Measuring tape for measuring the height of the drop
· Small ruler for measuring crater diameter
· Scale
· Slingshot (optional)
· 5 impactors of same density, but increasing diameter, for example…
Plasticine or clay rolled into balls of 1, 2, 4, 6, 8 cm diameter
Rocks of the same kind that are approximately 1, 2, 4, 6, 8 cm diameter
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PLANET SMASHERS
METHOD:
GRAPH #1 – MASS (g) VS. KINETIC ENERGY (J)
The x axis is the object’s mass; the y axis is the kinetic energy of each object.
Determine the weight of each object by weighing it on the scale. Mass will be expressed in grams (g).
Consider the following…
If an object is dropped from a height of one metre, it is possible to determine the time it takes to drop using the
following formula…
2y =t
g
Here y is the distance of the drop or 1 m. Therefore t is 0.45 s.
To determine the velocity of the object being dropped from 1 m the formula
v=gt can be used. In this case the velocity is 4.43 m/s.
Determine the kinetic energy (expressed in Joules or J) for each impactor when dropped from a height of one
metre using the following formula…
2
KE = 1 mv
2
Impactor
Mass (g)
Kinetic Energy (J)
Plot the results on GRAPH #1. You will have to determine the scales for the x and y axis’ to include your greatest
mass and kinetic energy.
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GRAPH #2 – KINETIC ENERGY (J) VS. CRATER DIAMETER
1. Pour sand evenly across the baking pan. Add the white flour on top. Pack down the material.
2. Spread the cocoa, tempera or glitter material layer evenly on top of the flour to create a uniformly pigmented layer.
3. Make predictions about which object, representing an extraterrestrial meteorite, will cause the largest crater and why.
4. Drop each impactor from one metre. For each drop, be sure to aim for an undisturbed section of the pan. You may
need to re-set the set-up depending on the size of the tray.
5. Measure the diameter of each crater in centimetres (cm). Measure from the raised crater edge. If it is not visible,
measure where the crater begins sloping downward. Measure each crater diameter in the same manner.
6. Plot the results on graph #2. You will have to determine the scales for the x and y axis’ to include your
greatest kinetic energy (x-axis) and crater diameter (y-axis).
7. Based on the data from the first experiment, have the students make predictions about what will happen
when the same objects are dropped from twice the height (2 m).
How large will the crater be from each impactor?
Which impactor will create the largest crater?
How much kinetic energy will be released by each impactor?
8. Repeat the experiment this time dropping the objects from a two metre height.
9. Plot the results on GRAPH #2 using a different colour pencil.
10. Compare test results with students’ predictions.
If you like, repeat the process from heights of three and four metres.
OPTIONAL EXPERIMENT:
Shoot the objects into the flour matrix with a slingshot to demonstrate the dramatic increase in kinetic energy
created by increasing the velocity. Try to keep the angle of the shot consistent. If you do not have a slingshot,
you can always throw the impactors. Just be consistent with angle and velocity.
The crater made by a slingshot propelled impactor will be much larger than one propelled only by gravitational
acceleration.
But how fast was it going?
Try to estimate the velocity of an impactor propelled by a slingshot based on the diameter of the crater it makes.
Ask the students how they could use the formulas already provided in this exercise to estimate the velocity.
Hint: The KE formula will have to be transposed.
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kinetic energy (J)
GRAPH #1: MASS OF IMPACTOR TO KINETIC ENERGY
0
0
mass (g)
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crater diameter (cm)
GRAPH #2: KINETIC ENERGY TO CRATER DIAMETER
0
0
kinetic energy (J)
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DISTANCE LEARNING PROGRAM
grades 10–12
HEAVY HITTERS
Ankylosaurus defended itself by swinging its heavy bone tail club at attackers. Learn how to calculate the rotational
inertia, angular velocity, and kinetic energy of an ankylosaur tail club. Recreate the circular motion of a tail club,
experiment with the length of the radius and the mass of the object to find out what effect it has on the kinetic
energy, or ‘smashing power.’
CONCEPTS:
To calculate the kinetic energy of an object that is propelled in a circular orbit, we use the formula:
Kinetic energy (K) is equal to one half of rotational inertia (I) multiplied by the square of the angular velocity (ω).
2
K= 1 lω
2
Rotational Inertia in this situation is calculated with the formula:
l = mr2
Where (m) equals mass and (r) equals radius of gyration.
Rotational Inertia is equal to the mass multiplied by the square of the radius. So an increase in the radius leads to an
exponential growth in the rotational inertia.
Angular velocity is another way of saying, “revolutions per second.”
Angular velocity is expressed in radians per second when there is less than one rotation per second.
A radian is a portion of the circumference of a circle.
Every circle contains 6.28 radians; each of those radians is equal in length to the radius of the circle.
If an object rotates at a speed of 6.28 radians per second, it is making exactly one rotation per second.
If it travels at less than 6.28 radians per second, it is making less than one full rotation per second.
For simplicity in this experiment, let’s assume an angular velocity of 6.28 radians per second.
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ACTIVITY 1: MEASURING THE KINETIC ENERGY OF A MODEL TAIL CLUB
In this activity, we will explore the relationship between the length of a tail club and the amount of energy it would
release during a swing.
MATERIALS:
· A spool of high test fishing line
· Three weights that can be fastened to the end of the rope, a one-hundred gram weight,
a two-hundred gram weight and a three-hundred gram weight
· Tape measure
METHOD:
1. Attach a weight to the end of the fishing line.
2. Using the tape measure, measure 1.2 metres from the weight to the end of the line and cut the end.
3. Mark 0.2 metres off of the loose end as the centre of the radius, this is where you would hang on to the line to
swing it.
4. Using the mass of the weight on the fishing line and the one metre length of fishing line as the radius, calculate
the rotational inertia of the club using the formula:
l = mr2
5. Now calculate kinetic energy of the club if the fishing line were swung in a perfect circle at one rotation per
second.
0.1 kg
1m
0.2 m
2
K= 1 lω
2
6. Insert the results on the following table.
7. Repeat calculations with the two metres of fishing line. Now the radius will be two metres.
8. Repeat calculations with three metres of fishing line. Now the radius will be three metres.
0.1
KG WEIGHT TABLE:
Kinetic energy
Radius length
0.2
1m
2m
3m
1m
2m
3m
1m
2m
3m
KG WEIGHT TABLE:
Kinetic energy
Radius length
0.3
KG WEIGHT TABLE:
Kinetic energy
Radius length
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ACTIVITY 2: EXPLORING THE EFFECTIVENESS OF A TAIL CLUB
In this activity, we will explore the effect of a tail club strike using everyday objects.
MATERIALS:
· Model tail club from previous activity
· A volleyball
· Tape measure
METHOD:
1. Grasp the model tail club with your hand at the 0.2 m mark. Carefully, swing the weight over your head in a circle,
and adjust the velocity so that it is traveling at one rotation per second, or 6.28 radians per second. Try to keep the
weight spinning without varying the one metre radius.
2. Place a volleyball on a pedestal (a chair or the top of a step ladder) in the path of the spinning weight so that
it collides with the spinning weight. Make sure there are no people in the path of your tail club!
3. Make note of how far the ball is propelled by the impact.
4. Have students make predictions about how far the ball will be propelled by an impact with the same weight
but a two metre radius.
5. Repeat the experiment with a two metre radius and a three metre radius.
6. Make note of how the results agreed or conflicted with the predictions.
7. Repeat the experiment with the 200 gram weight and the 300 gram weight at the different lengths.
Compare the results of each change to the experiment with students’ predictions.
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