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Warm Up Find the speed of a 10kg object with 2000 J of energy? AP Physics Monday Standards: 1b3 Calculate the change in speed or kinetic energy that results from performing a specified amount of work on an object. Objective: S WBAT to solve problems involving the work energy theroem ke=(1/2)mv2 Homework #E3 Agenda Warm Up Turn in Homework Packet Review Thanksgiving HW Kinetic Energy Notes & Guided Practice

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AP Physics Tuesday Standards: C1b2&3 Use the Work Energy Theorem Objective: SWBAT conceptualize the relationship between work and kinetic energy. 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 Agenda Warm Up Lab Report Instructions. Work / Energy Theorem

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AP Physics Wednesday 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 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? Agenda Warm Up Review E4 Conservative forces: Spring & Gravity Homework HW E5 Lab Report Due Friday

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AP Physics Thursday 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 Warm Up Collect Thanksgiving Break Problems Review #E5 Conservation of Energy Notes & Practice Homework E#6

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AP Physics Friday Standards: Cab Conservation of Energy 1b3 Objective: SWBAT find the kinetic and potential energy at each point in a chain of energy exchanges. 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? Agenda Warm Up Collect Lab Write Ups Review HW #6 Energy Lab Homework #E7

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**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.

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**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

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Work Practice E#2 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? (8) The largest mincemeat pie ever created had a mass of 1.02x103kg. 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 N at an angle of 45.00° above the horizontal. If the force of friction acting on the cart is N, what is the net work done on the cart and its contents during the delivery? (11) width of 78 m. the flag’s mass is 1.24x103 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?

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**Kinetic Energy Practice**

(Ex) Silvana Cruciata from Italy set a record in one-hour running by running km in 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 long-distance swimming by swimming km in h. What was Maroney’s average speed? If Maroney’s mass was 55 kg, what was her kinetic energy?

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**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

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**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)

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**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

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**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.

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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.

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**Work-Kinetic Energy Theorem #E4**

(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 Fg (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 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 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.

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**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.

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**Homework E#5 Potential Energy**

1. EXTRA CREDIT (DUE Monday) 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. If the spring stretches a total amount of 59.0 cm, what is the elastic potential energy associated with the spring-nugget 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)?

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**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?

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**Conservation of Mechanical Energy #E6**

(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 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 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?

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**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.

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Physics 151: Lecture 15, Pg 1 Today’s Topics l Potential Energy, Ch. 8-1 l Conservative Forces, Ch. 8-2 l Conservation of mechanical energy Ch.8-4.

Physics 151: Lecture 15, Pg 1 Today’s Topics l Potential Energy, Ch. 8-1 l Conservative Forces, Ch. 8-2 l Conservation of mechanical energy Ch.8-4.

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