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Work and EnergySection 1 Preview Section 1 WorkWork Section 2 EnergyEnergy Section 3 Conservation of EnergyConservation of Energy Section 4 PowerPower Section 5 Extra questionsExtra questions

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Work and EnergySection 1 What do you think? List five examples of things you have done in the last year that you would consider work. Based on these examples, how do you define work?

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Work and EnergySection 1 Work In physics, work is the magnitude of the force (F) times the magnitude of the displacement (d) in the same direction as the force. W = Fd What are the SI units for work? –Force units (N) distance units (m) –Nm are also called joules (J). How much work is 1 joule? –Lift an apple weighing about 1 N from the floor to the desk, a distance of about 1 m.

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Work and EnergySection 1 Work Pushing this car is work because F and d are in the same direction. Why aren’t the following tasks considered work? –A student holds a heavy chair at arm’s length for several minutes. –A student carries a bucket of water along a horizontal path while walking at a constant velocity.

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Work and EnergySection 1 Work How would you calculate the work in this case? –What is the component of F in the direction of d? F cos –If the angle is 90°, what is the component of F in the direction of d? F cos 90° = 0 –If the angle is 0°, what is the component of F in the direction of d? F cos 0° = F

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Work and EnergySection 1 Work

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Work and EnergySection 1 Work is a Scalar Work can be positive or negative but does not have a direction. What is the angle between F and d in each case?

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Work and EnergySection 1 Classroom Practice Problem A 20.0 kg suitcase is raised 3.0 m above a platform. How much work is done on the suitcase? Answer: 5.9 x 10 2 J or 590 J

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Work and EnergySection 1 Now what do you think? Based on the physics definition, list five examples of things you have done in the last year that you would consider work.

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Work and EnergySection 2 What do you think? You have no doubt heard the term kinetic energy. –What is it? –What factors affect the kinetic energy of an object and in what way? You have no doubt heard the term potential energy. –What is it? –What factors affect the potential energy of an object and in what way?

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Work and EnergySection 2 Kinetic Energy Since then or

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Work and EnergySection 2 Kinetic Energy What are the SI units for KE? –kgm 2 /s 2 or Nm or J

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Work and EnergySection 2 Work and Kinetic Energy KE is the work an object can do if the speed changes. W net is positive if the speed increases.

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Work and EnergySection 2 Classroom Practice Problems A 6.00 kg cat runs after a mouse at 10.0 m/s. What is the cat’s kinetic energy? –Answer: 3.00 x 10 2 J or 300 J Suppose the above cat accelerated to a speed of 12.0 m/s while chasing the mouse. How much work was done on the cat to produce this change in speed? –Answer: 1.32 x 10 2 J or 132 J

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Work and EnergySection 2 Potential Energy Energy associated with an object’s potential to move due to an interaction with its environment –A book held above the desk –An arrow ready to be released from the bow Some types of PE are listed below. –Gravitational –Elastic –Electromagnetic

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Work and EnergySection 2 Gravitational Potential Energy What are the SI units? –kgm 2 /s 2 or Nm or J The height (h) depends on the “zero level” chosen where PE g = 0.

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Work and EnergySection 2 Elastic Potential Energy The energy available for use in deformed elastic objects –Rubber bands, springs in trampolines, pole-vault poles, muscles For springs, the distance compressed or stretched = x

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Work and EnergySection 2 Click below to watch the Visual Concept. Visual Concept Spring Constant(k)

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Work and EnergySection 2 Elastic Potential Energy The spring constant (k) depends on the stiffness of the spring. –Stiffer springs have higher k values. –Measured in N/m Force in newtons needed to stretch a spring 1.0 meters What are the SI Units for PE elastic?

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Work and EnergySection 2 Classroom Practice Problems When a 2.00 kg mass is attached to a vertical spring, the spring is stretched 10.0 cm such that the mass is 50.0 cm above the table. –What is the gravitational potential energy associated with the mass relative to the table? Answer: 9.81 J –What is the spring’s elastic potential energy if the spring constant is N/m? Answer: 2.00 J

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Work and EnergySection 2 Now what do you think? What is kinetic energy? –What factors affect the kinetic energy of an object and in what way? –How are work and kinetic energy related? What is potential energy? –What factors affect the gravitational potential energy of an object and in what way? –What factors affect the elastic potential energy of an object and in what way?

