O Level Physics Questions

Understanding

'0' Level

through

Problem Solving

A Supplementary Practice

•

Latest MOE syllabus

•

Topics are categorised into

easily manageable sections

•

Questions are arranged in

increasing level of difficulty to

facilitate a better mderstam

•

Question types ..

",n

simple

recall to

foh ..

analysis an~

synthesis

-

an

aspect in tackling data-s

J

em

-COI>yright ~ 2()(YJ Panpac Education t·rivatc Limited Published by EPB Pan Pacific

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publisher. Paopac Education Pr,v31c Limired, TlJJleS Centre, J New lodusuj;l,1 Road. Singapore 536196, 'let: (65) 641 J 0820, Fa." (65) 6846 3440

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nRac Ed

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Email: p a n p m kt 8@ p a ll c:pa : e du c.a il o .n c ()Jn websue: ItIIp://\V\V\V. panpaceducarion.com

EI'B Pan Pacinc is a trademark ofTirncs Publishing Limited ISBN 918·981·273·004-6

First publiShed 2007 ReprinlBd 2008 Author: David Oon

Th

e

m

e

1

>-

Meas

ur

e

m

e

n

t

Chapter 1 Physical Quantities, Units and Measurements

1.4 Time Measurements and the Penduhllu

₆

1.5 Scalars, Vectors and Vector Diagram

1.6 Challenging Segment

9

Th

e

m

e

2

>-

Newt

o

ni

a

n M

ec

h

a

ni

c

s

Chapter 2 Kinematics U

2

.

1

Sl2eed, Velocity and Acceleration U

2.2 Graphical Analz:sis of Motion

l..4

2

.

3

Freefall

₂₂

2.4 Challenging Segment

24

Dynamics

1

.

1

Balanced Forces

21

21

1

.

2

IInbalanced Forces

₂₈

3

.

3

Friction

11

3.4 ChaUenging Segment

_3.3

Turning Effect of Forces

43

5

.

1

Moments

₄₃

5.2 Princil2le of Moments ~ 5.3 Centre of Gravity and Stability 4!i 5.4 Challenging Segment

_4.8

1

1.1 Base Quantities, Units and Prefixes

1

].2 Errors in Measurements

₂

1.3 Length Measurements with Calipers and Micrometer

3

1

Chapter 3 Chapter 4 Mass, Weight and Density

:N

4

.

1

Mass and [nerti;)

₃₂

4.2 Weight

_4:0

4.3 Density and Flotation

_4..1

4.4 Challenging Segment 42 Chapter 5 Copynghted matenal

8

.

3

Challenging Seg

m

en

t

Th

ermal Ener

g

y Tran

s

f

e

r

76

7

9

9

.1

Therma

l

Eq

u

i

li

b

riu

m

7

9

9

.

2

Conduction

₇

₉

9,

3

Co

n

vect

j

o

n

81

9

.

4

Radiat

i

on

₈₂

9

.5

Challengin

g

Segmen

t

₈₃

T

enl

p

e

r

a

l

w'e

87

10

.

1

Prin

ci

p

les of Thermom

e

try

₈

₇

10.2

T

h

ermoco

upl

e T

h

e

rm

o

m

e

t

e

r

s

₈₉

10

.

3

Challenainz Seament

₉₀

Chapter 6

Pres

su

r

6

,

1

P

e

ressll

r

e

49

₄₉

6

.

2

L

i

q

u

id

Pr

ess

ur

e and A

t

mos

p

h

er

ic

Pr

e

s

s

u

re

50

6.3

P

ressllre

D

iff

ere

n

ce

₅

_S

6

.

4

H

yd

r

a

u

lics

57

6,5

Pres

s

ll

re Meas

u

relne

n

t

₅

₈

6

.

6

Challen

gin

g Seg

m

en

t

₅₉

Chapter 7

W

o

rk

, Energy an

d P

ower

61

7,1

W

o

r

k

6

1

7

.2

Ki

net

i

c E

n

e

r

gy

a

n

d

G

r

av

i

t

a

ti

o

n

a

l P

o

t

en

ti

a

l

Energy 63

7

.

3

P

r

inci

p

l

e of Con

s

ervation of Ene

r

gy

₆₅

7.4

Power

₆₈

7

.5

C

h

allenging Se

gm

en

t

₆₉

Th

e

me 3

:>

Th

e

rma1 Phy

s

i

cs

Chapter

8

_K

_ine

_ti

_c

_M

_o

_d

_e

_l

_o

_{f Ma}

_tte

_r

₇₃

8

.

