1. Notes - Energy A. Work and Energy

2. What is Energy?  Energy is the ability to produce change in an object or its environment.  Examples of forms of energy: solar, thermal, mechanical (PE and KE), chemical

3. Moving objects  What kind of energy does a moving object have?  Kinetic energy  Where does it come from?  Comes from work done on an object  Equation: KE = 1/2 mv 2  Units: Joules (J)

4.  How is work calculated? What are its units?  W = Fd  1 Nm = 1 Joule  Note: work can be done ON an object, and work can be done BY an object Work

5.  How are work and kinetic energy related to each other?  W =  KE Work-Energy Theorem  Work done produces changes in kinetic energy  Work is done only when there is a change in position of an object Work and Kinetic Energy

6.  So….are you doing work on a book when you carry it across the room?  NO…Force is upward, displacement is forward…at least part of the force must be in the direction of the displacement (  )  Does the sun do work on the Earth?  NO…Force is toward center of circle, displacement is in direction of velocity (  ) So……..

7.  Sketch:  Resolve force into components, use only the component acting in the direction of the motion. What if the force is acting at an angle?

8. Example:  Joe Bleau is pushing a shovel along a driveway. The force applied to the shovel is 25N at an angle of 60° with the horizontal for a distance of 30 meters. Find the work done by Mr. Bleau. Neglect friction.

9. Solution:

10.  Graph:  Area under the curve How can you find work on a force- displacement graph?

11. Solution:  Rectangle:  Triangle:

12. Example:  John pushed a crate across the floor of a factory with a horizontal force. The roughness of the floor changes and John must exert a force of 20N for 5m, then 35N for 12m, then 10N for 8m. (a) Draw a graph of force as a function of distance, and (b) Find the work John does pushing the crate.

13. Graph: Find the area under the curve:

14. Example:  Mike pulls a sled across level snow with a force of 225N along a rope that is 35° above the horizontal. If the sled moved a distance of 65.3m, how much work did Mike do?

15. B. Power  How can we calculate power? What are its units?  Power - rate at which energy is transferred (rate at which work is done).  P = W/t = Fd/t = Fv  1 J/s = 1 watt

16. Example:  An electric motor lifts an elevator that weighs 1000N a distance of 5 meters in 10 seconds. What is the power in watts? In kilowatts?

17.  Which takes more power - lifting a pile of books all at once or lifting each one individually? 10 books Lift time =1 sec Lift distance= 1 meter Book weight= 1 Newton All at once: One at a time:

18. C. Kinetic Energy  What is kinetic energy? How is it related to work done on an object?  Kinetic energy is energy of motion.  KE = 1/2 mv 2  Comes from work done on an object  Units - Joules (J)

19. Example:  An 875 kg. car speeds up from 22 m/s to 44 m/s. What are its initial and final kinetic energies, and how much work was done on the car to increase its speed?

20. Solution: m=875 kg v i =22m/s v f =44m/s

21. D. Potential Energy  What is potential energy?  PE is stored energy.  In what forms can energy be stored?  Gravitational  Spring  Chemical

22. What is gravitational potential energy?  Comes from work done against gravity  PE = mgh (similar to W = Fd because force to lift an object is its weight mg, and distance lifted is height)  Units - Joules (J)

23. Example:  A 2 kg book is lifted from the floor to a shelf 2.1 meters above the floor. What is the gravitational potential energy relative to the floor?  What is the gravitational potential energy relative to the head of a 1.65 meter tall person?  YOU NEED A REFERENCE LEVEL

24. Solution:

25. What is elastic PE?  Stored energy in a spring  PE s = 1/2 kx 2  Units - Joules (J)  k is spring constant in N/m  x is spring stretch in m

26. Hooke’s Law  What is Hooke’s Law?  F = kx  x is the change in spring length, m  F is the force applied to the spring, N  K is spring constant, N/m

27. How can you determine k from a force-displacement graph?  Graph: Force (N) Spring stretch (m)  Slope is k

28. Conservation of Energy  What is the Law of Conservation of Energy?  The total energy in a closed system is constant.  In mechanical systems, the work equals the sum of the KE and PE, and work done against friction

29.  How does friction affect energy conversions?  Some energy is lost as heat  Total energy TE = PE + KE + IE  IE is internal energy (heat)

30. Collisions  Elastic vs. Inelastic  In a collision, colliding bodies change shape. KE is temporarily converted to PE during compression, then back to KE  Elastic collision - PE is converted completely back to KE…….KE is conserved  Inelastic collision - some KE is lost (changed to other forms)  In both types of collisions, momentum is conserved

31. Conservation of Energy Examples: Pendulum  Sketch:

32. Conservation of Energy Examples: Falling Object  Sketch:

33. Conservation of Energy Examples: Slide  Sketch:

34. Slide Animation: