w23 2.10 work-energy-power-and-efficiency module & exercise

7/25/2019 W23 2.10 Work-Energy-Power-And-Efficiency Module & Exercise

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Work(W), Energy (E) and Power (P) and Efficiency

(a) The Definition and S.I. unit of Work

Work is defined as the product of the applied force ,Fon the object and its displacement, s in the directionof the net force.

W = Fs where W = Work, F = force and s = displacement

The S.I. unit for Work is Joule()

I J = 1 mWork is a scalar !uantit".

Work done also can #et from the #raphforce$displacement.

Example 1

% horse pulls a carria#e with a total force &' for('m . )alculate the work done on the carria#e b" thehorse.

Solution

Example 2

Fi#ure shows an ice cube is pulled b" a force *'%t an an#le of +'oto the surface of the smooth

surface.

)alculate the done on the ice cube

Solution

Example 3

Fi#ure shows a #raph force$displacement of sprin#which is compressed b" a force increases from ' to 1'' for '.1( m.

)alculate the work done on the sprin#.

Solution

(!) The Definition and S.I. unit of Energy(E)-ner#" is the capacit" or abilit" of a s"stem to do

work.Without ener#" the work cannot done.When work is done , ener#" is transferred to theobject or chan#e into a different form.-ner#" can eist in /arious form 0 potentialener#"2ra/itational 3otential -ner#", -lastic3otential -ner#", -lectrical 3otential -ner#" , %tomic3otential -ner#" 4 kinetic ener#", mechanical ener#",heat ener#", sound ener#", electrical ener#" andnuclear ener#".

The S.I. of ener#" is Joule J4.-ner#" is scalar !uantit".

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"ESS#$ %.&'nderstanding work, energy,ower and efficiency.


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Example 4

% student lifts a brick of mass '.5 k# from the floor tothe table top of hei#ht 1.* m. 6eterminea4 work done on the brickb4 ener#" is used to lift the brick.

Solution

*inetic Energy ( Ek)7inetic ener#" is the ener#" possessed b" a mo/in#object.

Ek= + -% = ass ,

- = -eocity

Example 5

% bullet of mass '.'* k# mo/es at a /elocit" 1(' ms$1

What is the kinetic ener#" of the bullet

Solution

Example 6

% mo/in# lorr" of mass 5'' k# has an ener#" of

1+' k J. What is the /elocit" of the lorr".

Solution

/ra-itationa Potentia Energy ( Eg)

The 2ra/itational potential ener#" of an" object is the

ener#" stored in the object because of its hei#ht

abo/e the earth8s surface

Eg= g h

= ass

g = acceeration due to gra-ity

h = heightExample 7

% ball of mass '.* k# is thrown to a hei#ht 1( m. 9owmuch #ra/itational potential ener#" does the ball#ain

Solution

Example 8

% bo" of mass (' k# sittin# on the top end of an

inclined slidin# board has an ener#" of * kJ. What is

the hei#ht the inclined slidin# board from the #round

Solution

Princie of 0onser-ation of Energy-ner#" cannot be created or destro"ed.-ner#" can be transformed from one kind to another,but the total ener#" in a s"stem sta"s the same or is

conser/ed .

Example 9

% stone is thrown with a /elocit" *' ms $1.What is the maimum hei#ht can be reached b" thestone

Solution

Example 10

Fi#ure shows a ball of mass '.( k# slides from rest atpoint % throu#h a frictionless rail hei#ht '.5 m down .

What is the /elocit" of the ball at the bottom of therail.

Solution

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Example 11

Fi#ure shows a trolle" is released from a rest atpoint : throu#h a frictionless inclined plane.

What is the /elocit" of the trolle" at point ;.

Solution

Example 12

Fi#ure shows a ball mo/es on a frictionless cur/etrack with a /elocit" + ms$1at point %.

What is the /elocit" of the ball when it reaches atpoint


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Example 15

% crane lifts a load of &'' k# to a hei#ht of 1'' m in*' s. If the power input is *( ''' W, calculate

a4 the useful ener#" outputb4 the ener#" inputc4 the efficienc" of the crane.

Solution

(e) 2reciating the iortance of a3iising the

efficiency of de-ices.

-ner#" conser/ation demands that the total

ener#" output of a machine or de/ice must e!ual

its ener#" input.

9owe/er , when we measure the ener#" output as

work done on the load b" a machine or de/ice, we

find it is less than the ener#" input.

It is because the machine or de/ice also does

work a#ainst frictional forces and sometimes does

work in mo/in# itself.

The work done a#ainst friction con/erts inputener#" into wasted heat ener#" and a little noise

ener#".

So the ener#" e!uation now looks like this>

-ner#" = useful ener#" ? wasted ener#"

Input output output

@aimisin# the efficienc" of machine or de/ice

makes the best use of the input ener#" and

reduces wasted ener#" output.

