Work Power Energy Work Concepts Work W product

Work, Power, Energy

Work Concepts • Work (W) ~ product of the force exerted on an object and the distance the object moves in the direction of the force. – W is transfer of energy by mechanical means. – W is done on an object only if it moves in the direction of the force (or parallel to the force). – If the force and displacement are in opposite directions, the work done is negative. – Only the component of the force in the direction of the motion does work.

Work Formulas Work = Force x displacement W = Fd F d 1 Joule (J) = 1 Newton x meter (N m)

If force is exerted at an angle, use only the component of force that is parallel to the displacement: F d Since the displacement is horizontal (x direction), use only the horizontal component of force. F θ Fx Fy W x = F x dx W = (Fcos )d

Power • Power (P) ~ rate at which work is done or rate at which energy is transferred. Measured in watts. – Watt (W) ~ one joule of energy transferred in one second. Power = Work / time Units: 1 watt = 1 joule / second (J/s) 1 watt = 1 N m / s

Ideal Machines • Ideal machines exist only in a frictionless, air resistance-less world. • No energy or work is lost to the system through outside forces • For ideal machines: Work input = Work out put so: Findin = Fout dout

Efficiency • Efficiency ~ ratio of work output to work input expressed in percent. • Ratio of final energy to initial energy efficiency = (Wout / Win) * 100 Or efficiency = (Ef / Ei)*100

Types of Energy èMechanical Energy é Kinetic Energy é Elastic Potential Energy é Gravitational Potential Energy èChemical Potential Energy èThermal (Heat) Energy

Kinetic Energy -the energy an object has due to its motion KE = ½ m v 2 KE – kinetic energy, J m – mass, kg V – speed, m/s

Potential Energy Potential energy is the energy an object has because of its position, shape, or form

Gravitational P E GPE = gravitational potential energy, J GPE = m g h m = mass, kg GPE = Fg h h = height above reference level, m g = accleration due to gravity, m/s 2 (+h if above ref. , -h if below ref. ) Gravitational potential energy depends on the weight of the body (mass and g) and its separation from Earth (h)

Elastic Potential Energy • Energy stored in an elastic object that is stretched or compressed. • An elastic object is one that can be stretched or compressed and will return to its original or relaxed length. EPE = ½ k x 2 EPE - elastic potential energy, J k - the elastic or spring constant, N/m (indicates how easily a material stretches or compresses) ‘higher k, stiffer’ x - the distance that the object is stretched or compressed from its relaxed length (stretched length – relaxed length)

Mechanical Energy Mechanical energy is the energy which is possessed by an object due to its motion or its stored energy of position, shape, or form Mechanical Energy = KE + PE ME = KE + GPE + EPE

Law of Conservation of Energy • Energy can not be created or destroyed. • The total energy remains constant. • Energy can change forms. • Assumes a closed, isolated system. • We will only use mechanical energy. MEinitial = ME, final KEi + GPEi + EPEi = KEf + GPEf +EPEf ½ mvi 2 + mghi + ½ kxi 2 = ½ mvf 2 + mghf + ½ kxf 2

Work-Energy Theorem If work is done on an object (by the net force), its energy is changed. The change in energy is equal to the work done. Work = Δ KE F d = KEf – KEi F d = ½ m v f 2 – ½ m v i 2

Work Energy Theorem • When work is done, potential energy can also be changed.

Work Energy Theorem • When work is done, elastic potential energy can also be changed.