1. PHYS16 – Lecture 16 Work, Energy, and Power October 15, 2010

2. This Week… What is Energy? What is Work? Work-Energy Theorem – how energy and work are related What is Power?

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

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

5. 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

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

7. 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

8. 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

9. 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

10. 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

11. 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

12. Let’s define Power Power – the rate at which work is performed – Units = W = J/s – Scalar

13. Lingenfelter Corvette… What is the power of the 1420 kg Lingenfelter Corvette that can go 0 to 26.8 m/s in 1.97 s? Approach #1Approach #2 Answer = 259 kW Spec says 1100 kW, why?

14. Horsepower 1 hp = 33,000 ft lbs/min Comes from how much weight a horse could pull up a mine shaft a particular amount of feet in a given minute Horse Force

15. Estimating horsepower Car = 250-1475 hp – 1 hp = 746 W – Lingenfelter corvette = 1475 hp – Small compact= 250 hp Lawnmower = 5-25 hp Person = ~1 hp – Estimate using time it takes to run up stairs