@aimisin# the efficienc" of machine and de/ice

can helps

a4 to conser/e resources since fossil fuels

such as coal, petroleum and natural #as are

non$renewable resources

b4 to protect the en/ironment from

deforestation ,oil spills and radioacti/e

wastes

c4 to reduce the emission of air pollutants and

#reenhouse #ases from power stations

d4 to reduce the ener#" bills

The followin# are se/eral wa"s of increasin#the efficienc" of machines and de/ices>

Machines:

@o/in# surfaces are made as smooth as3ossible.Aubricants such as oil and silicone are used toseparate surfaces.Bollers and ball bearin#s are used to separaterotatin# ales from their mountin#s.)ushions of air are used as elastic lubricant.@achines which mo/e throu#h fluids are made

streamlined in shape to reduce the frictionaldra#.

Heat engines:9eat en#ine must be desi#ned with capabilit" todo a #reater amount of mechanical work whiledischar#in# waste heat at a lower temperature.

Electrical devices:i4 Aamp> % fluorescent lamp is more efficient than a

filament li#ht bulb.

Cse a lamp with a reflector so that theillumination can directed to specific area.

% li#htin# of a room should depend on thesiDe of the room.

ii4 Water heater When ha/in# a shower durin# a hot weather, a lower temperature is needediii4 Befri#erator The doors of the refri#erator must alwa"s

be shut ti#ht. Thermostat should be used in refri#erator

to control the temperature

The power of refri#erator needed dependon the siDe of the famil".

Another ways:Bec"clin# also conser/es ener#" resources.Bec"clin# sa/es ener#" because we do notha/e to make new bottles, papers e.t.c.

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& Which of the followin# is true

2 Work is a /ector !uantit"4 Work and ener#" has the same unit0 Work is the product of force and distance

% 1 J is e!ui/alent to

2 1 k# m 4 1 s

0 1 k# s D 1 m

5 )hoose the fi#ure which shows the studentdoin# the maimum work.

6 %n object of mass '.& k# is pulled b" a force of*' o/er a distance of 1.( m on horiDontalsurface. The an#le between the force to thehoriDontal surface is +'oto the horiDontal. Whatis the work done on the object

2 *+ J 4 *' J0 1( J D 1' J

E ( J

7 Fi#ure shows an object of mass 1.( k# lifted tothe top of a rou#h rail with a force of 5' .

What is the work done to lift the object to the topof the rou#h rail.

2 &' J 4 *&' J0 E*' J D &'' JE (+' m

8 %n object of mass & k# mo/es at a /elocit"*.( ms$1. What is the kinetic ener#" of the object.

2 (.' J 4 1'.' J0 1*.( J D *(.' JE E'.' J

9 % mo/in# car of mass 5'' k# has an ener#" of

*(' k J. What is the /elocit" of the car.

2 * ms$1 4 1' ms$1

0 *' ms$1 D *( ms$1

E E' ms$1

: The fi#ure shows a student runnin# up astaircase at a constant speed.

Which ph"sical !uantit" increases while thestudent is runnin# up the staircase

2 Inertia of the student4 @omentum of the student0 7inetic ener#" of the studentD 2ra/itational potential ener#" of the

student

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TT#;I2" %.&'


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< % bo" of wei#ht of ('' walkin# up a staircaseconsistin# of *' steps. -ach step is &' cmhei#ht. 9ow much #ra/itational potential doeshe #ain

2 &' J 4 &'' J0 &''' J D &'''' JE &''''' J

&' Which of the followin# is true re#ardin# the3rinciple of )onser/ation of -ner#"

2 -ner#" can be created or destro"ed4 Total ener#" in a s"stem sta"s the same0 -ner#" cannot be transformed from one

kind to another

&& Fi#ure shows a pendulum oscillatin# betweenpositions 3 and S.

What is the position of the bob possess both ofkinetic ener#" and #ra/itational potential

ener#"

2 3 4 0 B D S

&% Fi#ure shows a pendulum oscillatin# betweenpositions : and G.

Which one of the followin# #raphs is truere#ardin# the oscillation of the pendulum

&5 % mo/in# lorr" has kinetic ener#". When thelorr" stops ,its kinetic ener#" is Dero. This isbecause the kinetic ener#"

2 is destro"ed4 is used to stop the lorr"

0 con/erted to #ra/itational potential ener#"D con/erted to heat ener#" as result offriction

&6 The fi#ure shows the path of a ball rollin# downa smooth slope.

The ball has the #reatest chan#e in #ra/itationalpotential ener#" between

2 3 and 4 and B0 3 and S D B and T

&7 Fi#ure shows a ball is released from a rest atpoint % of a frictionless track.

Which of the followin# is true2 The total of ener#" at all the points is same

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4 The /elocit" of the ball at point % is sameas the /elocit" of the ball at point

0 The kinetic ener#" of the ball at point < issame as the kinetic ener#" of the ball atpoint )

D The #ra/itational potential ener#" of the

ball at point % is same as the #ra/itationalpotential ener#" of the ball at point -

&8 Fi#ure shows a trolle" is released from a rest atthe top end of a frictionless cur/e track.

