2 WorkThe work done by force is defined as the product of the magnitude of the displacement and the component of the force parallel to the displacementW = F∙d∙cosθThe unit of work is the newton-meter, called a joule (J)Work is a scalar
4 Energy Energy Mechanical energy Types of Energy The ability to do work Sources of energy?Mechanical energyenergy due to position or movement.Types of EnergyKinetic Energy = “Motion Energy”Potential Energy = “Stored Energy”
5 Kinetic EnergyKinetic Energy is the energy possessed by an object because it is in motion.What would the unit be?KE = ½ mv2(Translational Kinetic energy)
6 Work Energy TheoremThe amount of kinetic energy transferred to the object is equal to the work done. DKE = WMany of the problems can be worked from hereEx:How much force is required to stop a 1500kg car traveling 60.0 km/hr in a distance of 20m?
7 Gravitational Potential Energy Gravitational Potential Energy is the energy possessed by an object because of a gravitational interaction.Product of it’s weight and its height above some reference level.PEG = mghy
8 Properties of Gravitational Potential Energy Arbitrary Zero PointYou need to select a zero levelIndependent of PathAll that matters is the vertical height changeExample: which has more potential, which requires more work
9 Elastic Potential Energy Energy stored elastically by stretching or compressing.Examples?
10 SpringsThe more you compress or stretch them, the more force you need to stretch or compress.Hooke’s LawFspring=k xk is the spring constant which is a measure of stiffnessx is the displacement from equilibriumP.E. spring= ½ k x2Practice problem
11 Conservation of Mechanical Energy Energy can neither be created or destroyed, but only transformed from one form to another.Total initial energy = Total final energyWorks for systems with no losses (friction, air resistance, etc.)
12 Problem Solution Guidelines Determine that energy can be conserved (no losses)Pick the zero level for potential energyPick two interesting places in the problemWrite kinetic and potential energies at these placesConserve energy(KE + PE)1 = (KE + PE)2
13 ExampleIf a boulder is pushed off of a 15.0 m high cliff by Wile E. Coyote, and the road runner is 1.50 m tall, find the velocity of the boulder when it reaches the road runners head.
14 Forces Work and EnergyConservative forces- work done by these forces is independent of the pathExamples: gravity, elastic, electricNon-conservative forces- work done by these forces is dependant upon the pathExamples: friction, air resistance
15 Law of conservation with dissipative forces Dissipative forces- forces that reduce the total mechanical energy of a systemExample: friction (loss to thermal energy)Swinging pendulum of pain demo.In real situationsT.E.= K.E.+P.E+ Energy lost to n.c. ForcesWNC= ΔKE+ ΔPE-Ffriction d = ΔKE+ ΔPEExample 6-15 pg 168
16 Power Power is the rate at which work is done. The unit of power is a joule per second, called a Watt (W).1hp = 746 Watts
17 ExampleA 70.0 kg football player runs up a flight of stairs in 4.0 seconds while training. The vertical height of the stairs is 4.5 m.What is the power output of the player in W & hpHow much energy was required to climb the stairs?