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Physics for Scientists & Engineers, with Modern Physics, 4 th edition Giancoli

Piri Reis University 201 1-2012/ Physics - I. Physics for Scientists & Engineers, with Modern Physics, 4 th edition Giancoli. Piri Reis University 201 1-2012 Fall Semester Physics - I. Chapter 7 and 8 Work and Energy. Piri Reis University 201 1-2012 Lecture VII and VIII

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Physics for Scientists & Engineers, with Modern Physics, 4 th edition Giancoli

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  1. Piri Reis University 2011-2012/ Physics -I Physics for Scientists & Engineers, with Modern Physics, 4th edition Giancoli

  2. Piri Reis University 2011-2012 Fall Semester Physics -I Chapter 7 and 8 Work and Energy

  3. Piri Reis University 2011-2012 LectureVII and VIII I. Work Done by a Constant Force II. Kinetic Energy, and the Work-Energy Principle III. Potential Energy IV. Conservative andNonconservative Forces V. The Conservation of Mechanical Energy VI. Problem Solving Using Conservation of Mechanical Energy VII. Other Forms of Energy; Energy Transformations and the Law of Conservation of Energy VIII. Energy Conservation with Dissipative Forces: Solving Problems IX. Power

  4. I. Work Done by a Constant Force The work done by a constant force is defined as the distance moved multiplied by the component of the force in the direction of displacement:

  5. I. Work Done by a Constant Force W = Fd cosθ Simple special case: F & d are parallel: θ = 0, cosθ = 1  W = Fd Example: d = 50 m, F = 30 N W = (30N)(50m) = 1500 N m Work units: Newton - meter = Joule 1 N m = 1 Joule = 1 J F θ d

  6. I. Work Done by a Constant Force In the SI system, the units of work are joules: • As long as this person does not lift or lower the bag of groceries, he is doing no work on it. The force he exerts has no component in the direction of motion. • W = 0: • Could have d = 0  W = 0 • Could have F  d •  θ = 90º, cosθ = 0 •  W = 0

  7. I. Work Done by a Constant Force • Solving work problems: • Draw a free-body diagram. • Choose a coordinate system. • Apply Newton’s laws to determine any unknown forces. • Find the work done by a specific force. • To find the net work, either • find the net force and then find the work it does, or • find the work done by each force and add.

  8. Example W = F|| d = Fd cosθ m = 50 kg, Fp = 100 N, Ffr = 50 N, θ = 37º Wnet = WG + WN +WP + Wfr = 1200 J Wnet = (Fnet)x x = (FP cos θ – Ffr)x = 1200 J

  9. Example ΣF =maFH = mgWH = FH(d cosθ) = mghFG = mgWG = FG(d cos(180-θ)) = -mghWnet = WH + WG = 0

  10. I. Work Done by a Constant Force Work done by forces that oppose the direction of motion, such as friction, will be negative. Centripetal forces do no work, as they are always perpendicular to the direction of motion.

  11. II. Kinetic Energy, and the Work-Energy Principle Energy was traditionally defined as the ability to do work. We now know that not all forces are able to do work; however, we are dealing in these chapters with mechanical energy, which does follow this definition. Energy  The ability to do work Kinetic Energy  The energy of motion “Kinetic”  Greek word for motion An object in motion has the ability to do work

  12. II. Kinetic Energy, and the Work-Energy Principle Consider an object moving in straight line. Starts at speed v1. Due to presence of a net force Fnet, accelerates (uniform) to speed v2, over distance d.

