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Chapter 6. Work, Energy, Power. Work. The work done by force is defined as the product of the magnitude of the displacement and the component of the force parallel to the displacement. W = F∙d∙cos θ. The unit of work is the newton-meter, called a joule (J) Work is a scalar. q. Work.
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Chapter 6 Work, Energy, Power
Work • The work done by force is defined as the product of the magnitude of the displacement and the component of the force parallel to the displacement W = F∙d∙cosθ The unit of work is the newton-meter, called a joule (J) Work is a scalar
q Work F cos q
Energy • Energy • The ability to do work • Sources of energy? • Mechanical energy • energy due to position or movement. • Types of Energy • Kinetic Energy = “Motion Energy” • Potential Energy = “Stored Energy”
Kinetic Energy • Kinetic Energy is the energy possessed by an object because it is in motion. • What would the unit be? KE = ½ mv2 (Translational Kinetic energy)
Work Energy Theorem • The amount of kinetic energy transferred to the object is equal to the work done. DKE = W • Many of the problems can be worked from here Ex: How much force is required to stop a 1500kg car traveling 60.0 km/hr in a distance of 20m?
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
Properties of GravitationalPotential Energy • Arbitrary Zero Point • You need to select a zero level • Independent of Path • All that matters is the vertical height change • Example: which has more potential, which requires more work
Elastic Potential Energy • Elastic potential energy • Energy stored elastically by stretching or compressing. • Examples?
Springs • The more you compress or stretch them, the more force you need to stretch or compress. • Hooke’s Law • Fspring=k x • k is the spring constant which is a measure of stiffness • x is the displacement from equilibrium • P.E. spring= ½ k x2 • Practice problem
Conservation of Mechanical Energy • Energy can neither be created or destroyed, but only transformed from one form to another. • Total initial energy = Total final energy Works for systems with no losses (friction, air resistance, etc.)
Problem Solution Guidelines • Determine that energy can be conserved (no losses) • Pick the zero level for potential energy • Pick two interesting places in the problem • Write kinetic and potential energies at these places • Conserve energy • (KE + PE)1 = (KE + PE)2
Example • If 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.
Forces Work and Energy • Conservative forces- work done by these forces is independent of the path • Examples: gravity, elastic, electric • Non-conservative forces- work done by these forces is dependant upon the path • Examples: friction, air resistance
Law of conservation with dissipative forces • Dissipative forces- forces that reduce the total mechanical energy of a system • Example: friction (loss to thermal energy) • Swinging pendulum of pain demo. • In real situations • T.E.= K.E.+P.E+ Energy lost to n.c. Forces • WNC= ΔKE+ ΔPE • -Ffriction d = ΔKE+ ΔPE • Example 6-15 pg 168
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
Example • A 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 & hp • How much energy was required to climb the stairs?