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Work and EnergySection 3 What do you think? Imagine two students standing side by side at the top of a water slide. One steps off of the platform, falling directly into the water below. The other student goes down the slide. Assuming the slide is frictionless, which student strikes the water with a greater speed? –Explain your reasoning. Would your answer change if the slide were not frictionless? If so, how?

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Work and EnergySection 3 What do you think? What is meant when scientists say a quantity is conserved? Describe examples of quantities that are conserved. –Are they always conserved? If not, why?

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Work and EnergySection 3 Mechanical Energy (ME) ME = KE + PE g + PE elastic –Does not include the many other types of energy, such as thermal energy, chemical potential energy, and others ME is not a new form of energy. –Just a combination of KE and PE

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Work and EnergySection 3 Classroom Practice Problems Suppose a 1.00 kg book is dropped from a height of 2.00 m. Assume no air resistance. –Calculate the PE and the KE at the instant the book is released. Answer: PE = 19.6 J, KE = 0 J –Calculate the KE and PE when the book has fallen 1.0 m. (Hint: you will need an equation from Chapter 2.) Answer: PE = 9.81 J, KE = 9.81 J –Calculate the PE and the KE just as the book reaches the floor. Answer: PE = 0 J, KE = 19.6 J

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Work and EnergySection 3 Table of Values for the Falling Book h (m)PE(J)KE(J)ME(J)

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Work and EnergySection 3 Conservation of Mechanical Energy The sum of KE and PE remains constant. One type of energy changes into another type. –For the falling book, the PE of the book changed into KE as it fell. –As a ball rolls up a hill, KE is changed into PE.

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Work and EnergySection 3 Click below to watch the Visual Concept. Visual Concept Conservation of Mechanical Energy

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Work and EnergySection 3 Conservation of Energy Acceleration does not have to be constant. ME is not conserved if friction is present. –If friction is negligible, conservation of ME is reasonably accurate. A pendulum as it swings back and forth a few times Consider a child going down a slide with friction. –What happens to the ME as he slides down? Answer: It is not conserved but, instead, becomes less and less. –What happens to the “lost” energy? Answer: It is converted into nonmechanical energy (thermal energy).

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Work and EnergySection 3 Classroom Practice Problems A small 10.0 g ball is held to a slingshot that is stretched 6.0 cm. The spring constant is 2.0 10 2 N/m. –What is the elastic potential energy of the slingshot before release? –What is the kinetic energy of the ball right after the slingshot is released? –What is the ball’s speed at the instant it leaves the slingshot? –How high does the ball rise if it is shot directly upward?

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Work and EnergySection 3 Now what do you think? Imagine two students standing side by side at the top of a water slide. One steps off of the platform, falling directly into the water below. The other student goes down the slide. Assuming the slide is frictionless, which student strikes the water with a greater speed? –Explain your reasoning. Would your answer change if the slide were not frictionless? If so, how?

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Work and EnergySection 3 Now what do you think? What is meant when scientists say a quantity is “conserved”? Describe examples of quantities that are conserved. –Are they always conserved? If not, why?

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Work and EnergySection 4 What do you think? Two cars are identical with one exception. One of the cars has a more powerful engine. How does having more power make the car behave differently? –What does power mean? –What units are used to measure power?

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Work and EnergySection 4 Power The rate of energy transfer –Energy used or work done per second

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Work and EnergySection 4 Power SI units for power are J/s. –Called watts (W) –Equivalent to kgm 2 /s 3 Horsepower (hp) is a unit used in the Avoirdupois system. –1.00 hp = 746 W

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Section 4Work and Energy Watts These bulbs all consume different amounts of power. A 100 watt bulb consumes 100 joules of energy every second.

