Transcript Energy
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 Work F q F cos q d W d(F cosq ) 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. KE = ½ 2 mv (Translational Kinetic energy) What would the unit be? 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 Gravitational Potential 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 ( KE PE )inital ( KE PE ) final 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 Work Done Average Power Time W P t F *d t Force * Velocity 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?