Work and energy

PHYSICS

PROJECT WORK

made by- Archana pal class-9 roll no.7

Physicist’s definition Physicist’s definition of “workof “work””

dist

Work = F x dist∥

A scalar

(not a vector)

dist∥

Atlas holds up the Atlas holds up the EarthEarth

But he doesn’t move, dist∥ = 0

Work= Fx dist∥ = 0

He doesn’t do any work!

Garcon does work whenGarcon does work whenhe picks up the trayhe picks up the tray

but not while hecarries it around

the room

dist is not zero,but dist∥ is 0

Why this definition?Why this definition?

Newton’s 2nd law: F=m a

Definition of work+ a little calculus

Work= change in ½mv2

A scalar

equation

A vector

equation

This scalar quantity is givena special name: kinetic energy

Work = change Work = change in KEin KE

This is called:

the Work-Energy Theorem

Work done by Work done by gravitygravity

start

end

dist dist∥

W=mg

Work = F x dist∥

= -mg x change in height= -change in mg h

change in vertical height

Gravitational Potential Gravitational Potential EnergyEnergy

Workgrav = -change in mgh

This is called:“Gravitational Potential Energy” (or PEgrav)

Workgrav = -change in PEgravchange in PEgrav = -Workgrav

If gravity is the only force If gravity is the only force doing work….doing work….

-change in mgh = change in ½ mv2

0 = change in mgh + change in ½ mv2

change in (mgh + ½ mv2) = 0

mgh + ½ mv2 = constant

Work-energy theorem:

Conservation of energyConservation of energy

mgh + ½ mv2 = constant

GravitationalPotential energy

Kinetic energy

If gravity is the only force that does work:

PE + KE = constant

Energy is conserved

Free fallFree fall (reminder)(reminder)

V0 = 0

t = 0s

V1 = 10m/s

t = 1s

V2 = 20m/s

t = 2s

V3 = 30m/s

t = 3s

V4 = 40m/s

t = 4s

75m

60m

35m

0m

height

80m

m=1kg free falls from m=1kg free falls from 80m80m

V0 = 0 h0=80m

t = 0s

V1 = 10m/s; h1=75m

t = 1s

V2 = 20m/s; h2=60m 600J 200J 800J

t = 2s

V3 = 30m/s; h3=35m 350J 450J 800J

t = 3s

V4 = 40m/s; h4=0 0 800J 800J

t = 4s

mgh ½ mv2 sum

800J 0 800J

750J 50J 800J

pendulumpendulum

W=mg

T

Two forces: T and W

T is always ┴ to the motion

(& does no work)

Pendulum conserves Pendulum conserves energyenergy

hmax

E=mghmaxE=mghmax

E=1/2 m(vmax)2

Roller coasterRoller coaster

Work done by a springWork done by a spring

RelaxedPosition

F=0

Fx

I compressthe spring

(I do + work;spring does

-work)

Work done by spring = - change in ½ kx2

Spring Potential Spring Potential EnergyEnergy

Workspring = -change in ½ kx2

This is the:“Spring’s Potential Energy” (or PEspring)

Workspring = -change in PEspring

change in PEspring = -Workspring

If spring is the only force If spring is the only force doing work….doing work….

-change in ½ kx2 = change in ½ mv2

0 = change in ½ kx2 + change in ½ mv2

change in ( ½ kx2 + ½ mv2) = 0

½ kx2 + ½ mv2 = constant

Work-energy theorem:

Conservation of energyConservation of energysprings & gravitysprings & gravity

mgh + ½ kx2 + ½ mv2 = constant

Gravitationalpotential energy

Kinetic energy

If elastic force & gravity are the only force doing work:

PEgrav + PEspring + KE = constant

Energy is conserved

springpotential energy

Two types of forces:Two types of forces:

“Conservative” forcesforces that do + & – work

•Gravity

•Elastic (springs, etc)

•Electrical forces

•…

“Dissipative” forcesforces that only do – work

•Friction

•Viscosity

•….

-work change in PE

-work heat(no potential energy.)

