PHYS 16 Lecture 16 Work Energy and Power

PHYS 16 – Lecture 16 Work, Energy, and Power October 15, 2010

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

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

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

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

Work with a Variable Force Fx • Force = Constant, then can take force outside integral x

Practice Question • A force is given by Fx = 3 x 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

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

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

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

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

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

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 #1 Approach #2 Answer = 259 k. W Spec says 1100 k. W, why?

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

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