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Chapter 7

Subject to much change. Chapter 7. Energy and Energy Transfer February 22, 2006. HAPPY BIRTHDAY GEORGE!. Kalendar. Today we start the new TOPIC OF ENERGY No Quiz on Friday, but there MAY be one on Monday The BAD NEWS: EXAM #2 will be on March 3 (Friday). ENERGY.

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Chapter 7

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  1. Subject to much change Chapter 7 Energy and Energy Transfer February 22, 2006

  2. HAPPY BIRTHDAY GEORGE!

  3. Kalendar • Today we start the new TOPIC OF ENERGY • No Quiz on Friday, but there MAY be one on Monday • The BAD NEWS: • EXAM #2 will be on March 3 (Friday)

  4. ENERGY • We use energy to walk, run or even sleep • We use energy when we lift a weight • We use energy when we drive a car • We even use energy to THINK! • BUT ….. WHAT IS ENERGY??

  5. Introduction to Energy • The concept of energy is one of the most important topics in science • Every physical process that occurs in the Universe involves energy and energy transfers or transformations • Energy is not easily defined

  6. Systems • A system is a small portion of the Universe • We identify a number of particles or objects and draw a sphere around them • There are no forces acting on anything inside the sphere from outside the sphere • We will ignore the details outside of the sphere. • A critical skill is to identify the system

  7. Valid System • A valid system may • be a single object or particle • be a collection of objects or particles • be a region of space • vary in size and shape

  8. Environment • There is a system boundary around the system • The boundary is an imaginary surface • It does not necessarily correspond to a physical boundary • The boundary divides the system from the environment • The environment is “the rest of the Universe”

  9. Work • The work, W, done on a system by an agent exerting a constant force on the system is the product of the magnitude, F, of the force, the magnitude Drof the displacement of the point of application of the force, and cos q, where qis the angle between the force and the displacement vectors

  10. Working, Working, Working WORK = Component of the applied force x the displacement= Fcos(q) x Dr

  11. Work, cont. • W = FDr cos q • The displacement is that of the point of application of the force • A force does no work on the object if the force does not move through a displacement • The work done by a force on a moving object is zero when the force applied is perpendicular to the displacement of its point of application (Later for the dot!)

  12. Work Example • The normal force, n, and the gravitational force, m g, do no work on the object • cos q = cos 90° = 0 • The force F does do work on the object • Same amount as in the previous overhead

  13. More About Work • The system and the environment must be determined when dealing with work • The environment does work on the system • Work by the environment on the system • The sign of the work depends on the direction of F relative to Dr • Work is positive when projection of F onto Dr is in the same direction as the displacement • Work is negative when the projection is in the opposite direction

  14. Units of Work • Work is a scalar quantity • The unit of work is a joule (J) • 1 joule = 1 newton . 1 meter • J = N · m

  15. A block of mass 2.50 kg is pushed 2.20 m along a frictionless horizontal table by a constant 16.0-N force directed 25.0 below the horizontal. Determine the work done on the block by (a) the applied force, (b) the normal force exerted by the table, and (c) the gravitational force. (d) Determine the total work done on the block.

  16. A raindrop of mass 3.35  10–5 kg falls vertically at constant speed under the influence of gravity and air resistance. Model the drop as a particle. As it falls 100 m, what is the work done on the raindrop (a) by the gravitational force and (b) by air resistance?

  17. Work Is An Energy Transfer • This is important for a system approach to solving a problem • If the work is done on a system and it is positive, energy is transferred to the system • If the work done on the system is negative, energy is transferred from the system

  18. Work Is An Energy Transfer, cont • If a system interacts with its environment, this interaction can be described as a transfer of energy across the system boundary • This will result in a change in the amount of energy stored in the system

  19. Energy Energy Energy

  20. Shejule • Continue to work on energy. • Exam on March 3rd. • Material … as far as we get by March 1st. • Mucho WebAssign Stuff

  21. LAST TIME • We defined the “Dot Product” • We defined WORK • We discussed the “system” and the “environment” • System + Environment = Entire Universe (Dumb concept!)

  22. WORK F is the NET force acting on the block.

  23. Scalar or DOT Product of Two Vectors • The scalar product of two vectors is written as A . B • It is also called the dot product • A . B = A B cos q • q is the angle betweenA and B

  24. Scalar Product Properties • The scalar product is commutative • A . B = B . A • The scalar product obeys the distributive law of multiplication • A . (B + C) = A . B + A . C

  25. Dot Products of Unit Vectors • Using component form with A and B:

  26. A force acts on a particle that undergoes a displacement . Find (a) the work done by the force on the particle and (b) the angle between F and r.

  27. Work Done by a Varying Force

  28. 11. The force acting on a particle varies as in Figure P7.11. Find the work done by the force on the particle as it moves (a) from x = 0 to x = 8.00 m, (b) from x = 8.00 m to x = 10.0 m, and (c) from x = 0 to x = 10.0 m.

