PHYS16 – Lecture 15

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·m2/s2 • 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=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 θ=56° B

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 Fx 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 Fx = 3x2+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=mv2/2 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