Transcript Building the Ancient Pyramids…

Building the Ancient
Pyramids…
• Located on the Giza Plateau, the Great
Pyramid (or Pyramid of Khufu) is truly
marvelous
• How did the ancient Egyptians build it?
Some Stats
• Constructed from approximately 25802560 BCE
• The world’s tallest structure (480 ft, now
460ft) for over 3000 years
• The pyramid contains 2 million blocks,
each weighing 1.5 tons
• Some materials were transported over 500
miles to the construction site
• A truly massive undertaking (no pun
intended…)
• Let’s focus on how the blocks were
transported to their actual locations on the
pyramid
• The pyramid has a height of 480 ft
• How did they transport massive stones to
such heights?
Masters of Simple Machines
• The Egyptians were smart enough to
realize the practical value of simple
machines
• A machine is a device which can multiply
or change the directions of forces
• The primary machine used by Egyptians
was the ramp, or inclined plane
• What does the ramp do for us (think back
to the lab…)
• It reduces the amount of necessary force
to transport an object from one location to
the other
Egyptian Ramps
Some Numbers
• The force necessary to lift a 1.5 ton block
straight up in the air is about 14,000N
• The force required to push it up a ramp
inclined at 15° is 3500N
• The ramp reduces the amount of force
necessary to move the block
Mechanical Advantage
• Without the machine, we’d need 14000N
to move the block
• With the machine, we need 3500N
• The ratio of these two forces is called
Mechanical Advantage (MA)
• In this case, our MA is 14000N/3500N,
which equals 4
Which Force Goes Where?
• MA = Output Force/Input Force
• Input Force is the force we apply, using
our machine
• Output Force is the force we’d need
without the machine (or the effective force
we get with the machine)
Other Simple Machines
• Pulleys
• Levers
• Screws
Pulley Demo
• What is the Mechanical Advantage of this
pulley system?
A Choice of MA
• You have the choice of using four simple
machines to achieve a task. Machine 1
has a MA of 1.2; Machine 2, 0.5; Machine
3, 4.5; Machine 4, 1
• Which would you choose?
• Why?
• Which machine would do more harm than
good?
The Catch
• Using the ramps, the Egyptians needed
less force to push the blocks up the ramp
• What was the tradeoff?
• They had to move the stones further than
they would have by lifting them straight up
Think Back to the Lab
• What did you notice about the values in
the far right column in your data table?
• They should have been constant
• What does Force x distance represent?
• Work
Work
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We’re all familiar with work
Love it, hate it, we all have to do it
Scientific work however, is a bit different
Work = Force x Displacement
Units?
• There’s a better way to talk about work
than Newtons x meters
• To better deal with work, we define a new
unit, called a Joule (J)
• Find the work done by a 10N force that
moves an object 30m
• 300J
Direction Matters
• Imagine two situations:
• In situation 1, you pick a book up off the
ground and lift it up 1m
• In situation 2, you walk for 5 miles with the
book already in your hand
• In which situation do you do more work on
the book?
• One can only do work on an object if the
force is in the direction of motion, or
against it
• The entire force does not have to be in
that direction; a piece of a force can also
do work on an object
A Better Definition
• Work = Force x Distance x cos q
• W = Fd cos q
• **Note: F and d represent magnitudes,
not vectors
• q is the angle between the force vector
and your direction of motion
• In an airport, a traveler pulls her luggage
across the ground with a 20N force, which
is at an angle of 35 with the horizontal
• If she moves the suitcase 10m, calculate
the work done by her pull
• What is the work done by friction?
Machine Efficiency
• In an ideal machine, the work you do with
the machine = the work you would do
without the machine
• In reality, these values are never the same
Why?
• Think about an Egyptian worker pushing a
stone up the ramp
• Which other forces does the worker
experience?
• Friction
• He’s got to push a little harder than he
would without friction, which results in
more work
• The ratio of the work we get out of the
machine to the work we put into the
machine is called efficiency
• In an ideal machine, it is always 1
• In reality, it is always less than 1
• Efficiency = Output work/Input work
• If we multiply this number by 100, we
can represent efficiency by a %
Input vs. Output
• Using 40N of force, I push a 80kg object
5m up a ramp. Assuming the object starts
on the ground and ends 2m high
Give the input and out work, respectively:
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1. 80J, 40J
2. 160J, 200J
3. 200J, 160J
4. 40J, 80J
• In a rope/pulley system, a 4kg mass is
raised vertically 0.2m. To accomplish this,
a 25N horizontal force is applied over a
distance of 0.4m
• What is this pulley’s efficiency?
