Transcript Document
Chapter 4: Energy Energy ~ an ability to accomplish change Work: a measure of the change produced by a force Work = force through the displacement portion of the force along displacement * displacement W = F cos q x F F cos q x W = F cos q x F F cos q F F F F x F cos 90 = F0 W=Fx x W=0 Units: 1Newton . 1 meter = 1 joule = 1J p150c4:1 A person pulls a crate 20 m across a level floor using a rope 30° above the horizontal, exerting a 150 N force on the rope. How much work is done? F F x W = F cos q x p150c4:2 Work done against gravity: Work = force through the displacement W = F cos q x force * portion of displacement along force gravity force is always vertical => work = weight* height lifted W = mgh Work depends on height only Work does not depend upon path h Eating a banana enables a person to perform about 4.0x104 J of work. To what height does eating a banana enable a 60-kg woman to climb? p150c4:3 Power: the rate at which work is done work done Power time interval W Joules J P= units : Watts(W ) t second s An electric motor delivers 15 kW of power for a 1000 kg loaded elevator which rises a height of 30m. How much time does it take the elevator to reach the top floor from the ground floor? p150c4:4 Force, speed and power W Fxcosq P= Fvcosq t t P Fv (when F and v are parallel) Efficiency: how effective is power delivered power output Pout Eff power input Pin p150c4:5 Energy: the capacity to do work •Kinetic Energy: energy associated with motion •Potential Energy: energy associated with position •Rest Energy, Thermal Energy, ... Kinetic Energy, from motion in a straight line W Fx max 2 v f 2ax (initially at rest) 2 vf W max m 2 1 2 KE = mv 2 p150c4:6 Potential Energy energy associated with position gravitational potential energy Work done to raise an object a height h: W = mgh = Work done by gravity on object if the object descends a height h. identify source of work as Potential Energy PE = mgh other types of potential energy electrical, magnetic, gravitational, compression of spring ... p150c4:7 Conservation of Energy Conservation Principle: For an isolated system, a conserved quantity keeps the same value no matter what changes the system undergoes. Conservation of Energy: The total amount of energy in an isolated system always remains constant, even though energy transformations from one form to another may occur. Usually consider initial and final times: Ei = Ef p150c4:8 Example: A skier is sliding downhill at 8.0 m/s when she comes across an icy patch (negligible friction) 10m high. What is the skier’s speed at the bottom of the patch? h p150c4:9 Conservative and Nonconservative Forces Conservative forces are forces whose work can be expressed as a change in PE. Conservative forces are the forces which give rise to PE. The work done by a conservative force is independent of the path of the object, and depends only on the starting point and the ending point of the objects path. When considering forces and energies Work-Energy Theorem how “outside world” interacts with an object Work done on an object = change in object’s KE + change in object’s PE + work done by object p150c4:10 Example: A 25-kg box is pulled up a ramp 20 m long and 3.0 m high by a constant force of 120 N. If the box starts from rest and has a speed of 2.0 m/s at the top, what is the force for friction between the box and ramp? F = 120N 3.0m 20m W = Wf + DKE + DPE W =Fs Wf = Ff s p150c4:11 Problem 41: In the operation of a pile driver, a 500 kg hammer is dropped from a height of 5m above the head of a pile If the pile is driven 20 cm into the ground with each impact, what is the force of the hammer on the pile when struck. hammer: PE -> KE does this much work on pile work is through a distance of 20 cm. p150c4:12