9/17/2013PHY 113 C Fall Lecture 71 PHY 113 C General Physics I 11 AM – 12:15 PM MWF Olin 101 Plan for Lecture 7: Chapter 7 -- The notion of work and energy 1.Definition of work 2.Examples of work 3.Kinetic energy; Work-kinetic energy theorem 4.Potential energy and work; conservative forces

9/17/2013 PHY 113 C Fall Lecture ,7.15,7.31,7.34

9/17/2013PHY 113 C Fall Lecture 73 Webassign questions for Assignment 6 -- #1 52. Consider a large truck carrying a heavy load, such as steel beams. … Assume that a 10,000-kg load sits on the flatbed of a 20,000-kg truck initially moving at v i =12 m/s. Assume that the load on the truck bed has a coefficient of static friction of S =0.5. When the truck is braked at constant force, it comes to rest in a distance d. What is the minimum stopping distance d such that the load remains stationary relative to the truck bed throughout the breaking? vivi a f m

9/17/2013PHY 113 C Fall Lecture 74 Webassign questions for Assignment 6 -- #1 -- continued vivi a m f iclicker exercise -- Do we have enough information to calculate a? A.Yes B.No

9/17/2013PHY 113 C Fall Lecture 75 Webassign questions for Assignment 6 -- #1 -- continued vivi a m f

9/17/2013PHY 113 C Fall Lecture 76 A block of mass 3 kg is pushed up against a wall by a force P that makes an angle of =50 o with the horizontal. s =0.25. Determine the possible values for the magnitude of P that allow the block to remain stationary. f mg N f Webassign questions for Assignment 6 -- #4

9/17/2013PHY 113 C Fall Lecture 77 f mg N f

9/17/2013PHY 113 C Fall Lecture 78 Webassign questions for Assignment 6 -- #6 F

9/17/2013PHY 113 C Fall Lecture 79 Preparation for the introduction of work: Digression on the definition of vector dot product

9/17/2013PHY 113 C Fall Lecture 710 Digression: definition of vector dot product -- continued

9/17/2013PHY 113 C Fall Lecture 711 Digression: definition of vector dot product – component form Note that the result of a vector dot product is a scalar.

9/17/2013PHY 113 C Fall Lecture 712 Definition of work: F drdr riri rjrj

9/17/2013PHY 113 C Fall Lecture 713 Units of work: work = force · displacement = (N · m) = (joule) Only the component of force in the direction of the displacement contributes to work. Work is a scalar quantity. If the force is not constant, the integral form must be used. Work can be defined for a specific force or for a combination of forces

9/17/2013PHY 113 C Fall Lecture 714 iclicker question: A ball with a weight of 5 N follows the trajectory shown. What is the work done by gravity from the initial r i to final displacement r f ? (A) 0 J (B) 7.5 J (C) 12.5 J (D) 50 J 1m1m 1m1m 2.5m riri rfrf 10 m

9/17/2013PHY 113 C Fall Lecture 715 mg riri rfrf W= mg(r f r i )<0 mg riri rfrf W= mg(r f r i )>0 Gravity does negative work: Gravity does positive work:

9/17/2013PHY 113 C Fall Lecture 716 Work done by a variable force:

9/17/2013PHY 113 C Fall Lecture 717 Example:

9/17/2013PHY 113 C Fall Lecture 718 Example – spring force: F x = - kx

9/17/2013PHY 113 C Fall Lecture 719 x F Positive work Negative work

9/17/2013PHY 113 C Fall Lecture 720 Detail:

9/17/2013PHY 113 C Fall Lecture 721 More examples: Suppose a rope lifts a weight of 1000N by 0.5m at a constant upward velocity of 4.9m/s. How much work is done by the rope? (A) 500 J (B) 750 J (C) 4900 J (D) None of these Suppose a rope lifts a weight of 1000N by 0.5m at a constant upward acceleration of 4.9m/s 2. How much work is done by the rope? (A) 500 J (B) 750 J (C) 4900 J (D) None of these

9/17/2013PHY 113 C Fall Lecture 722 FPFP mg n fkfk xixi xfxf Assume F P sin <<mg Work of gravity? 0 Work of F P ? F P cos (x f -x i ) Work of f k ? k n (x f -x i )= k (mg- F P sin (x f -x i ) Another example

9/17/2013PHY 113 C Fall Lecture 723 iclicker exercise: Why should we define work? A.Because professor like to torture students. B.Because it is always good to do work C.Because it will help us understand motion. D.Because it will help us solve the energy crisis. Work-Kinetic energy theorem.

9/17/2013PHY 113 C Fall Lecture 724 Back to work: F drdr riri rjrj

9/17/2013PHY 113 C Fall Lecture 725 Why is work a useful concept? Consider Newtons second law: F total = m a F total · dr= m a · dr W total = ½ m v f 2 - ½ m v i 2 Kinetic energy (joules)

9/17/2013PHY 113 C Fall Lecture 726 Introduction of the notion of Kinetic energy Some more details: Consider Newtons second law: F total = m a F total · dr= m a · dr W total = ½ m v f 2 - ½ m v i 2 Kinetic energy (joules)

9/17/2013PHY 113 C Fall Lecture 727 Kinetic energy: K = ½ m v 2 units: (kg) (m/s) 2 = (kg m/s 2 ) m N m = joules Work – kinetic energy relation: W total = K f – K i

9/17/2013PHY 113 C Fall Lecture 728 Kinetic Energy-Work theorem iclicker exercise: Does this remind you of something youve seen recently? A.Yes B.No

9/17/2013PHY 113 C Fall Lecture 729 Kinetic Energy-Work theorem

9/17/2013PHY 113 C Fall Lecture 730 Kinetic Energy-Work theorem Example: A ball of mass 10 kg, initially at rest falls a height of 5m. What is its final velocity? i f h 0

9/17/2013PHY 113 C Fall Lecture 731 Example A block, initially at rest at a height h, slides down a frictionless incline. What is its final velocity? h h=0.5m 0

9/17/2013PHY 113 C Fall Lecture 732 Example A block of mass m slides on a horizontal surface with initial velocity v i, coming to rest in a distance d. vivi v f =0 d 1.Determine the work done during this process. 2.Analyze the work in terms of the kinetic friction force.

9/17/2013PHY 113 C Fall Lecture 733 Example -- continued vivi v f =0 d f

9/17/2013PHY 113 C Fall Lecture 734 ExampleA mass m initially at rest and attached to a spring compressed a distance x=-|x i |, slides on a frictionless surface. What is the velocity of the mass when x=0 ? k 0

9/17/2013PHY 113 C Fall Lecture 735 Special case of conservative forces conservative non-dissipative

9/17/2013PHY 113 C Fall Lecture 736 k

9/17/2013PHY 113 C Fall Lecture 737 iclicker exercise: Why would you want to write the work as the difference between two potential energies? A.Normal people wouldnt. B.It shows a lack of imagination. C.It shows that the work depends only on the initial and final displacements, not on the details of the path.

9/17/2013PHY 113 C Fall Lecture 738 Work-Kinetic Energy Theorem for conservative forces:

9/17/2013PHY 113 C Fall Lecture 739 Energy diagrams

9/17/2013PHY 113 C Fall Lecture 740 Example: Model potential energy function U(x) representing the attraction of two atoms