PHY 113 C General Physics I 11 AM

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 2013 -- Lecture 7 1

7. 3, 7. 15, 7. 31, 7. 34 9/17/2013 PHY 113 C Fall 2013 -- Lecture 7 2

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 vi=12 m/s. Assume that the load on the truck bed has a coefficient of static friction of m. 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? m a vi f 9/17/2013 PHY 113 C Fall 2013 -- Lecture 7 3

Webassign questions for Assignment 6 -- #1 -- continued m a vi f iclicker exercise -Do we have enough information to calculate a? A. Yes B. No 9/17/2013 PHY 113 C Fall 2013 -- Lecture 7 4

Webassign questions for Assignment 6 -- #1 -- continued m a vi f 9/17/2013 PHY 113 C Fall 2013 -- Lecture 7 5

Webassign questions for Assignment 6 -- #4 A block of mass 3 kg is pushed up against a wall by a force P that makes an angle of q=50 o with the horizontal. ms=0. 25. Determine the possible values for the magnitude of P that allow the block to remain stationary. f N f 9/17/2013 mg PHY 113 C Fall 2013 -- Lecture 7 6

f N f mg 9/17/2013 PHY 113 C Fall 2013 -- Lecture 7 7

Webassign questions for Assignment 6 -- #6 F 9/17/2013 PHY 113 C Fall 2013 -- Lecture 7 8

Preparation for the introduction of work: Digression on the definition of vector “dot” product q 9/17/2013 PHY 113 C Fall 2013 -- Lecture 7 9

Digression: definition of vector “dot” product -- continued q 9/17/2013 PHY 113 C Fall 2013 -- Lecture 7 10

Digression: definition of vector “dot” product – component form q Note that the result of a vector dot product is a scalar. 9/17/2013 PHY 113 C Fall 2013 -- Lecture 7 11

F Definition of work: dr ri 9/17/2013 PHY 113 C Fall 2013 -- Lecture 7 rj 12

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 9/17/2013 PHY 113 C Fall 2013 -- Lecture 7 13

iclicker question: A ball with a weight of 5 N follows the trajectory shown. What is the work done by gravity from the initial ri to final displacement rf? 2. 5 m rf ri 1 m 1 m (A) 0 J 9/17/2013 10 m (B) 7. 5 J (C) 12. 5 J (D) 50 J PHY 113 C Fall 2013 -- Lecture 7 14

Gravity does negative work: rf Gravity does positive work: ri mg mg ri W=-mg(rf-ri)<0 9/17/2013 rf W=-mg(rf-ri)>0 PHY 113 C Fall 2013 -- Lecture 7 15

Work done by a variable force: 9/17/2013 PHY 113 C Fall 2013 -- Lecture 7 16

Example: 9/17/2013 PHY 113 C Fall 2013 -- Lecture 7 17

Example – spring force: 9/17/2013 Fx = - kx PHY 113 C Fall 2013 -- Lecture 7 18

F Positive work x Negative work 9/17/2013 PHY 113 C Fall 2013 -- Lecture 7 19

Detail: 9/17/2013 PHY 113 C Fall 2013 -- Lecture 7 20

More examples: Suppose a rope lifts a weight of 1000 N by 0. 5 m at a constant upward velocity of 4. 9 m/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 1000 N by 0. 5 m at a constant upward acceleration of 4. 9 m/s 2. How much work is done by the rope? (A) 500 J (B) 750 J 9/17/2013 (C) 4900 J (D) None of these PHY 113 C Fall 2013 -- Lecture 7 21

Another example n q FP fk mg xi xf Assume FP sinq <<mg Work of gravity? Work of FP? Work of fk? 9/17/2013 0 FP cos q (xf-xi) -mkn (xf-xi)=-mk(mg- FP sin q) (xf-xi) PHY 113 C Fall 2013 -- Lecture 7 22

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. 9/17/2013 PHY 113 C Fall 2013 -- Lecture 7 23

Back to work: F dr ri 9/17/2013 rj PHY 113 C Fall 2013 -- Lecture 7 24

Why is work a useful concept? Consider Newton’s second law: Ftotal = m a Ftotal · dr= m a · dr Wtotal = ½ m vf 2 - ½ m vi 2 Kinetic energy (joules) 9/17/2013 PHY 113 C Fall 2013 -- Lecture 7 25

Introduction of the notion of Kinetic energy Some more details: Consider Newton’s second law: Ftotal = m a Ftotal · dr= m a · dr Wtotal = ½ m vf 2 - ½ m vi 2 Kinetic energy (joules) 9/17/2013 PHY 113 C Fall 2013 -- Lecture 7 26

Kinetic energy: K = ½ m v 2 units: (kg) (m/s)2 = (kg m/s 2) m N m = joules Work – kinetic energy relation: Wtotal = Kf – Ki 9/17/2013 PHY 113 C Fall 2013 -- Lecture 7 27

Kinetic Energy-Work theorem iclicker exercise: Does this remind you of something you’ve seen recently? A. Yes B. No 9/17/2013 PHY 113 C Fall 2013 -- Lecture 7 28

Kinetic Energy-Work theorem 9/17/2013 PHY 113 C Fall 2013 -- Lecture 7 29

Kinetic Energy-Work theorem Example: A ball of mass 10 kg, initially at rest falls a height of 5 m. What is its final velocity? i 0 h f 9/17/2013 PHY 113 C Fall 2013 -- Lecture 7 30

Example A block, initially at rest at a height h, slides down a frictionless incline. What is its final velocity? h=0. 5 m h 0 9/17/2013 PHY 113 C Fall 2013 -- Lecture 7 31

Example A block of mass m slides on a horizontal surface with initial velocity vi, coming to rest in a distance d. vi vf=0 d 1. Determine the work done during this process. 2. Analyze the work in terms of the kinetic friction force. 9/17/2013 PHY 113 C Fall 2013 -- Lecture 7 32

Example -- continued vi vf=0 f d 9/17/2013 PHY 113 C Fall 2013 -- Lecture 7 33

Example k A mass m initially at rest and attached to a spring compressed a distance x=-|xi|, slides on a frictionless surface. What is the velocity of the mass when x=0 ? 0 9/17/2013 PHY 113 C Fall 2013 -- Lecture 7 34

Special case of “conservative” forces conservative non-dissipative 9/17/2013 PHY 113 C Fall 2013 -- Lecture 7 35

k 9/17/2013 PHY 113 C Fall 2013 -- Lecture 7 36

iclicker exercise: Why would you want to write the work as the difference between two “potential” energies? A. Normal people wouldn’t. 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. 9/17/2013 PHY 113 C Fall 2013 -- Lecture 7 37

Work-Kinetic Energy Theorem for conservative forces: 9/17/2013 PHY 113 C Fall 2013 -- Lecture 7 38

Energy diagrams 9/17/2013 PHY 113 C Fall 2013 -- Lecture 7 39

Example: Model potential energy function U(x) representing the attraction of two atoms 9/17/2013 PHY 113 C Fall 2013 -- Lecture 7 40