1. Physics 101: Lecture 9, Pg 1 Physics 101: Lecture 9 Work and Kinetic Energy  Hour Exam 1, Tomorrow! – Exam 2

2. Physics 101: Lecture 9, Pg 2 Energy (and mass) is Conserved l Energy is “Conserved” meaning it can not be created nor destroyed  Can change form  Can be transferred l Total Energy does not change with time. l This is a BIG deal! 10

3. Physics 101: Lecture 9, Pg 3 Energy l Forms  Kinetic Energy Motion (Today)  Potential Energy Stored (Thursday)  Heat later  Mass (E=mc 2 ) p102 l Units Joules = kg m 2 / s 2 12

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 = mg  Case b 2T b - mg =0 or T = 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 W = F dcos(  )

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  rr F rr F rr F rr F 18 A) W>0B) W=0C) W<0 1) 2) 3) 4)

6. Physics 101: Lecture 9, Pg 6 Example: Ball Toss You toss a ball in the air. What is the work done by gravity as the ball goes up? A) PositiveB) NegativeC) Zero What is the work done by gravity as the ball goes down? 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 T mg N f 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? mg 90 rr T mg N f f rr 180 25

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

10. Physics 101: Lecture 9, Pg 10 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 mg N f x y Y direction: F=ma Work W =  K 44

11. Physics 101: Lecture 9, Pg 11 Falling Ball Example l Ball falls a distance 5 meters, What is final speed? Only force/work done is gravity mg

12. Physics 101: Lecture 9, Pg 12 Example: block on incline 5kg 30 o 25N 4.5m A 5kg block is at rest on a frictionless incline. It is pulled 4.5m by a 25N force. What is the final velocity of the block?

13. Physics 101: Lecture 9, Pg 13 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 48

14. Physics 101: Lecture 9, Pg 14 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