1. Physics 101: Lecture 9, Pg 1 Physics 101: Lecture 9 Work and Kinetic Energy l Today’s lecture will be on Textbook Sections 6.1 - 6.4

2. Physics 101: Lecture 9, Pg 2 Energy l Forms  Kinetic Energy (Motion) Today, Wed  Potential Energy (Stored) Today, Wed)  Heat Later  Mass (E=mc 2 ) Phys 102 l Units Joules = kg m 2 / s 2 12

3. Physics 101: Lecture 9, Pg 3 Energy is Conserved l Energy is “Conserved” meaning it cannot be created nor destroyed  Can change form  Can be transferred l Total Energy does not change with time. “no such thing as a free lunch” l This is a BIG deal. 10

4. Physics 101: Lecture 9, Pg 4 Work: Energy Transfer due to Force l Force to lift trunk at constant speed  Case a T a – mg = 0 T a = mg  Case b 2T b - mg =0 or T b = ½ mg l But in case b, trunk only moves ½ distance you pull rope. l F * distance is same in both! TaTa mg TbTb TbTb 15 “Work” W = F dcos(  ) (a) (b)

5. Physics 101: Lecture 9, Pg 5 Work by Constant Force l Only component of force parallel to direction of motion does work!  W = F  r cos  F  rr F W F = 0.  =90  cos(  ) =0 rr F W F < 0. 90 <  < 270  cos(  ) < 0 rr F W F > 0. 0 0 18 A) W>0B) W=0C) W<0 1) 2) 3) Note Change in r! rr F 

6. Physics 101: Lecture 9, Pg 6 ACTS: Ball toss You throw a ball up in the air. The work done by gravity by the time the ball reaches the top is … A) PositiveB) NegativeC) Zero The ball then falls to the ground. The work done by gravity during this part of the ball’s motion is … A) PositiveB) NegativeC) Zero 20

7. Physics 101: Lecture 9, Pg 7 Work by Constant Force l Example: You pull a 30 N chest 5 meters across the floor at a constant speed by applying a force of 50 N at an angle of 30 degrees. How much work is done by the 50 N force? 30 50 N 21

8. Physics 101: Lecture 9, Pg 8 Where did the energy go? l Example: You pull a 30 N chest 5 meters across the floor at a constant speed, by applying a force of 50 N at an angle of 30 degrees. l How much work did gravity do? l How much work did friction do? 25

9. Physics 101: Lecture 9, Pg 9 Preflight 1 You are towing a car up a hill with constant velocity. The work done on the car by the normal force is: 1. positive 2. negative 3. zero V 28

10. Physics 101: Lecture 9, Pg 10 Preflight 2 You are towing a car up a hill with constant velocity. The work done on the car by the gravitational force is: 1. positive 2. negative 3. zero 30 V

11. Physics 101: Lecture 9, Pg 11 Preflight 3 You are towing a car up a hill with constant velocity. The work done on the car by the tension force is: 1. positive 2. negative 3. zero 32 V

12. Physics 101: Lecture 9, Pg 12 Kinetic Energy: Motion l Apply constant force along x-direction to a point particle m. W = F x  x = m a x  x = ½ m (v f 2 – v 0 2 ) l Work changes the quantity ½ m v 2 l Define Kinetic Energy K = ½ m v 2 W =  K (For Point Particles) 35

13. Physics 101: Lecture 9, Pg 13 Preflight 4 You are towing a car up a hill with constant velocity. The total work done on the car by all forces (including gravity) is: 1. positive 2. negative 3. zero 37

14. Physics 101: Lecture 9, Pg 14 Example: Block w/ friction l A block is sliding on a surface with an initial speed of 5 m/s. If the coefficent of kinetic friction between the block and table is 0.4, how far does the block travel before stopping? 5 m/s x y 44

15. Physics 101: Lecture 9, Pg 15 Falling Ball Example l Ball falls a distance 5 meters, What is final speed? mg 47

16. Physics 101: Lecture 9, Pg 16 Work by Variable Force W = F x  x  Work is area under F vs x plot  Spring F = k x »Area = ½ k x 2 =W spring Force Distance Work Force Distance F=kx Work 49

17. Physics 101: Lecture 9, Pg 17 Summary l Energy is Conserved l Work = transfer of energy using force  Can be positive, negative or zero  W = F d cos(  ) l Kinetic Energy (Motion)  K = ½ m v 2 l Work = Change in Kinetic Energy   W =  K 50