  29. Work Done By Multiple Forces • AGAIN … If more than one force acts on a system and the system can be modeled as a particle, the total work done on the system is the work done by the net force

  30. Hooke’s Law • The force exerted by the spring is Fs = - kx • x is the position of the block with respect to the equilibrium position (x = 0) • k is called the spring constant or force constant and measures the stiffness of the spring • This is called Hooke’s Law

  31. Hooke’s Law, cont. • When x is positive (spring is stretched), F is negative • When x is 0 (at the equilibrium position), F is 0 • When x is negative (spring is compressed), F is positive

  32. Work Done by a Spring • Identify the block as the system • Calculate the work as the block moves from xi = - xmax to xf = 0 • The total work done as the block moves from –xmax to xmax is zero ENERGY IS STORED IN THE SPRING AND THEN RECOVERED AND THEN STORED AND THEN RECOVERED AND THEN STORED AND THEN RECOVERED AND THEN STORED AND THEN RECOVERED AND THEN ….

  33. Spring with an Applied Force • Suppose an external agent, Fapp, stretches the spring • The applied force is equal and opposite to the spring force • Fapp = -Fs = -(-kx) = kx • Work done by Fapp is equal to ½ kx2max

  34. 19. If it takes 4.00 J of work to stretch a Hooke's-law spring 10.0 cm from its unstressed length, determine the extra work required to stretch it an additional 10.0 cm.

  35. 21. A light spring with spring constant 1 200 N/m is hung from an elevated support. From its lower end a second light spring is hung, which has spring constant 1 800 N/m. An object of mass 1.50 kg is hung at rest from the lower end of the second spring. (a) Find the total extension distance of the pair of springs. (b) Find the effective spring constant of the pair of springs as a system. We describe these springs as in series.

  36. F Consider the following:

  37. Kinetic Energy • Kinetic Energy is the energy of a particle due to its motion • K = ½ mv2 • K is the kinetic energy • m is the mass of the particle • v is the speed of the particle • A change in kinetic energy is one possible result of doing work to transfer energy into a system With no friction or other strange forces, the work done by a force on a particle (or system of particles) = the change in the particles kinetic energy.

  38. Work-Kinetic Energy Theorem • The Work-Kinetic Energy Principle states SW = Kf– Ki= DK • In the case in which work is done on a system and the only change in the system is in its speed, the work done by the net force equals the change in kinetic energy of the system. • We can also define the kinetic energy • K = ½ mv2

  39. Nonisolated System • A nonisolated system is one that interacts with or is influenced by its environment • An isolated system would not interact with its environment • The Work-Kinetic Energy Theorem can be applied to nonisolated systems

  40. BREAK POINT February 27, 2006

  41. Stuff Happens • Today and Wednesday • More on potential energy • some material from the next chapter • Friday • EXAMINATION #2 • All material since last exam. • You should be studying by now.

  42. Internal Energy • The energy associated with an object’s temperature is called its internal energy, Eint • In this example, the surface is the system • The friction does work and increases the internal energy of the surface FRICTION HEAT

  43. Potential Energy • Potential energy is energy related to the configuration of a system in which the components of the system interact by forces • Examples include: • elastic potential energy – stored in a spring • gravitational potential energy • electrical potential energy

  44. Conservation of Energy • Energy is conserved !!!! • This means that energy cannot be created or destroyed • If the total amount of energy in a system changes, it can only be due to the fact that energy has crossed the boundary of the system by some method of energy transfer

  45. A 2 100-kg pile driver is used to drive a steel I-beam into the ground. The pile driver falls 5.00 m before coming into contact with the top of the beam, and it drives the beam 12.0 cm farther into the ground before coming to rest. Using energy considerations, calculate the average force the beam exerts on the pile driver while the pile driver is brought to rest.

  46. 31. A 40.0-kg box initially at rest is pushed 5.00 m along a rough, horizontal floor with a constant applied horizontal force of 130 N. If the coefficient of friction between box and floor is 0.300, find (a) the work done by the applied force, (b) the increase in internal energy in the box-floor system due to friction, (c) the work done by the normal force, (d) the work done by the gravitational force, (e) the change in kinetic energy of the box, and (f) the final speed of the box.

  47. 63. The ball launcher in a pinball machine has a spring that has a force constant of 1.20 N/cm (Fig. P7.63). The surface on which the ball moves is inclined 10.0° with respect to the horizontal. If the spring is initially compressed 5.00 cm, find the launching speed of a 100-g ball when the plunger is released. Friction and the mass of the plunger are negligible.

  48. 32. A 2.00-kg block is attached to a spring of force constant 500 N/m as in Figure 7.10. The block is pulled 5.00 cm to the right of equilibrium and released from rest. Find the speed of the block as it passes through equilibrium if (a) the horizontal surface is frictionless and (b) the coefficient of friction between block and surface is 0.350.

  49. 35. A sled of mass m is given a kick on a frozen pond. The kick imparts to it an initial speed of 2.00 m/s. The coefficient of kinetic friction between sled and ice is 0.100. Use energy considerations to find the distance the sled moves before it stops.

  50. Power • The time rate of energy transfer is called power • The average power is given by when the method of energy transfer is work

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