What is the /elocit" of the trolle" when it reaches

the bottom of the track

2 ( ms$1 4 H ms$1

0 5 ms$1 D ms$1

E 1' ms$1

&9 Fi#ure shows a simple pendulum has a 1('$#bob at the end of a strin# is released from astate of rest at point %.

6etermine the /elocit" of the bob at the lowestpoint


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What is the power of the motor

2 & W 4 1' W0 1+ W D & ' WE 1+' W

%5 % motor can raise a mass of 1' k# with auniform /elocit" *' ms$1. What is the power ofthe motor

2 * W 4 *'' W0 * ''' W D & ''' WE 5 ''' W

%6 Fi#ure shows a worker pullin# a borrow up aramp.

What is the efficienc" of the ramp

2 *( 4 &' 0 (' D H( E 5'

%7 % pump lifts *'' k# water per minute throu#h a/ertical hei#ht of 1( m. )alculate the powerinput ratin# of the pump if it is +( efficient

2 &5' W 4 ('' W0 +&' W D HH' WE 5' W

%8 Fi#ure shows an electric motor on a buildin# sitelifts a load of mass * k# top of a house. Thehouse is 1( m hi#h and it takes H.( s to lift theload.

(a) 6etermine the wei#ht of the load.

(!) What is the work to lift the load b" themotor

(c) 9ow much #ra/itational ener#" does theload #ain

(d) )ompare "our answer in b4 and #i/e thereason.c4

....................................................................

....................................................................

(e) What is the power of the motor.

%9 Fi#ure shows two bo"s %li and %bu of masses&* k# and +' k# respecti/el" runnin# up astaircase in a competition. The" start runnin# atthe same time. %bu is announced as the winnerof the competition.

(a) 6etermine the work done b" %bu.

(!) What is the difference in #ra/itationalpotential ener#" of %li and %bu

(c) %lthou#h %bu is the winner, the power of%li is bi##er than the power of %bu. 2i/ethe reason for "our answer.

....................................................................

....................................................................

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%: Fi#ure shows an athlete of mass +' k# in a pole/aultin# e/ent. J, 7,A,@,,,3 and are thepositions taken b" the athlete. The hei#ht of thebar from #round is ( m. The hi#hest hei#htreaches b" the athlete from the bar is '.* m.

a4 -plain wh" at the position 7, the athleteaccelerates at a specific speed before he starts

to jump.

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b4 Wh" is the pole is bent at the position A.



KKKKKKKKKKKKKKKKKK..c4 )alculate the maimum #ra/itational potential

ener#" of the athlete.

d4 What is the acceleration of the athlete at theposition 3

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e4 Wh" is the thick mattress with a soft surface isused in this e/ent.

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%< The fi#ure shows smooth inclined track, 3,and a rou#h surface B is used to transfer aba# of cement into a lorr" .The ba# of cement of (' k# mass is releasedfrom 3 at a hei#ht of ( m and slides to andstops at B.

a4 i4 ame the t"pe of ener#" theba# of cement has at 3.KKKKKKKKKKKK

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ii4 )alculate the ener#" in a4 i4.

b4 State the t"pe of motion of the ba# ofcement alon# the track 3.

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KKKKKKKKKKKKKKKc4 The ba# of cement eperiences an

a/era#e frictional force of 1'' alon#B and stops at B.i4 )alculate the /elocit" of the ba#

of cement at .

ii4 )alculate the distance B.

iii4 State the chan#es of ener#"when the ba# of cement mo/esfrom to B.KKKKKKKKKKKKKK.

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10/10

5' Fi#ure shows a crane lifts a load of 5'' k# to ahei#ht of 1(' m in *' s. The power input of thecrane is H( kW.

a4 6eterminei4 the useful ener#" output

iii4 the ener#" input

ii i4 the efficienc" of the crane

b4 )ompare "our answer in a4i4 and a4ii4and #i/e "our reason for "our answer.

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5& -ach fi#ure below shows two positions of astudent on a swin#. The initial position in eachfi#ure is different.

bser/e the positions of each of the swin# ineach dia#ram and the appearance of thestudent when she swin#s.

a4 State one suitable inference that can be

made.

b4 State oneappropriate h"pothesis for anin/esti#ation.

c4 With the use of apparatus such as trolle",ticker timer and other apparatus , describean eperimental framework to test "ourh"pothesis.

In "our description , state clearl" thefollowin#>i4 %im of the eperimentii4 Lariables in the eperimentiii4 Aist of apparatus and materialsi/4 %rran#ement of the apparatus/4 The procedure of the eperiment

which include the method ofcontrollin# the manipulated /ariableand the method of measurin# therespondin# /ariable.

/i4 Wa" "ou would tabulate the data

/ii4 Wa" "ou would anal"sis the data

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w23 2.10 work-energy-power-and-efficiency module & exercise

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