AP Physics
Monday 13.12.02
Standards: 1b3 Calculate
the change in speed or
kinetic energy that results
from performing a
specified amount of work
on an object.
Warm Up
Find the speed of a 10kg object with
2000 J of energy?
ke=(1/2)mv2
Objective: S WBAT to solve
problems involving the work
energy theroem
Agenda
1. Warm Up
2. Turn in Homework Packet
3. Review Thanksgiving HW
4. Kinetic Energy Notes &
Guided Practice
Homework
#E3
AP Physics
Tuesday 13.12.03
Standards: C1b2&3 Use the
Work Energy Theorem
Objective: SWBAT conceptualize
the relationship between work
and kinetic energy.
Agenda
1. Warm Up
2. Lab Report Instructions.
3. Work / Energy Theorem
Warm Up
The male polar bear when standing is 3
m tall with a mass of 500 kg. The polar
bear can run up to 56.0 km/hr. Find the
kinetic energy of the polar bear.
Homework
E4
Lab Report Due Friday
AP Physics
Wednesday 13.12.04
Standards: C2b4&5 conservative forces &
potential energy from gravity and springs
Objective: SWBAT distinguish between
conservative and non-conservative forces
in order to determine whether or not it
stores energy solve problems involving
conservative forces
Agenda
1. Warm Up
2. Review E4
3. Conservative forces: Spring &
Gravity
Warm Up
A 2kg marble traveling at 2m/s runs
into a 1kg block moving it 0.5 m. How
much Force did the marble hit the
block with?
Homework
HW E5
Lab Report Due Friday
AP Physics
Thursday 13.12.05
Standards:
C3ab: Conservation of Energy
Objective: SWBAT solve problems using
the understanding that energy changes
form but does not disappear.
Warm Up
In 1992, Ukranian Sergei Bubka used a
short pole to jump to a height of 6.13m. If
the maximum potential energy associated
with Bubka was 4.80 kj at the midpoint of
his jump, what was his mass?
Agenda
1. Warm Up
2. Collect Thanksgiving Break Problems
3. Review #E5
4. Conservation of Energy Notes &
Practice
Homework
E#6
AP Physics
Friday 13.12.06
Standards: Cab Conservation of
Energy
1b3 Objective: SWBAT find the kinetic
and potential energy at each point in a
chain of energy exchanges.
Agenda
1. Warm Up
2. Collect Lab Write Ups
3. Review HW #6
4. Energy Lab
Warm Up
A 60.0 kg ball of clay is tossed vertically in
the air with an initial speed of 4.60 m/s.
Ignoring air resistance, what is the change
in its potential energy when it reaches its
highest point?
Homework
#E7
AP Lab Write Up Rubric
Section
4
3
2
1
Question/Hypothesis
The central question the lab is
asking is stated along with a
plausible hypothesis
The central question is stated
and something resembling a
hypothesis is stated
Only the central question is
stated
The section is missing or
contains the wrong central
question.
Materials/Procedures
The procedures are written
step by step in complete
sentences and the materials
are clearly listed.
The procedures and materials
are listed but unorganized. The
procedure does not explain the
lab
Either the procedures or the
materials are incomplete.
Only procedures are present,
or only materials are present.
Data Collection
The lab contains a table and a
graph that represents the data
accurately and is labeled
correctly with the equation of
the line written.
The lab contains a table and a
graph but it may be missing
some labels and the graph may
not be done correctly.
The lab is missing a graph
completely.
The data is incomplete.
Calculations
Students have all calculations
completed, with work shown,
and they are correct.
Students have all calculations
completed and at least half are
done correctly and all work is
shown.
Students do not have all
calculations completed, and
little work is shown.
Calculations section is mostly
or entirely missing.
Analysis
The student gives evidence
from their lab data why their
hypothesis is true, false, or
inconclusive. The discuss the
relationships between the
variables that were graphed
and if linear they write down
the equation of the line.
The students gives evidence
from their lab data and
attempts to prove that the
hypothesis is false, true or
inconclusive, but the data is
misapplied and doesn’t support
their claim. For linear graphs,
no equation is given.
This section discusses whether
the hypothesis is true,
inconclusive, or false but no
data is used to support the
hypothesis and any reference
to the graph or the data is too
general to be helpful.
