Work and Kinetic Energy Energy and mass is

Work and Kinetic Energy –

Energy (and mass) is Conserved l Energy is “Conserved” meaning it can not be created nor destroyed ØCan change form ØCan be transferred l Total time. Energy does not change with l. This is a BIG deal! 10

Energy l Forms ØKinetic Energy ØPotential Energy ØHeat ØMass (E=mc 2) l Units Motion (Today) Stored (Wednesday) later p 122 Joules = kg m 2 / s 2 12

Work by Constant Force A) W>0 B) W=0 C) W<0 l Only component of force parallel to direction of motion does work! ØW = F Dr cos q F 1) Dr F 2) F 3) 4) Dr Dr Dr F 18

Example: Ball Toss You toss a ball in the air. What is the work done by gravity as the ball goes up? A) Positive B) Negative C) Zero What is the work done by gravity as the ball goes down? A) Positive B) Negative C) Zero 20

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? N T f mg 50 N 30 21

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? Dr 90 mg l N How much work did friction do? T f mg f Dr 180 25

Kinetic Energy: Motion l Apply constant force along x-direction to a point particle m. l Work changes ½ m v 2 l Define W=DK Kinetic Energy K = ½ m v 2 For Point Particles 35

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 y stopping? N Y direction: F=ma f x mg W=DK Work 5 m/s 44

Falling Ball Example l Ball falls a distance 5 meters, What is final speed? Only force/work done is gravity mg

Example: block on incline A 5 kg block is at rest on a frictionless incline. It is pulled 4. 5 m by a 25 N force. What is the final velocity of the block? 4. 5 25 N m 5 kg 30 o

Work by Variable Force l. W = Fx Dx Force ØWork is area under F vs x plot Work Distance ØSpring F = k x » Area = ½ k x 2 =Wspring Force x k F= Work Distance 48

Summary l Energy is Conserved l Work = transfer of energy using force ØCan be positive, negative or zero ØW = F d cos(q) l Kinetic Energy (Motion) ØK = ½ m v 2 l Work = Change in Kinetic Energy ØS W = DK 50