PHY 102: Lecture 4A 4.1 Work/Energy Review 4.2 Electric Potential Energy

PHY 102: Lecture 4A Electric Potential Energy Electric Potential 4.1 Work / Energy Review

Work vs. Energy Energy is a property of matter –Mass, Inertia and Electric Charge are other properties Matter that has energy can do work by means of a force Work transfers or changes energy

Work – Constant Force Work is a scalar Work done on an object by a constant force F is:  W = (F cos  d F is magnitude of constant force d is the magnitude of the displacement along a line   is angle between force and displacement SI Unit of Work: Newton meter = joule (J)

Kinetic Energy KE = Kinetic Energy KE is the energy of a moving object KE = (1/2)mv 2 m is the mass of the object v is the speed of the object

Work – Energy Theorem A net external force does work W on an object The kinetic energy of the object changes from its initial value of KE i to a final value of KE f The difference between the two values is equal to the work  W = KE f – KE i = ½ mv f 2 – ½ mv i 2

Work Done by Force of Gravity An object moves from initial height h i to final height h f The force of gravity acts on the object  W gravity = Fd  F = mg = weight  d = h i - h f  W gravity = mg(h i – h f ) = mgh i - mgh f

Gravitational Potential Energy The gravitational potential energy PE is the energy that an object of mass m has because of its position relative to the surface of the earth That position is measured by the height h of the object relative to an arbitrary zero level  PE = mgh

Conservative Force Version 1  A force is conservative when the work it does on a moving object is independent of the path between the object’s initial and final position Version 2  A force is conservative when it does no net work on an object moving around a closed path starting and finishing at the same point

Conservative Forces Nonconservative Forces Conservative Forces –Gravity –Spring force –Electrostatic force –Magnetic force Nonconservative Forces –Friction –Air resistance

Principle Conservation of Mechanical Energy Total mechanical energy (E = KE + PE) of an object remains constant as the object moves Provided that the net work done by external nonconservative forces is zero, W nc = 0 J

Kinetic Energy vs. Potential Energy The sum of the kinetic and potential energies at any point is conserved Kinetic and Potential Energies may be converted or transformed into one another

PHY 102: Lecture 4A Electric Potential Energy Electric Potential 4.2 Electric Potential Energy

Gravitational Potential Energy A basketball of mass m falls from point A to point B The gravitational force is mg in the downward direction Work done by gravity is  W AB = mgh A – mgh B  W AB = GPE A – GPE B

Electric Potential Energy Positive test charge moves from point A to B between plates of capacitor The electric force is q 0 E in the downward direction Work done by electric force is  W AB = q 0 Es A – q 0 Es B  W AB = EPE A – EPE B  s is distance from negative plate

Work by Gravity / Electricity The gravitational and electrical forces are conservative The work done in going from point A to point B does not depend on the path taken