ENERGY Different forms; Chemical, Electrical, Heat, Electromagnetic, Nuclear and Mechanical Energy can be transformed from one type to another but the total amount never changes If one form of energy decreases then another must increase Mechanical Energy = the sum of kinetic and potential energies ( motion & position)

WORK Work is done if an object is moved through a displacement while a force is being applied to it If either the force or displacement is doubled so is the work W=F delta x Force and displacement are in the same direction Joule= newton.meter = kg.m 2 /s 2

Facts about Work Work is a scalar quantity (no direction) Work does not depend on time Units are joule or foot-pound When force is not in the same direction as displacement only the component parallel to displacement does work on the object W= (F cos a) x where a is the angle to the horizontal

Frictional Work Frictional Work is the work done due to friction during motion. Energy dissipates (lost) W fric = -f k x = -u k n.x = -u k mg.x W net = W applied - W fric

Kinetic Energy K.E is the energy of movement K.E. = ½ mv 2 As W = F.S = m.a.s ; s= displacement From v 2 = v o 2 + 2as; then as =(v 2 – v o 2 )/2 Then W = m(v 2 – v o 2 )/2 Therefore Work = K.E. final – K.E. initial

Potential Energy P.E is the energy an object has due to its position in space (units Joules) Gravitational P.E. = m. g. y where y = vertical height and g = gravity Gravitational P.E is the energy of an object based on its position in space Work = P.E initial – P.E final

Conservative Forces The work done on an object moving between two points, is independent of the path taken. It depends only on the initial and final positions. Gravitational force is conservative If the work done by a force on an object moving through a closed path is zero Potential energy functions can be defined only for conservative forces.

Non-conservative Forces The work done on an object is dependent on the path taken. Ex. Work due to friction will differ for different paths. Path 1 W= F.S Path 2 W= F.(22/7d)/2 ab If the force leads to the dissipation of mechanical energy

Conservation A physical quantity is conserved when the value of the quantity remains constant. The form of the quantity may change but the final value is the same as the initial value. For example the gravitational potential energy of a falling object will change to kinetic energy, but the total energy will remain the same.

Mechanical Energy The total mechanical energy in any isolated system remains constant if the objects within the system interact only through conservative forces. Total mechanical energy in a system is the sum of the total kinetic and potential energies in the system Therefore 1/2mv i 2 +mgy i =1/2mv f 2 +mgy f

Spring Potential Energy A spring neither stretched or compressed is in equilibrium When compressed or stretched by a force there is stored potential energy in the spring Stored spring energy is called elastic P.E. Hooke’s law F = k.x Where k is the spring constant particular to a spring (heavy spring = a large k value)

Work done to store spring energy The force require is proportional to the distance the spring is change from equilibrium Therefore F ave. = F o + F x /2 = 0 + kx/2=1/2kx As work is F.x then W = 1/2kx 2 =P.E s The potential energy is maximum when the spring has reached its max. compression or stretch P.E s is always positive

New Mechanical energy Formula Incorporating the value of spring potential energy in the previous formula (KE + PE g + PE s ) I = (KE + PE g + PE s ) f Where g is for gravity and s is for spring

Non-conservative forces and work In the real world non-conservative forces such as friction are present. Therefore; W nc = (KE f – KE i ) + (PE f - PE i ) The work done by all non-conservative forces equals the change in kinetic energy plus the change in potential energy.

Power Power is the rate of energy transfer with time P = W/t SI units (watt W = J/s ) kg.m 2 /s 3 Also P = F.x/t as x/t = v then P = F.v Power therefore is a constant force times the average speed The component of force is in the direction of the average velocity

Power cont. U.S. customary system unit of power is the horsepower (hp) =746W Power consumption is referred to in kilowatt-hours 1kWh = (10 3 W) (3600s) = 3.60 x 10 6 J A kilowatt-hour is a unit of energy not power A 100 watt bulb consumes 3.6 x 10 5 J in 1h

Mechanical Advantage MA. Is the advantage granted to us by the use of machines MA. = F r /F e where F r is the resistance force F e is the effective force MA. Is usually greater than 1

Ideal Mechanical Advantage IMA. Is mechanical advantage based on a distance. Ex. The rope one pulls in a pulley system to move an object. IMA.= d e /d r where d e is the distance of effort d r is the distance of resistance IMA. Is usually greater than 1

Efficiency e is the extent that a machine is efficient e = Work out/Work in e = F r.d r /F e.d e e =( MA./IMA ).100