Work is only done by a force on anWork is only done by a force on anobject if the force causes the objectobject if the force causes the objectto move in the direction of the force.to move in the direction of the force.

Objects that are at rest mayObjects that are at rest mayhave many forces acting on them,have many forces acting on them,

but no work is donebut no work is doneif there is no movement.if there is no movement.

Work,Work,by definition, is

the product of the the product of the forceforce exerted on exerted onan object and the an object and the distancedistance the object the objectmoves in the direction of the force.moves in the direction of the force.

WW == F·dF·dWork is a Work is a scalarscalar quantity. quantity.

The SI unit of workis the joule,

named in honor ofJames Prescott Joule.

One joule, J, of workOne joule, J, of workis the work done whenis the work done when1.0 N of force is applied1.0 N of force is applied

through a distance of 1.0 m.through a distance of 1.0 m.

Graphically, work isGraphically, work isthe area under athe area under a

““Force vs. Displacement” graph.Force vs. Displacement” graph.

displacement, mdisplacement, m

If the force and displacement are notin the exact same direction, then

work = Fd(cos),where is the angle between the forcedirection and displacement direction.

F =40 N

d = 3.0 m

The work done in moving the block 3.0 mThe work done in moving the block 3.0 mto the right by the 40 N force at an angleto the right by the 40 N force at an angle

of 35 to the horizontal is ...of 35 to the horizontal is ...

35

W = Fd(cos W = Fd(cos ) = (40N)(3.0 m)(cos 35) = 98 J) = (40N)(3.0 m)(cos 35) = 98 J

Power,Power,by definition, isby definition, is

the the time ratetime rate of doing of doing workwork;;or the or the time rate transfertime rate transfer of of energyenergy..

PP == WW // ttPower is a scalar quantity.

The SI unit of poweris the watt,

named in honor ofJames Watt.

One watt, W, of powerOne watt, W, of poweris the power achievedis the power achieved

when when 1.0 J of work1.0 J of work is done or is done or1.0 J of energy is transferred1.0 J of energy is transferred

in a in a time of 1.0 stime of 1.0 s..

Simple MachinesSimple Machines

““a device that is used to manipulate the a device that is used to manipulate the amountamount

and/or direction of force when work is and/or direction of force when work is done”done”

A common misconception is that A common misconception is that machines are used to do a task with less machines are used to do a task with less

work than would be needed to do the work than would be needed to do the task without the machine. They do not! task without the machine. They do not! In fact (mainly because of friction), you In fact (mainly because of friction), you actually do more work with a machine actually do more work with a machine than without it (for the same task). than without it (for the same task).

The major benefit of a machine is thatThe major benefit of a machine is thatthe work can be done with less applied the work can be done with less applied

force, but at the expense of the distance force, but at the expense of the distance through which the force must be applied. through which the force must be applied.

Work = Force x DistanceWork = Force x Distance

“large force x small distance = small force x large distance”

For example, 1000 J of work is neededto lift 1000 N onto a table 1.0 m high.If the object were pushed up a 4.0 m

ramp (inclined plane), a minimum of 250 Nof force would be needed (250 N x 4.0 m

= 1000 J). In reality, friction betweenthe object and the ramp would make the

necessary force greater than 250 N.

If a 10 m ramp were used, a minimumof 100 N of force would be needed.

The greater the distance, thesmaller the necessary force.

Efficiency of a MachineEfficiency of a Machine

““the ratio of useful workthe ratio of useful workoutput to useful work input”output to useful work input”

It is impossible to get as much “useful” It is impossible to get as much “useful” workwork

or energy out of a machine as you put into or energy out of a machine as you put into it.it.

Consider the lever, pulley, and inclined plane as Consider the lever, pulley, and inclined plane as examples of simple machines:examples of simple machines:

Inclined planeInclined plane: decreases: decreasesnecessary force becausenecessary force becauseof an increase in distanceof an increase in distance

Lever: used to decreaseforce by increasing distance;force by increasing distance;changes direction of force (link)changes direction of force (link)

Pulley: used to decrease force by increasing Pulley: used to decrease force by increasing distance; distance; may change direction of force may change direction of force (link)(link)

Click here to performan interesting activityon simple machines.

Sample Inclined Plane

• A person must lift a 1000N box into the back of a truck which is 3 m high. The person has a 5 m ramp to use what work must be done to lift the box? What effort force will be used with the ramp?

1000 N

Click here to explore energy, work, and theClick here to explore energy, work, and theWork-Energy Theorem in more depth.Work-Energy Theorem in more depth.

EnergyEnergythe ability (capacity) to do workthe ability (capacity) to do work

Energy comes in many forms:Energy comes in many forms:mechanical, electrical , magnetic, solar,mechanical, electrical , magnetic, solar,

thermal, chemical, etc...thermal, chemical, etc...

The SI unit of energy is the The SI unit of energy is the joulejoule..

Energy, like work and power, is a Energy, like work and power, is a scalarscalar..

Kinetic EnergyKinetic Energyenergy of motion

All moving objects thatAll moving objects thathave mass have kinetic energy.have mass have kinetic energy.

KE = 1/2 mvKE = 1/2 mv22

mm - mass of the object in - mass of the object in kgkgvv - speed of the object in - speed of the object in m/sm/sKEKE - the kinetic energy in - the kinetic energy in JJ

Work-Energy TheoremWork-Energy Theoremthe net work done on an object is

equal to its change in kinetic energy

W KEnet

Learn more about theLearn more about theWork-Energy TheoremWork-Energy Theorem

here and here.

A net force causesA net force causesan object to change its KE becausean object to change its KE because

a net force causes an object to accelerate,a net force causes an object to accelerate,and acceleration means a change in velocity,and acceleration means a change in velocity,

and if velocity changes, KE changes.and if velocity changes, KE changes.

Potential EnergyPotential Energyenergy of position or conditionenergy of position or condition

gravitational potential energygravitational potential energy

UUgg = ma = magghh mm - mass of object in - mass of object in kg kg aagg - acceleration of gravity in - acceleration of gravity in m/sm/s22

h h - height of object, in - height of object, in mmUUgg – gravitational potential energy in – gravitational potential energy in JJ

Potential EnergyPotential Energyenergy of position or conditionenergy of position or condition

elastic potential energyelastic potential energy

PEPEee = ½ = ½ kxkx22

kk – elastic constant in – elastic constant in N/mN/m xx - elongation or compression in - elongation or compression in mm PEPEee – elastic potential energy in – elastic potential energy in JJ

Click Click here to investigate elastic constants.

Law of Conservation of EnergyLaw of Conservation of Energy““Energy can be neither created nor destroyed.Energy can be neither created nor destroyed.

It may only change forms.”It may only change forms.”

all types of energy before the event all types of energy before the event = = all types of energy after the event all types of energy after the event

Examples:Examples:•A dropped object loses gravitational PE as it gains KE.A dropped object loses gravitational PE as it gains KE.•A block slides across the floor and comes to a stop.A block slides across the floor and comes to a stop.•A compressed spring shoots a ball into the air.A compressed spring shoots a ball into the air.