Phys141 Principles of Physical Science Chapter 4 Work and Energy Instructor: Li Ma Office: NBC 126 Phone: (713) Webpage: Department of Computer Science & Physics Texas Southern University, Houston Sept. 20, 2004

Topics To Be Discussed Work Kinetic Energy and Potential Energy Conservation of Energy Power

About Work & Energy Common meaning of Work –Work is done to accomplish some task or job –When work is done, energy is expended Mechanically, Work involves force & motion Energy is a concept, is abstract, is stored work

Work The work done by a constant force F acting on an object is the product of the magnitude of the force (or component of force) and the parallel distance d through which the object moves while the force is applied W = F·d

Work (cont) If only apply force but no motion, then there is technically no work Only the component of force in the direction of motion has contribution to work Example: d F FhFh FvFv W = F h ·d

Work (cont) Unit of Work –In Metric system: N·m, or joule (J) –In British system: pound·foot (ft·lb) Newton’s third law force pair –When the force is applied, work is done against this force pair –Moving box forward: do work against friction –Lifting the box: do work against gravity

Energy Common sense: –when work is done, some physical quantity changes: work against gravity, height is changed; work against friction, heat is produced; etc. With concept of energy: –When work is done, there is a change in energy, and the amount of work done is equal to the change in energy

Energy (cont) Energy is described as a property possessed by an object or system Energy is ability to do work: –An object or system that possess energy has the ability or capability to do work Unit of Energy –Same as work

Work and Energy Doing work is the process by which energy is transferred from one object to another: –When work is done by a system, the amount of energy of the system decreases –When work is done on a system, the system gains energy Both work and energy are scalar quantities

Work and Energy (cont) One scenario: when work is done on an object (at rest initially), the object’s velocity changes d = ½a·t 2, v = a·t, F = m·a, W = F·d W = m·a·d = m·a·(½a·t 2 ) = ½ m·(a·t) 2 = ½ m·v 2 So W = ½ mv 2 This amount of work is now energy of motion, or kinetic energy

Work and Energy (cont) Another scenario: when work is done on an object, the object’s position changes There is also a change in energy, since the object has potential ability to leave that position and do work This amount of work is energy of position, or potential energy Kinetic & Potential energy: two forms of Mechanical energy

Kinetic Energy Kinetic energy is the energy an object possesses because of its motion, or simply stated, it is energy of motion: kinetic energy = ½ x mass x (velocity) 2 E k = ½ mv 2

Kinetic Energy (cont) If the work done goes into changing the kinetic energy, then work = change in kinetic energy W = ΔE k = E k2 – E k1 SoW = ½ mv ½ mv 2 1

Potential Energy An object does not have to be in motion to have energy Potential energy is the energy an object has because of its position or location, or simply, it is energy of position Examples: lifted weight, compressed or stretched spring, drawn bowstring

Potential Energy (cont) One scenario: Lift an object at a (slow) constant velocity up to a height h from the ground (or saying sea level) Work is done against gravity Work = weight x height W = m·g·h(W = F·d)

Gravitational Potential Energy The object has potential ability to do work, it has energy Gravitational potential energy is equal to the work done against gravity gravitational potential energy = weight x height E p = m·g·h More generally, E p = m·g·Δh

Conservation of Energy Understanding of conservation –Energy can be neither created nor destroyed –Energy can change from one form to another, but the amount remains constant –Energy is always conserved The total energy of an isolated system remains constant

Conservation of Mechanical Energy Ideal systems –Energy is only in two forms: kinetic and potential Conservation of mechanical energy –The mechanical energy of the ideal system remains constant Initial Energy = Final Energy (E k + E p ) 1 = (E k + E p ) 2 (½ mv 2 + mgh) 1 = (½ mv 2 + mgh) 2

Conservation of Mechanical Energy (cont) Want the velocity of a freely falling object when fallen a height of Δh: –velocity and acceleration: V t = gt, Δh = ½ gt 2 (Δh = d) =>V t = (2gΔh) ½ –Conservation of mechanical energy: (½ mv 2 + mgh) i = (½ mv 2 + mgh) t ½ m(v 2 t - v 2 i ) = mg(h i - h t ) =>V t = (2gΔh) ½

Power Do same thing in different amount of time: the rate at which the work is done is different Power is the time rate of doing work power = work / time P = W/t = F·d/t Unit: watt in the SI, 1 W = 1 J/s

Power (cont) The greater the power of an engine or motor, the faster it can do work Power may be thought of as energy produced or consumed divided by the time taken P = E/t =>E = p·t