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Chapter 7

Chapter 7. Kinetic Energy and Work. Forms of Energy. Mechanical focus for now chemical electromagnetic nuclear. Using Energy Considerations. Energy can be transformed from one form to another Essential to the study of physics, chemistry, biology, geology, astronomy

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Chapter 7

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  1. Chapter 7 Kinetic Energy and Work

  2. Forms of Energy • Mechanical • focus for now • chemical • electromagnetic • nuclear

  3. Using Energy Considerations • Energy can be transformed from one form to another • Essential to the study of physics, chemistry, biology, geology, astronomy • Can be used in place of Newton’s laws to solve certain problems more simply

  4. Work Done by a constant Force • Provides a link between force and energy • The work, W, done by a constant force on an object is defined as the product of the component of the force along the direction of displacement and the magnitude of the displacement

  5. Work, cont. • F cos θ is the component of the force in the direction of the displacement • Δ x is the displacement

  6. Work, cont. • This gives no information about • the time it took for the displacement to occur • the velocity or acceleration of the object

  7. Units of Work • SI • Newton • meter = Joule • N • m = J • US Customary • foot • pound • ft • lb • no special name

  8. More About Work • Scalar quantity • The work done by a force is zero when the force is perpendicular to the displacement • cos 90° = 0 • If there are multiple forces acting on an object, the total work done is the algebraic sum of the amount of work done by each force

  9. More About Work, cont. • Work can be positive or negative • Positive if the force and the displacement are in the same direction • Negative if the force and the displacement are in the opposite direction

  10. When Work is Zero • Displacement is horizontal • Force is vertical • cos 90° = 0

  11. Work Can Be Positive or Negative • Work done by F is positive when lifting the box

  12. |A| and |B| are the magnitudes of vectors A and B. • q is the angle between A and B. The Scalar Product of Two vectors • Scalar product or dot product is a mathematical tool. A.B = |A||B|cos(q)

  13. The Scalar Product of Two vectors • Comparing A.B = |A||B|cos(q), with We see that the work is the dot product between the force and the displacement: W = F.Dr

  14. The Scalar Product of Two vectors • The Scalar product is commutative: A.B = B.A • The scalar Product obey the distributive law of Multiplication: A.(B + C) = A.B + A.C

  15. The Scalar Product of Two vectors • If A is perpendicular to B, then: A.B = 0 It follows that the dot product between two units vectors is: Since the units vectors I, j and k are mutually perpendicular one to another. Also we have:

  16. The Scalar Product of Two vectors Consider the following vectors:

  17. Example: • The vectors A and B are given by: • Determine the scalar product A.B • Find the angle q between A and B

  18. q = 60.2° Solution: 1. 2.

  19. Example: • A particle moving in the xy-plane undergo a displacement in meters, as a constant force in Newtons acts on the particle. 1. Calculate the work done by F. 2. Calculate the magnitudes of F and Dr. W = F.Dr = 52 + 23 = 16 J

  20. Work Done by a varying Force • Consider a particle being displaced along the x-axis under the action of a force that varies with position. • In the small interval Dx, Fx can be considered to be constant and the work for the small displacement Dx: W = FxDx

  21. Work Done by a varying Force • If we imagine that the Fx versus x is divided into a large number of intervals, the total work done for the displacement from xi to xf is given by:

  22. Work Done by a varying Force • When the number of small intervals is very large we can approximate the discrete sum () into a continues integral:

  23. Work Done by a varying Force • The work is the area under the curve.

  24. Example: • A force acting on a particle varies with x, as shown in the adjacent figure. Calculate the work done by the force as the particle moves from x = 0 to x=6.0 m.

  25. Solution: • The work is the area under the curve = Area of the trapezoid:

  26. Example The adjacent Figure a) shows two horizontal forces that act on a block that is sliding to the right across a frictionless floor. Figure b) shows three plots of the block’s kinetic energy K versus time t. Which of the plots best corresponds to the following three situations: (a) F1 = F2, (b) F1 > F2, (c) F1 < F2     ?

  27. Example: In the below figure, a greased pig has a choice of three frictionless slides along which to slide to the ground. Rank the slides according to how much work the gravitational force does on the pig during the descent, greatest first.

  28. Fs = -kx  Work done by a spring: • A block being pulled from xi = 0 to xf = xmax on a frictionless surface by a force Fapp. The applied force is equal in magnitude and opposite in direction to the spring force Fs at all times.

  29. Fapp = kx  Work done by a spring: • The work done by Fapp = -Ws

  30. Kinetic Energy • Energy associated with the motion of an object • Scalar quantity with the same units as work • Work is related to kinetic energy

  31. Work-Kinetic Energy Theorem • When work is done by a net force on an object and the only change in the object is its speed, the work done is equal to the change in the object’s kinetic energy • Speed will increase if work is positive • Speed will decrease if work is negative

  32. An object’s kinetic energy can also be thought of as the amount of work the moving object could do in coming to rest The moving hammer has kinetic energy and can do work on the nail Work and Kinetic Energy

  33. Example: • A 6.0 kg block initially at rest is pulled to the right along a horizontal frictionless surface by a constant horizontal force of 12 N. Find the speed of the block after it has moved 3 m.

  34. WF = F.Dx = DKE  F.Dx = ½ m(vf)2 – ½ m(vi)2 But vi = 0  x Solution: • Neither of the vertically directed forces (mg and n) does work on the block, Since the displacement is horizontal. Applying the work kinetic energy theorem:

  35. Transferring Energy • By Work • By applying a force • Produces a displacement of the system

  36. Transferring Energy • Heat • The process of transferring heat by collisions between molecules

  37. Transferring Energy • Mechanical Waves • a disturbance propagates through a medium • Examples include sound, water, seismic

  38. Transferring Energy • Electrical transmission • transfer by means of electrical current

  39. Transferring Energy • Electromagnetic radiation • any form of electromagnetic waves • Light, microwaves, radio waves

  40. Notes About Conservation of Energy • We can neither create nor destroy energy • Another way of saying energy is conserved

  41. Power • Often also interested in the rate at which the energy transfer takes place • Power is defined as this rate of energy transfer • SI units are Watts (W)

  42. Power, cont. • US Customary units are generally hp • need a conversion factor The instantaneous power is defined as:

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