• 78-80%
+ and - Work
• So what happens when your angle = 180,
and work is negative?
• Work is a scalar, so the + and – do not
represent direction
• They give us some indication of the
energy gain or loss of a system
What is Energy?
• Scientifically, energy gives us the ability to
do work
• Like work, it has units of Joules
• Suppose I do 40J of work on an object;
what is this object’s change in energy?
– (use a – sign if it loses energy…)
• Bonus: What if it does 40J of work on
me?
Work/Energy Theorem
• A fancy way of saying what we already
know: doing + work on an object gives it
energy and doing – work on an object
takes energy away
Energy Types
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Kinetic
Potential
Radiant
Like work, energy is a scalar quantity
Kinetic Energy
• Kinetic Energy (KE) is energy associated
with motion
How Much KE?
• We calculate an object’s kinetic energy by
the equation:
• KE = ½ (mass) x (speed)2
• The 2 may not seem important to you, but
it explains everything from why baseball
players cork bats to why comets are more
dangerous than asteroids
An elephant (1) and mouse (2)
both have the same amount of
Kinetic Energy. Which is moving
faster?
Do they have the same amount
of momentum?
Assume the elephant from the
previous problem (m=1500kg) is
running at 10m/s. How much
kinetic energy does this
elephant have while running?
Two objects (A and B) have the
same mass, but object A is moving
3 times as fast as object B. What
is the ratio KEA/ KEB?
Corking Bats and Dangerous
Asteroids
• The 2 may not seem important to you, but
it explains everything from why baseball
players cork bats to why comets are more
dangerous than asteroids
Potential Energy
• Potential is “stored” energy that has the
potential to do work
• A stretched rubber band, a compressed
spring, TNT, a nucleus, and a rock on the
edge of a cliff all have potential energy
Gravitational Potential Energy
• Gravitational Potential energy is the
potential energy of an object due to its
position
• GPE = weight x height = mgh
• So…
• The higher an object relative to the
ground, the more gravitational potential
energy it has…
Imagine 3 objects, A, B, and C. Object A is
located 2m above the ground; object two
has ½ the mass of A and is also 2m off the
ground; Object C has ¼ the mass of A and is
located 10m off the ground. Rank the GPE
of these objects in increasing order
• 1. A, B, C
• 3. B, A, C
• 5. A, C, B
2. B, C, A
4. C, A, B
An astronaut in full space gear
climbs a vertical ladder on Earth
(1). Later, she makes the same
climb on the moon (2). In which
location does her GPE change
less?
A 10kg object is lifted from the
floor to a shelf, 2m off the
ground. What is the change in
this object’s GPE?
Bonus: How much work did it
take to get the object up to the
ledge?
Elastic Potential Energy
• The energy stored in a stretched spring
• Depends upon the amount the spring is
stretched/compressed, the type of spring
Chemical Potential Energy
• A combustion reaction releases a large
amount of energy…
• What is this energy’s origin?
• From the chemical bonds between atoms
Nuclear Potential Energy
• Using a nuclear device, we can take an
object the size of a soccer ball and destroy
a city
• The energy released comes from the
nuclei of the constituent atoms
Electrical Potential Energy
• Energy dependent upon the location of
charged particles
• We can use this energy to move charges
(electricity)
Energy Conservation
• One of the pillars of science is the law of
energy conservation:
• You can neither make nor destroy
energy, you can only change it from
one form to another
• Basically, in any situation you always start
and end with the same amount of energy
• That energy can be rearranged in different
ways
Pendulums
• Energy Skate Park:
• http://phet.colorado.edu/new/simulations/si
ms.php?sim=Energy_Skate_Park
• Mass/Spring Applet
• http://phet.colorado.edu/new/simulations/si
ms.php?sim=Masses_and_Springs
Energy Conservation Clips
• http://www.youtube.com/watch?v=tbhT6Kb
HvZ8
• http://www.youtube.com/watch?v=yVE81B
HBD0E
Suppose I throw a 5kg ball up in the air.
Assuming it has 200J of kinetic energy
when it leaves my hand, how high will it
rise?