Energy

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.

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) mv2

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 v1 v2 v3 v4 Work done by the ball

Work-Energy Principle The change in kinetic energy is due to net work done on the object. Wnet = K2 – K1 = DK The sign of work is positive when energy is added Kinetic energy K or KE

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 K1 = (0.5)(300 kg)(2.0 m/s)2 = 600 J. The final kinetic energy is K2 = (0.5)(300 kg)(4.0 m/s)2 = 2400 J. The work done on the piano is 1800 J. v1 Dx v2 mg

Height Work is a process. When a block is lifted, work is done on the box. At the end, the block is resting – no kinetic energy. Where did the work go? y2 F = -mg h y1

Energy of Position Raise a block The state of the block changes Work is stored in a new position Energy due to position is called potential energy (U or PE). An object has the potential to do work The potential energy of gravity: U = mgy y2 Dy y1

No Absolute Potential energy reflects the work that may be done. The point U = 0 is arbitrary At the top of a table of height h: U = mg(y+h) The same experiment is shifted by a constant potential mgh: U = mgy + mgh = mgy + C y2 y y1 h

Using Potential Energy A man is letting a 300 kg piano slide 4 m at constant velocity down a 30° incline. What is the change in potential energy? Piano weight, mg = 3000 N The change in height is (4 m)(-sin 30) = -2 m Negative since it is down The change in potential energy is DU = -6000 J Dx W=mg