This section is omitted or the
student may mention the
hypothesis and its validity, but
doesn’t explain or the
explanation is not plausible
Conclusion
The conclusion includes a
summary of your lab results,
(which will include numbers or
equations), gives %error and
discusses sources of error. It
also gives a suggestion about
how to improve the lab.
The conclusion includes a
summary of your lab results. It
includes data. % error is given.
Either and least 1 source of
error discussed or a suggestion
is given to improve the lab.
The conclusion includes a
summary and either % error, or
mentions types of error, or
mentions improving the
experiment.
The conclusion is omitted or
only includes a brief summary.
Conservation of Energy Lab
Objective: Students will use the concept of conservation of energy to
verify the mass of the marble by rolling it down ramps of different
heights.
Theory: Conservation of Energy: As Potential Energy decreases, kinetic
energy increases, so by the time the ball reaches the flat surface all
the potential energy should have been converted into kinetic energy.
How will you know you’re successful?
-The slope of your ___ vs ____ graph will equal (½)m. Using that slope
you will be able to calculate mass.
-You can compare your experimental mass value with the found found
using a spring scale and/or a triple beam balance using a percent error
calculation.
Lab Write Up, Using Standard Lab Write Up Rubric Due Wednesday
Work Practice E#2
1.
2.
3.
4.
5.
6.
7.
A child pulls a wagon full of toys using a rope over his/her shoulder. If the angle of the rope is 60
degrees above the horizontal, how much work will s/he do if he moves the cart 12m after applying
320 N of Force?
(ex)The largest palace in the word is the Imperial Palace in Beijing, China, Suppose you were to push
a lawn mower around the perimeter of a rectangular area identical to that of the palace, applying a
constant horizontal force of 60.0 N. If you did 2.05x105 J of work, how far would you have pushed
the lawn mower? If the Imperial Palace is 9.60x102 m long, how wide is it?
(1) Lake Point Tower in Chicago is the tallest apartment building in the United States (although not
the tallest building in which there are apartments). Suppose you take the elevator from street level
to the roof of the building. The elevator moves almost the entire distance at constant speed, so
that it does 1.15x105 J of work on you as it lifts the entire distance. If your mass is 60.0 kg, how tall
is the building. Ignore the effects of friction.
(3) A hummingbird has a mass of about 1.7g. Suppose a hummingbird does 0.15 J of work against
gravity, so that it ascends straight up with a net acceleration of 1.2m/s2 How far up does it move?
3
(8) The largest mincemeat pie ever created had a mass of 1.02x10 kg. Suppose that a pie with this
mass slides down a ramp that is 18.0 m long and is inclined to the ground by 10.0°. If the
coefficient of kinetic friction is 0.13, what is the net work done on the pie during its descent?
(9) The longest shish kebab ever made was 881 m long. Suppose the meat and vegetables need to
be delivered in a cart from one end of this shish kebab’s skewer to the other end. A cook pulls the
cart by applying a force of 40.00 N at an angle of 45.00° above the horizontal. If the force of
friction acting on the cart is 28.00 N, what is the net work done on the cart and its contents during
the delivery?
3
(11) width of 78 m. the flag’s mass is 1.24x10 kg, which may explain why the flag has never been
flown from a flagpole. Suppose this flag is being pulled by two forces: a force of 8.00x103N to the
east and a force of 5.00x103 N that is directed 30.0°south of east. How much work is done in
moving the flag 20.0 m directly south?
Kinetic Energy Practice
1.
2.
3.
4.
#E3
(Ex) Silvana Cruciata from Italy set a record in one-hour running by
running 18.084 km in 1.000 h. If Cruciata’s kinetic energy was 694
J, what was her mass?
(2) The fastest helicopter, the Westland Lynx, has a top speed of
4.00x102 km/h. If its kinetic energy at this speed is 2.10x107 J,
what is the helicopter’s mass.
(7) The brightest, hottest, and most massive stars are the brilliant
blue stars designated as spetral class O. If a class O star with a
mass of 3.38x1031kg has a kinetic energy of 1.10x1042J, what is its
speed? Express your answer in km/s (a typical unit for describing
the speed of stars)
(6) Susie Maroney from Australia set a women’s recond in longdistance swimming by swimming 93.625 km in 24.00 h.