  13. II. Kinetic Energy, and the Work-Energy Principle Newton’s 2nd Law: Fnet= ma (1) 1d motion, constant a (v2)2 = (v1)2 + 2ad  a = [(v2)2 - (v1)2]/(2d) (2) Work done: Wnet = Fnetd(3) Combine (1), (2), (3):  Wnet = mad = md [(v2)2 - (v1)2]/(2d) OR Wnet = (½)m(v2)2 – (½)m(v1)2

  14. II. Kinetic Energy, and the Work-Energy Principle If we write the acceleration in terms of the velocity and the distance, we find that the work done here is We define the translational kinetic energy:

  15. II. Kinetic Energy, and the Work-Energy Principle This means that the work done is equal to the change in the kinetic energy: • If the net work is positive, the kinetic energy increases. • If the net work is negative, the kinetic energy decreases.

  16. Net work on an object = Change in KE. • Wnet = KE •  The Work-Energy Principle • Note:Wnet = work done by the net (total) force. • Wnet is a scalar. • Wnet can be positive or negative (because KE can be both + & -) • Units are Joules for both work & KE.

  17. II. Kinetic Energy, and the Work-Energy Principle Because work and kinetic energy can be equated, they must have the same units: kinetic energy is measured in joules. Work done on hammer: Wh = KEh = -Fd = 0 – (½)mh(vh)2 Work done on nail: Wn = KEn = Fd = (½)mn(vn)2 - 0

  18. III. Potential Energy • An object can have potential energy by virtue of its surroundings. • Familiar examples of potential energy: • A wound-up spring • A stretched elastic band • An object at some height above the ground

  19. III. Potential Energy In raising a mass m to a height h, the work done by the external force is We therefore define the gravitational potential energy: WG = -mg(y2 –y1) = -(PE2 – PE1) = -PE

  20. III. Potential Energy Wext = PE The Work done by an external force to move the object of mass m from point 1 to point 2 (without acceleration) is equal to the change in potential energy between positions 1 and 2 WG = -PE

  21. III. Potential Energy This potential energy can become kinetic energy if the object is dropped. Potential energy is a property of a system as a whole, not just of the object (because it depends on external forces). If , where do we measurey from? It turns out not to matter, as long as we are consistent about where we choose y = 0. Only changes in potential energy can be measured.

  22. III. Potential Energy Potential energy can also be stored in a spring when it is compressed; the figure below shows potential energy yielding kinetic energy.

  23. III. Potential Energy The force required to compress or stretch a spring is: FP = kx (6-8) Restoring force “Spring equation or Hook’s law” where k is called the spring constant, and needs to be measured for each spring.

  24. III. Potential Energy The force increases as the spring is stretched or compressed further (elastic) (not constant). We find that the potential energy of the compressed or stretched spring, measured from its equilibrium position, can be written: (6-9)

  25. IV. Conservative andNonconservative Forces • Conservative Force  The work done by that force depends only on initial & final conditions & not on path taken between the initial & final positions of the mass. •  A PE CAN be defined for conservative forces • Non-Conservative Force  The work done by that force depends on the path taken between the initial & final positions of the mass. • A PE CAN’T be defined for non-conservative forces • The most common example of a non-conservative force is FRICTION

  26. IV. Conservative andNonconservative Forces If friction is present, the work done depends not only on the starting and ending points, but also on the path taken. Friction is called a nonconservative force.

  27. IV. Conservative andNonconservative Forces Potential energy can only be defined for conservative forces.

  28. IV. Conservative andNonconservative Forces Therefore, we distinguish between the work done by conservative forces and the work done by nonconservative forces. We find that the work done by nonconservative forces is equal to the total change in kinetic and potential energies: Wnet = Wc + Wnc Wnet = ΔKE = Wc + Wnc Wnc = ΔKE - Wc = ΔKE – (– ΔPE)

  29. V. The Conservation of Mechanical Energy If there are no nonconservative forces, the sum of the changes in the kinetic energy and in the potential energy is zero – the kinetic and potential energy changes are equal but opposite in sign. KE + PE = 0 This allows us to define the total mechanical energy: And its conservation: (6-12b)

  30. PE1 = mgh KE1 = 0 The sum remains constant  KE+ PE = same as at points 1 & 2 KE1 + PE1 = KE2 + PE2 0 + mgh = (½)mv2 + 0 v2 = 2gh PE2 = 0 KE2 = (½)mv2

  31. VI. Problem Solving Using Conservation of Mechanical Energy In the image on the left, the total mechanical energy is: The energy buckets (right) show how the energy moves from all potential to all kinetic.