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Work and EnergySection 4 Classroom Practice Problems Two horses pull a cart. Each exerts a force of N at a speed of 2.0 m/s for 10.0 min. –Calculate the power delivered by the horses. –How much work is done by the two horses? Answers: 1.0 x 10 3 W and 6.0 x 10 5 J

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Work and EnergySection 4 Now what do you think? Two cars are identical with one exception. One of the cars has a more powerful engine. How does having more power make the car behave differently? –What does power mean? –What units are used to measure power?

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Work and EnergySection 4 Preview Multiple Choice Short Response Extended Response

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Work and EnergySection 4 Multiple Choice 1. In which of the following situations is work not being done? A. A chair is lifted vertically with respect to the floor. B. A bookcase is slid across carpeting. C. A table is dropped onto the ground. D. A stack of books is carried at waist level across a room.

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Work and EnergySection 4 Multiple Choice, continued Use the graph below to answer questions 3–5. The graph shows the energy of a 75 g yo-yo at different times as the yo-yo moves up and down on its string.

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Work and EnergySection 4 Multiple Choice, continued 3. By what amount does the mechanical energy of the yo-yo change after 6.0 s? A. 500 mJ B. 0 mJ C. –100 mJ D. –600 mJ

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Work and EnergySection 4 Multiple Choice, continued 4. What is the speed of the yo-yo after 4.5 s? F. 3.1 m/s G. 2.3 m/s H. 3.6 m/s J. 1.6 m/s

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Work and EnergySection 4 Multiple Choice, continued 5. What is the maximum height of the yo-yo? A m B m C m D m

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Work and EnergySection 4 Multiple Choice, continued 6.A car with mass m requires 5.0 kJ of work to move from rest to a final speed v. If this same amount of work is performed during the same amount of time on a car with a mass of 2m, what is the final speed of the second car?

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Work and EnergySection 4 Multiple Choice, continued Use the passage below to answer questions 7–8. A 70.0 kg base runner moving at a speed of 4.0 m/s begins his slide into second base. The coefficient of friction between his clothes and Earth is His slide lowers his speed to zero just as he reaches the base. 7. How much mechanical energy is lost because of friction acting on the runner? A J B. 560 J C. 140 J D. 0 J

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Work and EnergySection 4 Multiple Choice, continued Use the passage below to answer questions 7–8. A 70.0 kg base runner moving at a speed of 4.0 m/s begins his slide into second base. The coefficient of friction between his clothes and Earth is His slide lowers his speed to zero just as he reaches the base. 8. How far does the runner slide? F m G m H m J. 1.2 m

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Work and EnergySection 4 Multiple Choice, continued Use the passage below to answer questions 9–10. A spring scale has a spring with a force constant of 250 N/m and a weighing pan with a mass of kg. During one weighing, the spring is stretched a distance of 12 cm from equilibrium. During a second weighing, the spring is stretched a distance of 18 cm.

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Work and EnergySection 4 Extended Response Base your answers to questions 14–16 on the information below. A projectile with a mass of 5.0 kg is shot horizontally from a height of 25.0 m above a flat desert surface. The projectile’s initial speed is 17 m/s. Calculate the following for the instant before the projectile hits the surface: 14. The work done on the projectile by gravity.

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Work and EnergySection 4 Extended Response, continued Base your answers to questions 14–16 on the information below. A projectile with a mass of 5.0 kg is shot horizontally from a height of 25.0 m above a flat desert surface. The projectile’s initial speed is 17 m/s. Calculate the following for the instant before the projectile hits the surface: 15. The change in kinetic energy since the projectile was fired.

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Work and EnergySection 4 Extended Response, continued Base your answers to questions 14–16 on the information below. A projectile with a mass of 5.0 kg is shot horizontally from a height of 25.0 m above a flat desert surface. The projectile’s initial speed is 17 m/s. Calculate the following for the instant before the projectile hits the surface: 16. The final kinetic energy of the projectile.

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Work and EnergySection 4 Extended Response, continued 17. A skier starts from rest at the top of a hill that is inclined at 10.5° with the horizontal. The hillside is m long, and the coefficient of friction between the snow and the skis is At the bottom of the hill, the snow is level and the coefficient of friction is unchanged. How far does the skier move along the horizontal portion of the snow before coming to rest? Show all of your work.

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