Chapter 6. Work and Kinetic Energy. Richard Feynman Nobel Prize in physics (1965)

Transcription

1 Chapter 6 ork and Kinetic Energy 1 Deinitions ebster s dictionary: Energy the capacity to do work ork the transer o energy Richard Feynman Nobel Prize in physics (1965) The Feynman Lectures on Physics....in physics today, we have no knowledge o what energy is. e know how to calculate its value or a great variety o situations, but beyond that it s just an abstract thing which has only one really important property - conservation 1

2 Newton s Laws 1 st Law: An object at rest or traveling in uniorm motion will remain at rest or traveling in uniorm motion unless and until an eternal orce is applied r r F net ma nd Law: F ma, F ma F ma net, net, y y, net, z z 3 rd Law: For every Action, there is an equal but opposite Reaction 3 On the practical side Newton s laws o motion allow us to analyze many kinds o motion. 4

3 On the practical side : However, the analysis is oten complicated, requiring details about the motion that we may not know 5 There is another idea, sometimes more powerul, or analyzing motion Energy There are very many orms (or types) o energy 6 3

4 Part 1 Kinetic Energy 7 Kinetic Energy K is energy associated with the state o motion o an object 1 K mv Units: joule (J) 1 joule 1 J 1 kg m /s Energy is a scalar quantity (a number) that is associated with a state (or condition) o one or more objects. 8 4

5 5 9 Connection between energy and orce - hint Let side the kinetic energy has been changed Right side the change is equal to F d mv mv K Δ ) ( a v v ) ( ) ( 1 ma v v m K Δ ) ( 1 1 F mv mv ( ) F 1 Part ork

6 ork is energy transerred to or rom an object by means o a orce acting on the object. The work done by the orce acting on an object which moves through a displacement d F d r hint: the scalar product o two vectors a b abcosθ Only component o orce parallel to dr contributes to work done by the orce 11 ork: math deinition Total ork done by a orce moving an object rom point a and to point b b a F d r b a F cosϑ dr Special case: ork done by a constant orce F d F d cosϑ Units: joule (J) (same as energy!) 1 joule 1 J 1 kg m /s 1 N m 1 6

7 Three-Dimensional analysis F F iˆ + F y ˆj + F zkˆ dr d iˆ + dy ˆj + dz zkˆ y d F d r F d + Fydy + Fzdz Fd + Fydy + i y y i z z i F dz z 13 positive and negative work Energy transerred to the object is positive work, and energy transerred rom the object is negative work. F d cosϑ A orce does positive work when it has a vector component in the same direction as the displacement, and it does negative work when it has a vector component in the opposite direction. It does zero work when it has no such vector 14 component 7

8 ork done by a gravitational orce F d cosϑ A particle-like tomato is thrown upward with initial speed mg d cosϑ mg d cos18 mgd 15 F d cosϑ ork done by a constant orce Block with constant velocity on inclined plane 16 8

9 or a pig sliding down F d cosϑ ork done by gravity mgh The answer does not depend on the angle 17 ork done by a spring orce The spring orce Hook s law F -k F restoring orce k spring constant displacement S ( k) d k d 1 k( ) 18 9

10 continue S 1 k( The work done by the spring can have a positive or negative value! orks S is positive i the block ends up close to the relaed point () than it was initially. It is negative i the block ends up urther away rom. It is zero i the block ends up at the same distance rom ) special case S 1 k 19 More on connection between orce and work 1

11 ork Kinetic Energy Theorem 1 1 mv mvi change in the energy o the ΔK K K i kinetic net work done particle the particle on K Ki + Let side the kinetic energy has been changed Right side the change is equal to F d 1 Mass in ree all K Ki + 11

12 about the same pigs K Ki + According to the ork-kinetic-energy Theorem speed will be the same or all three slides! 3 Block moving on surace K Ki + 4 1

13 Stopping distance K Ki + 5 Power The time rate at which work is done by a orce Units: watt () 1 watt 1 1 J/s P d dt t t i Pdt and or constant power PΔt 1 kilowatt-hour 1 k h 1 36 s J 6 13

14 Power, orce and velocity 7 14