1. Kinetic Energy

2. Origin of Work  Work describes a process.  Where does work come from, and go to?  The ability to do work can come from our bodies, electricity, chemicals, nuclear reactions, and motion.  Energy measures the state of an object, and its ability to do work.

3. Energy of Motion  Consider the work done on an object with constant acceleration in a straight line.  The distance is related to the acceleration. F=ma d The work done becomes kinetic energy: (1/2) mv 2

4. Changing Energy  The definition of kinetic energy applies to all objects. If an object speeds up it gains kinetic energy. If an object slows down it loses kinetic energy.  This matches the work done on or by an object. Work done on the ball v2v2 v1v1 Work done by the ball v4v4 v3v3

5. Work-Energy Principle  The change in kinetic energy is due to net work done on the object. W net = K 2 – K 1 =  KW net = K 2 – K 1 =  K The sign of work is positive when energy is addedThe sign of work is positive when energy is added

6. Work-Energy Theorem  The work-energy principle can be proved for any force using calculus. Use the integral definition of workUse the integral definition of work Replace force with mass times accelerationReplace force with mass times acceleration Arrange to integrate in vArrange to integrate in v Use the initial and final speedUse the initial and final speed Convert to kinetic energyConvert to kinetic energy

7. Using Kinetic Energy  A man lets the 300 kg piano pick up speed from 2.0 m/s to 4.0 m/s over 3.0 m. What work is done on the piano? The initial kinetic energy is K 1 = (0.5)(300 kg)(2.0 m/s) 2 = 600 J. The final kinetic energy is K 2 = (0.5)(300 kg)(4.0 m/s) 2 = 2400 J. The work done on the piano is 1800 J. mg v1v1 v2v2 xx

8. Limits of Kinetic Energy  At very high speed the work-energy principle fails. Nothing goes faster than the speed of lightNothing goes faster than the speed of light Kinetic energy can continue to increaseKinetic energy can continue to increase Contradiction – energy increases but not speedContradiction – energy increases but not speed  At speeds close to the speed of light we use Einstein’s special relativity. next