(-)Work done by (-)Work done by frictionfrictionheatheat

Work-energy theoremWork-energy theorem(all forces)(all forces)

Workfric = change in (PE+KE)Work done

dissipative

Forces(always -)

Kinetic energy

-Workfric = change in heat energy

potential energyFrom all

Conservative forces

-change in Heat Energy = change in (PE+KE)

Workfric = -change in heat energy

Work – Energy TheoremWork – Energy Theorem(all forces)(all forces)

0 = change in Heat Energy + change in (PE+KE)

0 = change in (Heat Energy+PE+KE)

Heat Energy + PE + KE = constant

Law of Conservation of Energy

Energy conversion while Energy conversion while skiingskiing

Friction: energy gets converted to heat

Potential energy

Potential energykinetic energy

PowerPower

Rate of using energy:amout of energy

elapsed time

Units:Joule

second 1 = 1 Watt

Power =

A 100 W light bulbconsumes 100 J of

electrical energy eachsecond to produce light

Other unitsOther units

Over a full day, a work-horse can

have an average work output of more than 750 Joules each

second

1 Horsepower = 750 Watts

Kilowatt hoursKilowatt hours

energytimePower = energy = power x time

power unit x time unit = energy unit

Elec companies use:Kilowatts(103 W)

hours(3600 s)

1 kilowatt-hour = 1kW-hr

= 103 W x 3.6x103

s = 3.6x106 WsJ

HECO charges us about 15 cents /kW-hr

x

Multiple choice questionsMultiple choice questions1)The work done by a weight of 1kg mass when it 1)The work done by a weight of 1kg mass when it moves up through 1m is:moves up through 1m is:

(a)10 joule (a)10 joule (b)-10 joule(b)-10 joule

(c)0.1 joule (c)0.1 joule (d)-0.1 joule(d)-0.1 joule

2)A stone is tied to a string and then whirled in a 2)A stone is tied to a string and then whirled in a circle. The work done on it by the stringcircle. The work done on it by the string is: is:

(a)Positive (a)Positive (b)negative(b)negative

(c)zero (c)zero (d)undefined (d)undefined

ans ans -1)--1)-10 joule 10 joule 2)2)zerozero

3)3)When a force retards the motion of a body, the When a force retards the motion of a body, the work done is:work done is:

(a)positive (a)positive (b)zero (b)zero

(c)negative (c)negative (d)undefined (d)undefined

4)The speed of a particle is doubled. Its 4)The speed of a particle is doubled. Its kinetic energy:kinetic energy:(a)remains the same (a)remains the same (b)becomes two (b)becomes two timestimes

(c)becomes half (c)becomes half (d)becomes four (d)becomes four timestimes

ans-3) ans-3)negative negative 4) 4)becomes becomes four timesfour times

5)5)A body of mass 5kg falls through a height of 5m. The A body of mass 5kg falls through a height of 5m. The loss in potential energy of the mass is:loss in potential energy of the mass is:

(a)(a)250 j 250 j (b)25 j(b)25 j

(c)2.5 kj (c)2.5 kj (d)50 j(d)50 j

6)Potential energy of a person is minimum when:6)Potential energy of a person is minimum when:

(a)person is standing (a)person is standing (b)person is sitting in a (b)person is sitting in a chairchair

(c)person is sitting on the ground (c)person is sitting on the ground (d)person is lying (d)person is lying on the groundon the ground

ans-5) ans-5)250 j 250 j 6) 6) person is lying on the person is lying on the ground ground

7)An electric motor creates a tension of 4500N in 7)An electric motor creates a tension of 4500N in hoisting a cable and reels it at a rate of 2m/s.The hoisting a cable and reels it at a rate of 2m/s.The power of the motor is:power of the motor is:

(a)25kW (a)25kW (b)9kW(b)9kW

(c)225kW (c)225kW (d)90kW(d)90kW

8)A engine develops a power of 10kW.How much 8)A engine develops a power of 10kW.How much time will it take to lift a mass of 200 kg to a height time will it take to lift a mass of 200 kg to a height of 40m?(g=10m/sof 40m?(g=10m/s):):

(a)4s (a)4s (b)5s(b)5s

(c)8s (c)8s (d)10s(d)10s

ans- 7) ans- 7)9kW9kW 8) 8)8s8s

9)The power (p) is expressed as:9)The power (p) is expressed as:

(a)p=work* distance (a)p=work* distance (b)p=force*distance(b)p=force*distance

(c)p=force* velocity (c)p=force* velocity (d)p=work/ time(d)p=work/ time

10)1 kWh is equal to:10)1 kWh is equal to:

(a)3.6j (a)3.6j (b)3.6kj(b)3.6kj

(c)3.6*10(c)3.6*1066 j j (d)36j (d)36j

ans-9)ans-9)p=work/time p=work/time 10) 10)3.6*103.6*1066j j