Work & Power Physics 2014

Work In Physics, Work is done when a force moves a body through a distance. WORK = Force x Displacement

Work Units Since, Force  Newton (N) displacement  meter (m) DERIVED unit for work  Newton meter (Nm). The FUNDAMENTAL unit for work is the Joule. Joule (J) = N m 1 JOULE = the ability to exert a force of 1 NEWTON over a distance of 1 METER.

Is it possible to do work on an object that remains at rest? 1) yes 2) no ConcepTest 7.1To Work or Not to Work ConcepTest 7.1 To Work or Not to Work

Is it possible to do work on an object that remains at rest? 1) yes 2) no force acts over a distance no displacementno work done Work requires that a force acts over a distance. If an object does not move at all, there is no displacement, and therefore no work done. ConcepTest 7.1To Work or Not to Work ConcepTest 7.1 To Work or Not to Work

Work Atlas bears the weight of the world on his shoulders. How much work is done? NONE…… the world did not move…The force must move the object.

Work or No Work Lifting your bookbag  Carrying your bookbag  A waitress carrying a tray around? No work because the supporting force is perpendicular to the motion. Work is done on an object only if the object moves and only if the force and displacement are in the same direction. DIRECTION IS THE KEY TO WORK…. nics/energy/work/work2.gif work no work No work occurs when:

ConcepTest 7.4Lifting a Book ConcepTest 7.4 Lifting a Book You lift a book with your hand in such a way that it moves up at constant speed. While it is moving, what is the total work done on the book? 1) mg   r 2) F HAND   r 3) (F HAND + mg)   r 4) zero 5) none of the above mg rrrr F HAND v = const a = 0

ConcepTest 7.4Lifting a Book ConcepTest 7.4 Lifting a Book You lift a book with your hand in such a way that it moves up at constant speed. While it is moving, what is the total work done on the book? total work is zeronet forcezero Note that the kinetic energy of the book does not change either! The total work is zero since the net force acting on the book is zero. The work done by the hand is positive, while the work done by gravity is negative. The sum of the two is zero. Note that the kinetic energy of the book does not change either! 1) mg   r 2) F HAND   r 3) (F HAND + mg)   r 4) zero 5) none of the above mg rrrr F HAND v = const a = 0 Follow-up: What would happen if F HAND were greater than mg?

Work Problems A force of 825 N is required to push a car across a lot. Two students push the car 35 m. How much work is done? F= 825 N d = 35 m W = Fd Cutnell & Johnson, Wiley Publishing, Physics 5 th Ed.

Work Only force that is in the same direction of the motion counts. If you pull a wagon at an angle, only the horizontal part of motion counts – only the horizontal part of the pull does any work! Cutnell & Johnson, Wiley Publishing, Physics 5 th Ed.

Work Problems An airplane passenger carries a 215N suitcase up a flight of stairs a displacement of 4.2m vertically and 4.6m horizontally. How much work have they done?

Work If the angle between force and displacement is θ then F x = F cos θ Then the work done is W = F x d= F cos θ d Cutnell & Johnson, Wiley Publishing, Physics 5 th Ed. W=Fd (cos θ)

Work W = Fd cos θ If θ = 90 o  W = Fd cos 90 o So, W = 0 Work is a scalar quantity. No direction is associated with work even though it depends on two vector quantities. Copywrited by Holt, Rinehart, & Winston

Work To move a refrigerator into the back of a moving van. Would you prefer to lift it straight up or walk it up a ramp? Calculate which method required less work? Equal amounts of work are done. The ramp reduces the amount of effort it takes to do work, but DOES NOT CHANGE the amount of work that is done.

Copywrited by Holt, Rinehart, & Winston Work Direction Positive and Negative Work When positive work is done on an object, its speed increases; when negative work is done, its speed decreases. Cutnell & Johnson, Wiley Publishing, Physics 5 th Ed.

ConcepTest 7.2aFriction and Work I ConcepTest 7.2a Friction and Work I 1) friction does no work at all 2) friction does negative work 3) friction does positive work A box is being pulled across a rough floor at a constant speed. What can you say about the work done by friction?

f N mg displacement Pull opposite negative W = F d cos   = 180 o W < 0 Friction acts in the opposite direction to the displacement, so the work is negative. Or using the definition of work (W = F d cos  ), since  = 180 o, then W < 0. ConcepTest 7.2aFriction and Work I ConcepTest 7.2a Friction and Work I 1) friction does no work at all 2) friction does negative work 3) friction does positive work A box is being pulled across a rough floor at a constant speed. What can you say about the work done by friction?

Can friction ever do positive work? 1) yes 2) no ConcepTest 7.2bFriction and Work II ConcepTest 7.2b Friction and Work II

Can friction ever do positive work? 1) yes 2) no moves along with the truck force of friction that is making the box move Consider the case of a box on the back of a pickup truck. If the box moves along with the truck, then it is actually the force of friction that is making the box move. ConcepTest 7.2bFriction and Work II ConcepTest 7.2b Friction and Work II

Work Problems A 10-N frictional force slows a moving block to a stop after a displacement of 5.0 m to the right. What is the net work done on the block? A 10-N force is applied to push a block across a frictional surface at constant speed for a displacement of 5.0 m to the right. What is the net work done on the block?

