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 Objects that are at rest may have many rest may have many forces acting on them, forces acting on them, but no work is done if but no work is done if there is no movement.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 that quantity thatmay be positive or negative.may be positive or negative.

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

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, is a scalar, andEnergy, like work, is a scalar, andmay be positive or negative.may be positive or negative.

Kinetic EnergyKinetic Energyenergy of motionAll moving objects thatAll moving objects that

have 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 kgkg vv – 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 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

PEPEgg = mgh = mgh mm – mass of object in – mass of object in kg kg g g – acceleration of gravity in – acceleration of gravity in m/sm/s22

h h – height of object, in – height of object, in mm,, from some arbitrary reference pointfrom some arbitrary reference pointPE PE – 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 x x – elongation– elongation or compression in or compression in mm PEPEee – elastic potential energy in – elastic potential energy in JJ

Click Click here to investigate elastic constants. 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.

Energy (and work) may also be specified in Energy (and work) may also be specified in units of units of caloriescalories. This unit is commonly used . This unit is commonly used when referring to thermal (heat) energy.when referring to thermal (heat) energy.

By definition, a calorie is the amount of energy By definition, a calorie is the amount of energy needed to raise the temperature of 1.0 gram of needed to raise the temperature of 1.0 gram of water (= 1.0 mL) at standard atmospheric water (= 1.0 mL) at standard atmospheric pressure 1pressure 1°° C. C.

The food calorie, which is commonly The food calorie, which is commonly capitalized (Calorie) is equal to 1000 calories.capitalized (Calorie) is equal to 1000 calories.

1 cal = 4.184 J1 cal = 4.184 J 1 Cal = 4184 J1 Cal = 4184 J

http://science.howstuffworks.com/life/human-biology/calorie.htm

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 // tt

Power 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 amounta device that is used to manipulate the amountand/or direction of force when work is done”and/or direction of force when work is done”

A common misconception is that machines A common misconception is that machines are used to do a task with are used to do a task with lessless workwork than than

would be needed to do the task without the would be needed to do the task without the machine. They do not! In fact (mainly because machine. They do not! In fact (mainly because

of friction), you actually do of friction), you actually do more workmore work with a with a machine than without it (for the same task). machine 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 needed to 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 N of force would be needed (250 N x 4.0 m = 1000 J). In

reality, friction between the object and the ramp would make the necessary force greater than 250 N.

A simple task illustrating this idea is to have students lift a wooden block from the floor to the table (desk) top and calculate the work done. Then have them

slide the block up a ramp to the top of the table (desk) and again calculate the work done.

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” workIt is impossible to get as much “useful” workor energy out of a machine as you put into it.or energy out of a machine as you put into it.

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

Inclined plane: decreases: decreasesnecessary force becausenecessary force becauseof an increase in distance (link)of an increase in distance (link)

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

Click here to performan interesting activityon simple machines.

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.

Click here to explore energy and Click here to explore energy and its conservation in more detail.its conservation in more detail.