  32. VI. Problem Solving Using Conservation of Mechanical Energy If there is no friction, the speed of a roller coaster will depend only on its height compared to its starting point.

  33. VI. Problem Solving Using Conservation of Mechanical Energy For an elastic force, conservation of energy tells us:

  34. VII. Other Forms of Energy; Energy Transformations and the Law of Conservation of Energy Some other forms of energy: Electric energy, nuclear energy, thermal energy, chemical energy. Work is done when energy is transferred from one object to another. Accounting for all forms of energy, we find that the total energy neither increases nor decreases. Energy as a whole is conserved.

  35. VIII. Energy Conservation with Dissipative Forces: Solving Problems If there is a nonconservative force such as friction, where do the kinetic and potential energies go? They become heat; the actual temperature rise of the materials involved can be calculated.

  36. VIII. Energy Conservation with Dissipative Forces: Solving Problems • We had, in general: • WNC = KE + PE • WNC = Work done by non-conservative forces • KE = Change in KE • PE = Change in PE (conservative forces) • Friction is a non-conservative force! So, if friction is present, we have • (WNC  Wfr) • Wfr = Work done by friction • In moving through a distance d, force of friction Ffr does work • Wfr = - Ffrd

  37. When friction is present, we have: Wfr= -Ffrd = KE + PE = KE2 – KE1 + PE2 – PE1 • Also now, KE + PE  Constant! • Instead, KE1 + PE1+ Wfr = KE2+ PE2 • OR: KE1 + PE1 - Ffrd = KE2+ PE2 • For gravitational PE: • (½)m(v1)2 + mgy1 = (½)m(v2)2 + mgy2 + Ffrd • For elastic or spring PE: • (½)m(v1)2 + (½)k(x1)2 = (½)m(v2)2 + (½)k(x2)2 + Ffrd

  38. VIII. Energy Conservation with Dissipative Forces: Solving Problems • Problem Solving: • Draw a picture. • Determine the system for which energy will be conserved. • Figure out what you are looking for, and decide on the initial and final positions. • Choose a logical reference frame. • Apply conservation of energy. • Solve.

  39. IX. Power Power is the rate at which work is done – (6-17) In the SI system, the units of power are watts: • British units: Horsepower (hp). 1hp = 746 W The difference between walking and running up these stairs is power – the change in gravitational potential energy is the same.

  40. IX. Power Power is also needed for acceleration and for moving against the force of gravity. The average power can be written in terms of the force and the average velocity:

  41. Summary of Chapter VII and VIII • Work: • Kinetic energy is energy of motion: • Potential energy is energy associated with forces that depend on the position or configuration of objects. • The net work done on an object equals the change in its kinetic energy. • If only conservative forces are acting, mechanical energy is conserved. • Power is the rate at which work is done.

  42. Example 1 Pulling a Suitcase-on-Wheels Find the work done if the force is 45.0-N, the angle is 50.0 degrees, and the displacement is 75.0 m.

  43. Example 2

  44. Example 3 Accelerating a Crate The truck is accelerating at a rate of +1.50 m/s2. The mass of the crate is 120-kg and it does not slip. The magnitude of the displacement is 65 m. What is the total work done on the crate by all of the forces acting on it?

  45. Example 3 Accelerating a Crate The angle between the displacement and the friction force is 0 degrees.

  46. Example 4 Deep Space 1 The mass of the space probe is 474-kg and its initial velocity is 275 m/s. If the .056 N force acts on the probe through a displacement of 2.42×109m, what is its final speed?

  47. Example 4 Deep Space 1

  48. Example 4 Deep Space 1

  49. Example 5 In this case the net force is

  50. Example 6

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