ocw skaa1213 10 work and energy 2

7/30/2019 OCW SKAA1213 10 Work and Energy 2

1/34

SKAA1213 EngineeringMechanics

TOPIC10

Lecturers:

Rosli AnanDr. Mohd Yunus IshakDr. Tan Cher Siang


2/34

TheWorkofaForce

Princip eo Wor an Energy

ConservativeForcesandPotentialEnergy ConservationofEnergy


3/34

itundergoes

adisplacement

(dr)

in

the

.

drFU

Fsin Fsin

rr

Fcos Fcos

dr

r r'


4/34

displacementalong

its

path

from

r1 to

r2 (or

1 2 ,

integration.

,

F(s),

11

cos.21sr

dsFdrFU


5/34

Consideraparticle

which

moves

up

along

the

path

kdzjdyidxjWdrFU

r

r 21 )

~~~

).(

~

(.

2

1

yyWWdyy

y 12 )(

2

1s2

y

y21 drs1 y2

F=-Wjx

y1


6/34

Magnitudeof

force

in

alinear

elastic

spring

positionisFs =ks

The work is ne ative since F acts in the

oppositesensetods.

22 ssUnstretched

22

21

11

11 sss ss s

s

ds

22 kF


7/34

Work: )(cos 1221 ssFU

Workof

aweight: yWU 21

22

11

22


8/34

moves2m to

the

right.

Determine

the

work

.2 m

P

100 N


9/34

Looking at the right pulley:

m

P

NP 50

2

100

100 N


10/34

Looking at the bottom pulley,because there are 2 cables, the

m

P

distance moved by the 100 N is:

m2

100 NJFsU 100)1)(100(

2


11/34

inertialcoordinate

system

Forthe articleinthetan entialdirection2

1

2

1

dvmvdsFv

v

s

s

t tt maF

21

22

22

2

1

mvmvdsFs

st

21

2221

11mvmvU


12/34

2211 TUT 2

112

1mvT 222

2

1mvT

Definition:

alltheforcesactingontheparticle asitmovesfrom

initialtoitsfinalpositionisequaltotheparticlesfinal

kineticenergy


13/34

.

Whenan

applied

force

P just

balances

the

,

aconstantvelocityv ismaintained:

22 1122

k

v v

P PW

dr

s1 s2N

F=kN


14/34

Principleof

Work

and

Energy: 2211 TUT

Kineticenergy: 2 mv

Workoffriction: 2222mvsNPsmv k

Workofspring:

2

1

2

2212

1

2

1ksksU


15/34

inclinedroad

at

aspeed

of

6m/s.

if

the

driver

jams

onthebrakes,causinghiswheelstolock,determine

howfars histiresskidontheroad.Thecoefficientof

thekinetic

friction

between

the

wheels

and

the

road

sk = .


16/34

Work(FreeBodyDiagram)NA doesnoworkasandtheweight1500kg,isdisplaceds

sin15.Applyingequationofequilibriumnormaltothe

road,

NN

NF

A

An

6.14213

015cos)81.9(1500;;0

NNF Akk 1.4264)6.14213(3.0


17/34

PrincipleofWorkandEnergy

TUT

222111mvUUmv kW

01.426415sin14715615001 2 ss

m27.592

s


18/34

ConservativeForcesandPotential

Energy

Definedby

the

work

done

in

moving

aparticle

thepath followedbytheparticle

Energyisdefinedasthecapacityfordoingwork

particle


19/34


Energy

Whenaparticle

is

located

adistance

yabove a

datum,

the

weightW haspositivegravitationalpotentialenergyV

Ifyispositiveupward,gravitationalpotentialenergyofthe

particle

of

weight

W

is: Vg =+Wy

WyVg y

+yW

Datum-y Vg =0

W

g =- y


20/34


Energy

Whenan

elastic

spring

is

elongatedorcompressed

position:s =0

fromunstretchedposition,

theelasticpotentialenergyk

e

2

2

1ksVe

+s

k

2

2

1ksVe

-s

21ksV

k2


21/34

interms

of

the

difference

in

their

potential

energies

Ifonl conservative orces area liedtothebod whenmovingfromstatetostate,wehave

conservationofenergy(orconservationof

mechanicalenergy)


22/34

Gravitationalpotential

energy: WyVg

Elasticpotential

energy

:

21ksVe


23/34

floorto

the

twelve

floor,

with

the

height

for

.

potentialenergyofthelift?


24/34

Usethe

eight

floor

as

datum:

WhV

JV

mN

00018

)12)(1500(

g


25/34

.

up,abox

is

left

at

each

floor

or

the

first

box

at

.

heightforeachstoreyis3.5m andthelift

.

liftingtheliftandtheboxes.


26/34

, ,

theelevation

drop

of

400

m.

Determine

its


27/34

platformat

A.

The

initial

downward

speed

is

2m/s.

Thestiffnessoftheelasticcordisk=5kN/m.The

lengthofthecordislo.BytakingB asthedatumand

neglecting

the

size

of

Johnson,

200m

A

B

FIGUREP3


28/34

a Whatisthe ravitational otentialener V ofJohnson

atpositionA andB?

b) Calculatetheelasticpotentialenergy,Ve oftheelastic

cor w en o nson sa epos on . ve eanswer

intermoflo.

c Determinethe

re uired

un

stretched

len th

of

the

cord

sothatJohnsonstopsmomentarilyjustabovethesurface

ofthewater.


29/34

andis

connected

to

a25

kg

mass

located

on

an

inclinedroughsurfaceatC.Bothmassesare

connectedbyaninelasticweightlessropepassing

through

a

frictionless

pulley

at

B.

The

25

kg

mass

is

n a y e npos ona an s enre ease o

slidedowntheinclinedsurface.Thecoefficientof

,s

,k

massesand

the

rough

surface

is

0.25

and

0.20

respectively.


30/34

a Showthatbothmasses will move as soon as the 25

kg mass isreleased.

b) Determinetheaccelerationofbothmasses.

c) Usingprincipleofworkandenergy,determinethe

distancetravelledbythe5kgmassbeforecomingtoa

sto

afterthe

25

k

mass

comes

to

asto

at

D.

5kg

AB

C

12 D

5


31/34

alongarough

horizontal

surface

AB,

and

then

up

an

inclinedroughsurfaceuntiltheblockstopsatCas

showninFigureP5(a).TheforceFremainshorizontal

as

it

pushes

the

block

up

the

inclined

plane.

The

va ueo ecoe c en o ne c r c on k

betweentheblockandboththehorizontaland

. .

showsthe

atand

vtgraphs

of

the

block

as

it

is

in

motionfromAtoC.


32/34

A B

CF

a(m/s2)

3

v(m/s)

t(s)B C

1.2

v

FIGUREP5(b)

2

t(s)tB tC

FIGUREP5(c)


33/34

a Determinethean leoftheinclined lane.

b) Using

the

principle

of

work

and

energy,

determine:i. thevelocityoftheblockasitpassesbypointB(vB)giventhat

e s ance rom o s m,

ii. thedistancefromBtoC.

c) Validateyour

answers

in

part

(b)

by

using

rectilinear

kinematics.


34/34

TheEnd

ocw skaa1213 10 work and energy 2

Documents