Chapter 5: Work, Power, and Energy
5.1 Objectives Understand the concepts of work and power. Be able to make work and power calculations.
Work work: a force applied through a distance (not a displacement!) Work is a scalar. force (F) f distance (x) W = (F·cosf)·x James Joule: studied the relationship between work and thermal energy units: N·m = J (joules) shake can!
Work Problem A 107 N golf bag is dragged 125 meters (at constant speed) with a force of 8.5 N. The force is oriented 32o above the horizontal. How much work is done by the golfer? By friction? By gravity? By the normal force? W = F·x·cosf
Power power: the rate at which work is done (work ÷ time) units: J/s = W (watts) W in an equation is work W as units are Watts 746 W = 1 hp James Watt: inventor of the steam engine
Power Problem A weightlifter lifts a 275 kg mass from the floor to a height of 1.92 m in only 1.48 seconds. How much work is done by the weightlifter? How much power is used?
5.2 Objectives Understand the concepts of potential energy and kinetic energy. Make GPE and KE calculations.
Potential Energy Something is required to do work. That “something” is called energy. potential energy: stored energy (due to the presence of a force) gravitational potential energy (GPE)… W = F·x·cos f W = FW·h·cos(0o) = FW·h height (h) W = m·g·h GPE = m·g·h units: N·m = J
GPE Problem A 425 N television is moved from the bottom to the top of a flight of stairs that is 2.62 m high. The stairs angle upward at 45o. How much work is done? How much GPE does the TV have at the top of the stairs?
Kinetic Energy A moving object is capable of doing work if it runs into something else—it has stored energy. kinetic energy: the energy held by a moving object (due to relative motion) F = m·a KE = ½·m·v2 F·d = m·a·d Why? W = m·a·d force W = m·a·½·a·t2 distance W = ½·m·a2·t2 W = ½·m·v2
KE Problem How much energy does the space shuttle have as it travels along in its orbit? The shuttle has a mass of 2 x 106 kg and its orbital speed is 8 km/s.
Objectives Understand the work-energy theorem. Be able to make work-energy theorem calculations.
Work-Energy Theorem If the sum of all the work done on an object (by all the forces) is calculated, then the SW will equal the change in kinetic energy of the object. SW = SF · d = DKE = KEf - KEi SW = SF·d = ½·m·v2, or d ~ v2
Work-Energy Theorem Problem Brakes apply a SF when applied. How much SW is done to stop a 1450 kg car traveling at (a) 15.6 m/s and (b) 31.2 m/s? [ 35 mph and 70 mph ] What is the stopping distance in each case if the brakes apply 7.5 kN of force?
Stopping Distance Chart
5.3 Objectives Understand the law of conservation of energy. Use the law of conservation of energy to solve assorted dynamics problems.
Conservation of Energy Mechanical energy (ME) is the sum of KE and all PE. law of conservation of energy: energy is conserved when converted from one form to another (the total ME remains constant). SPEi + KEi = SPEf + KEf Why? vf2 = vi2 + 2·a·d vf2 = 2·g·h GPE KE = ½·m·v2 KE = ½·m·2·g·h height (h) KE = m·g·h (= GPE = m·g·h) KE = ?
Conservation of Energy Problem With what speed must a ball be thrown upward to reach a height of 28 meters?
Conservation of Energy Problem A roller coaster traveling at 16 m/s drops down a steep incline that is 25 meters high and then moves up another incline. What is the height of the second incline if the roller coaster is moving at 12 m/s at its crest? Assume the effect of friction is negligible. website
Bullseye Lab h1 razor h2 dx = ? It is an extremely simple equation! dx
Objectives Be able to identify simple machines. Be able to explain how simple machines make doing work “easier.” Be able to calculate the ideal mechanical advantage (IMA), actual mechanical (AMA) advantage, input work (WI), output work (WO), and efficiency (e) of a simple machine.
Simple Machines 4 kinds: lever, inclined plane, pulley, wheel and axle Simple machines generally make doing work easier by reducing applied force (but distance is increased). input work: WA = FA·dA output work: WO = FO·dO If no friction: WA = WO If friction is present: WA > WO
Simple Machines mechanical advantage (MA): factor by which input force is multiplied by the machine “ideal” “actual” efficiency: ratio of output work to input work (indicates amount of friction in machine)