1. PHYS16 – Lecture 15 Work and Energy October 13, 2010

2. Agenda Administration – Homework for Week 5 – Exam What have we learned so far? What do we still need to know? Energy Mechanical Work

3. Description of Motion – What else do we need? We have: – Laws of Calculus – Displacement, Velocity and Acceleration – Newton’s Laws – F=ma – Concept of Momentum

4. We need energy…

5. Definition of Energy Energy – A quantity whose expenditure or transformation allows for physical activity – An ability to drive motion – A capacity for action Scalar Quantity Unit = Joule (J) = kg·m 2 /s 2 Comes in many forms – Thermal – Chemical – Mechanical!!!!!

6. Mechanical Energy Kinetic Energy (K)– energy stored in the movement of an object Potential Energy (U) – energy stored in the configuration of a system – Gravitational Potential Energy – Spring Potential Energy

7. Energy can be transformed Wyle E. Coyote http://www.youtube.com/watch?v=Jnj8mc04r9E&feature=relatedwww.youtube.com/watch?v=Jnj8mc04r9E&feature=related

8. Practice Question A 0.50 kg vase falls from 3.0 m. What is the kinetic energy of the vase just before it hits the ground? A) 0 J B) 15 J C) 1.5 J D) 2.3 J

9. Practice Question A 0.50 kg vase falls from 3.0 m. What is the potential energy of the vase before it falls? A) 0 J B) 15 J C) 1.5 J D) 2.3 J

10. We need work…

11. Definition of Work Mechanical Work (W) – energy transferred to an object due to the action of a force (+) transfer to object (-) transfer from object

12. Aside on Dot Product Dot Product is one way to multiply two vectors – Basically just multiply components and add – Dot Product is a scalar A B

13. Aside on Dot Product Dot Product is one way to multiply two vectors – Basically just multiply components and add – Dot Product is a scalar A B

14. Aside on Dot Product Dot Product is one way to multiply two vectors – Basically just multiply components and add – Dot Product is a scalar – Or multiply magnitudes and cosine angle between the vectors A B θ=56°

15. Work with a Constant Force Force = Constant, then can take force outside integral

16. Work with a Variable Force Force = Constant, then can take force outside integral FxFx x

17. Practice Question I pull a 4.0 kg sled a distance of 5.0 m. I pull the sled using a rope at a 30.0 degree angle with a force of 5.0 N. What is the work done by me? A) 0 J B) 20 J C) 25 J D) 22 J

18. Practice Question A force is given by F x = 3x 2 +2. What is the work done by the force for moving an object from x=0.0 m to x=4.0 m? A) 72 J B) 50 J C) 0 J D) 200 J

19. Work – Energy Theorem Work = the transfer of Energy Energy = the ability to do work Work done by External Force Change in Energy to the system

20. Work and grav. potential energy If I lift an object, how much work did I do on the object? Use work-energy theorem to derive gravitational potential energy Force and displacement are both downward

21. Work and spring potential energy If mass on a spring moves, how much work is done by spring? Use work-energy theorem to derive spring potential energy Work done by system is negative Force and displacement are in opposite directions

22. Work and Kinetic energy If an object speeds up, how much work is done on object? Use work-energy theorem to derive kinetic energy Assume K=mv 2 /2 and prove left side = right side Just multiply and divide by dt since dt/dt=1 Now take derivative and remember to use chain rule