1.
2.
What was Maroney’s average speed?
If Maroney’s mass was 55 kg, what was her kinetic energy?
Conservative Forces & Potential
Energy
If a Force is a conservative Force, then the work done by that
Force is stored for later use. In essence, work is done against the
Force and it is stored as potential energy.
Some Examples
Some Non-examples
Gravity
Friction
Springs
Air Resistance
Gravitational Potential Energy
-Work=F * D
- Fg=mg
-W=mgh=ΔU
- When work is done on an object against gravity, (I pick up a pen
from the floor and put it in my pocket). The object I do work on
(the pen) gains potential energy. So for the Gravitational Force
and all conservative Forces (W=ΔU)
Potential Energy From a Spring
The spring force is a conservative force.
Spring Force F=-kx
W=f*d
Since W=ΔU and the distance d in work is equivalent to x in the
spring force equation.
Energy Stored by a Spring Usp=1/2kx^2
Conservation of Energy
Energy is not created or destroyed. It is conserved. Energy can change
forms, but in any system the total energy you start with will be the
total energy you end up with.
- This means: If you have two objects falling from the same height
taking two different paths to the ground, they will have the same
speed when they hit the ground. Energy calculations are path
independent. This makes sense because Energy is a scalar quantity.
Direction doesn’t actually matter, so why would the specific path an
objects takes matter. Only the starting point and ending point matter.
Energy
What is Energy? The ability to do work.
Kinetic Energy - the energy of motion KE=1/2mv2
Potential Energy (U) – energy stored for later use. The most
common type of potential energy we’ll see is gravitational
potential energy. Ug=mgh mass times the accelerations due to
gravity times the height of the object.
When potential energy is used up, it converts to kinetic energy,
alternatively is can be dissipated by friction and other forces and
converted into heat, sound, or deformation energy.
Work-Kinetic Energy Theorem #E4
1.
2.
3.
4.
(1) The tops of the towers of the Golden Gate Bridge, in San Francisco,
are 227 m above the water. Suppose a worker drops a 655 g wrench
from the top of a tower. If the average force of air resistance is 2.20 %
of the force of free fall, what will the kinetic energy of the wrench be
when it hits the water? Hint: Fnety=Fg-Far since Far is 2.20% of Fg we
can write Fnety=Fg- 0.022Fg
(2) Bonny Blair of the United States set a world record in speed
skating when she skated 5.00x102 m with an average speed of 12.92
m/s. Suppose Blair crossed the finish line at this speed and then
skated to a stop. If the work done by friction over a certain distance
was -2830 J, what would Blair’s kinetic energy be, assuming her mass
to be 55.0 kg.
(3) The CN Tower in Toronto, Canada, is 553 m tall, making it the
tallest free-standing structure in the world. Suppose a chunk of ice
with a mass of 25.0 g falls from the top of the tower. The speed of the
ice is 30.0 m/s as it passed the restaurant, which is located 353m
above the ground. What is the magnitude of the average force due to
air resistance?
(6) In 1990, Roger Hicky of California reached a speed of 35.0 m/s on
his skateboard. Suppose it took 21 kj of work for Roger to reach this
speed from a speed of 25.0 m/s. Calculate Hickey’s mass.
Guided Practice:
Work & Kinetic Energy Theorem
W=ΔKE
The Great Pyramid of Khufu in Egypt, used to have a height of
147 m and sides that sloped at an angle of 52.0° with respect to
the ground. Stone blocks with masses of 1.37x104 kg were used
to construct the pyramid. Suppose that a block with this mass
at rest on top of the pyramid begins to slide down the side.
Calculate the block’s kinetic energy at ground level if the
coefficient of kinetic friction is 0.45.
Homework E#5 Potential Energy
1. EXTRA CREDIT (DUE Monday)
1.
2.
3.
1.
Use the 3rd equation of motion, Newton’s 2nd Law equation & the equation for Work to derive the
kinetic energy equation. (include a diagram that contains all symbols you used)
Use the equation for Work & Weight to derive the Gravitational potential energy equation (include
a diagram containing all symbols used)
Use the equation for Spring Force and Work to derive the Elastic potential energy equation
(include a diagram containing all symbols used)
(Ex) In 1993, Javier Sotomayor from Cuba set a record in the high jump by clearing a vertical distance of 2.45m.
If the gravitational potential energy associated with Sotomayor at the top point of his trajectory was 1.59x10^3
J, what was his mass?
(4)The highest-caliber cannon ever built (though never used) is located in Moscow, Russia. The diameter of the
cannon’s barrel is about 89 cm, and the cannon’s mass is 3.6x10^4 kg. Suppose this cannon were lifted by
airplane. If the potential enregy associated with this cannon were 8.88x10^8 J, what would be its height above
sea level? Assume that constant free-fall acceleration at this altitude is the same as at sea level.
(6) In 1992, David Engwall of California used a slingshot to launch a dart with a mass of 62g. The dart traveled
a horizontal distance of 477 m. Suppose the slingshot had a spring constant of 3.0x10^4 N/m. If the elastic
potential energy stored in the slingshot just before the dart was launched was 1.4x10^2 J, how far was the
slingshot stretched.
(9.) In 1872, a huge gold nugget with a mass of 286 kg was discovered in Australia. The nugget was displayed
for the public before it was melted down to extract pure gold. Suppose this nugget is attached to the ceiling by
a spring with a spring constant of 9.5x10^3 N/m. The nugget is released from a height of 1.70 m above the
floor, and is caught when it is no longer moving downward and is about to be pulled back up by the elastic
force of the spring.
2.
3.
4.
1.
2.
3.
4.
If the spring stretches a total amount of 59.0 cm, what is the elastic potential energy associated with the springnugget system.?
What is the gravitational potential energy associated with the nugget just before it is dropped?
What is the gravitational potential energy associated with the nugget after the spring has stretched 59.0 cm?
What is the difference between the gravitational potential energy values in parts (b) and ©? How does this
compare with your answer for part (a)?
Guided Practice Mechanical
Energy
The largest apple ever grown had a mass of about 1.47 kg.
Suppose you hold such an apple in your hand. You accidentally
drop the apple, then manage to catch it just before it hits the
ground. If the speed of the apple at that moment is 5.42 m/s,
what is the kinetic energy of the apple? From what height did
you drop it?
Conservation of
Mechanical Energy #E6
1.
2.
3.
4.
5.
(2) One species of eucalyptus tree, Eucalyptus regnens, grows to heights similar to those
attained by California redwoods. Suppose a bird sitting on top of one specimen of
eucalyptus tree drops a nut. If the speed of the falling nut at the moment it is 50.0 m
above the ground is 42.y m/s, how tall is the tree? Do you need to know the mass of the
nut to solve this problem? Disregard Air resistance.
(3) In 1989, Michel Menin of France walked on a tightrope suspended under a balloon
nearly at an altitude of 3150 m above the ground. Suppose a coin falls from Menin’s
pocket during his walk. How high above the ground is the coin when its speed is 60.0
m/s?
(5) Suppose a motorcyclist rides a certain high-speed motorcycle. He reaches top speed
and then coasts up a hill. The maximum height reached by the motorcyclist is 250.0 m.
If 2.55x105 J of kinetic energy is dissipated by friction, what was the initial speed of the
motorcycle?
(6) The deepest mine ever drilled has a depth of 12.3 km (by contrast, Mount Everest has
height of 8.8 km.) Suppose you drop a rock with a mass of 120.0 g down the shaft of this
mine. What would the rock’s kinetic energy be after falling 3.2 km? What would the
potential energy associated with the rock be at that same moment? Assume no air
resistance and a constant free-fall acceleration.
(7) Desperado, a roller coaster built in Nevada, has a vertical drop of 68.6 m. The roller
coaster is designed so that the speed of the cars at the end of this drop is 35.6m/s.
Assume the cars are at rest at the start of the drop. What percent of the initial
mechanical energy is dissipated by friction?
Conservation of Mechanical Energy
For a system with only conservative forces.
E=Eo
or
K+Uf=K+Uo
where K=(1/2)mv2 and U=mgh
For a system with both conservative and non-conservative forces.
Energy Loss= ΔE=E-Eo
where ΔEloss is the energy lost to the system by the non-conservative
force. (Note: The energy still exists but is not is a very usable form. e.g. heat)
The Energy lost is the same as the work done by the non conservative
force such as Friction.