Work Problems A physics student pulls a box of books as shown. The 455 N force is applied along the rope itself. How much work is done by the student on the books if the box is dragged 24.5 m.

Questionable Work Which ramp requires more work to move the car up a set height? a.30° b.45 ° c.60 ° d.work is equal

ConcepTest 7.3Force and Work ConcepTest 7.3 Force and Work 1) one force 2) two forces 3) three forces 4) four forces 5) no forces are doing work A box is being pulled up a rough incline by a rope connected to a pulley. How many forces are doing work on the box?

ConcepTest 7.3Force and Work ConcepTest 7.3 Force and Work N f T mg displacement Any force not perpendicular to the motion will do work: no work N does no work positive T does positive work f does negative work mg does negative work 1) one force 2) two forces 3) three forces 4) four forces 5) no forces are doing work A box is being pulled up a rough incline by a rope connected to a pulley. How many forces are doing work on the box?

Work Done by a Variable Force If the force changes with the displacement, W=Fd is no longer valid –Calculus is needed to calculate this directly However, If force is plotted vs displacement the work can be graphically found as the area under the curve. Constant Force Changing Force

Work Done by a Variable Force Varying Force of a Spring Recall the spring force is F s = kx So, the work is Calculate the work

Work Overview

ConcepTest 7.11a ConcepTest 7.11a Time for Work I 1) Mike 2) Joe 3) both did the same work Mike applied 10 N of force over 3 m in 10 seconds. Joe applied the same force over the same distance in 1 minute. Who did more work?

same forcesame displacementsame amount of workTime does not matter for determining the work done Both exerted the same force over the same displacement. Therefore, both did the same amount of work. Time does not matter for determining the work done. ConcepTest 7.11a ConcepTest 7.11a Time for Work I 1) Mike 2) Joe 3) both did the same work Mike applied 10 N of force over 3 m in 10 seconds. Joe applied the same force over the same distance in 1 minute. Who did more work?

Review Work is dependent on  force and displacement. The amount of work that is done in moving a 50N box a distance of 30 m is the ______ whether it takes 1 minute, 1 hour, or 1 day. Power is different. It takes ______ power to move that 50 N box 30 meters in 1 minute than it takes to move it the same distance in 1 hour. When you’re talking about power… TIME MATTERS! same more

Power Power is the rate at which work is done. Since work is equal to force x displacement: 

Power Units Derived Units: Fundamental Units: 1 kilowatt = 1 kW = 1000 watts 1 kWh (kilowatt hour) = 3.60 x 10 6 J 1 horsepower (hp) = W

Power Derivation P=Fv

Mike performed 5 J of work in 10 secs. Joe did 3 J of work in 5 secs. Who produced the greater power? 1) Mike produced more power 2) Joe produced more power 3) both produced the same amount of power ConcepTest 7.11b ConcepTest 7.11b Time for Work II

Mike performed 5 J of work in 10 secs. Joe did 3 J of work in 5 secs. Who produced the greater power? 1) Mike produced more power 2) Joe produced more power 3) both produced the same amount of power Mike produced 0.5 W Joe produced 0.6 W Since power = work / time, we see that Mike produced 0.5 W and Joe produced 0.6 W of power. Thus, even though Mike did more work, he required twice the time to do the work, and therefore his power output was lower. ConcepTest 7.11b ConcepTest 7.11b Time for Work II

Power Problems A small motor does 4000J of work in 20 seconds. What is the power of the motor in watts? W = 4000 J T = 20 s P = ?

Power Problems An electric motor lifts an elevator that weighs 1.2 x 10 4 N a distance of 9.00 meters in 15.0 s. What is the power of the motor in kilowatts? F = 1.2 x 10 4 N d = 9.00 m t = 15.0 s P = ? (kW)

Engine #1 produces twice the power of engine #2. Can we conclude that engine #1 does twice as much work as engine #2? 1) yes 2) no ConcepTest 7.11c ConcepTest 7.11c Power

Engine #1 produces twice the power of engine #2. Can we conclude that engine #1 does twice as much work as engine #2? 1) yes 2) no No!! We cannot conclude anything about how much work each engine does. work will depend upon how much time is used No!! We cannot conclude anything about how much work each engine does. Given the power output, the work will depend upon how much time is used. For example, engine #1 may do the same amount of work as engine #2, but in half the time. ConcepTest 7.11c ConcepTest 7.11c Power

Efficiency (η) In an ideal world, work out equals work in. However, in the real world work is lost to friction, heat and other inefficiencies (bureaucracy). Efficiency (η) measures how much work is produced for the work inputted the ratio of useful work actual work η greek letter ‘eta’