1

State

s

Qf

Matt

e

r

an

d

t

h

e

Kin

e

ti

c

MQd

e

l

₇

₃

8

,2

Bro

w

nian

M

ot

i

o

n

7S

C

h

a

pt

er

9

Chapter 10

Chapter 11

T

h

erma

l Pr

o

p

e

rti

es of

M

a

tt

e

r

91

1

1

.1

H

eat Ca

pacit

y a

nd

S

p

eCifi

c

H

ea

l

Ca

p

ac

i

ty

11

.

2

Melting

,

B

oiJing

!

U1dEva

p

ora

t

io

n

11.3

L

a

t

e

nt H

eat

an

d S

p

ec

i

fic

L

ate

n

t

H

ea

t

11.4

C

h

allenging Segnlent

91

94

96

100

Copynghted material

Th

e

nl

e

4

»

Wave

s

Chapter 12 General Wave Propenies

12.1 Longitudinal and Transverse Waves

12.2 Wave Terms and Graphical Representation of a Wave

12.3 Ripple Tank 12.4 Challenging Segment

1.03

un

1.04

J..06

1

0

7

Chapter 13 Chapter 14 Light 13.1 Reflection 13.2 Refraction

13

.3

Total Internal Reflection 13.4 Thin l.enses

1

3.

5

Chal.lenging Segnlent Electromagnetic Spectrum

1

09

1

0

9

I 1

1

ill

ill

ill

119

14.1 Properties of

El

ectr

om

ag

n

e

ti

c

Waves and Applications

₁

₁

₉

14.2 Challenging Segment

₁₂

₀

Chapter 15 Sound

12.3.

15.1 Sound Wave and its Graphical Representation

_ill

15

.

2

Speed of Sound

₁₂₆

15.3 Echo and Ultrasound

1

2

7

15.4 Challenging

S

eg

m

e

nt

]

28

T

h

e

m

e 5

» E

l

ec

tr

i

ci

t

y a

nd

Magne

t

i

s

m

Chapter 16 Static Electricity

_ill

1

6

.

1

[

a

ws

of Electrostatics

_l.3..l

16.2 Eleclrostatic Charging

₁

₃₂

1

6.

3

Electric Field

_ill

16.4 Challenging Segment

_l..34

Chapter 17 Current of Electricity 17.1 Current

17.2 ElectTomotive Force (E.M.F.) and Potential Difference

1

7

.

3

Resistance 17.4 Ohm's

L

aw

17.5 Challenging Segment

ill

131 138

ill

.

lAO.

14

1

Copynghted matenal

Chapter 18

D

.

C

,

Circ

u

i

t

s

1

43

I R.l

S

e

r

i

es C'

i

[

c

il

it

14.3

18

.

2

Pa

r

all

e

l

Circuir

1

44

18.

3

S

e

r

i

es a

nd

Pa

ra lie

l Ci

[CU

i

l

l'

1

46

18,4

P

o

t

e

ntilll

Di

v

i

d

e

r

C

i

r

c

u

it

s

1

41

18

.

5

Use of Cat

h

ode

-

R

a

~

1

Osci

l

losco

p

e

1

48

18

.

6

C

h

a

ll

e

n

gi

n

g

S

egme

n

t

1

50

Chapter 19

Pr

ac

ti

ca

l

Elec

tri

c

i

t

y

1

53

19.1

Elect

r

ic Powe

r

a

nd

E

n

e

r

,!!,

y 1

53

19.2 D

angers of Electricity

1

54

19.3

Safe Use of Elec

t

ric

i

ty

156

19.4

Challenging

Segment

157

Chapter 20

M

ag

n

e

t

ism

1

6

1

20.1

Laws of

M

ag

n

et

i

s

m

a

n

d

I

n

du

ced

M

ag

n

et

i

sm

1

6

l

20.2

M

ag

n

e

ri

sa

t

i

on a

n

d

D

e

m

a~

n

et

i

sa

t

io

n

163

20.3

Magnetic

Fie

l

d 16

4

20.4

Challeng

i

ng

Segment

1

65

Chapter 21

E

l

ec

t

r

o

n

,a

gn

e

t

i

s

m 1

6

7

21.1

M

ag

n

e

ti

c Effect of a C

u

rrent

1

67

21.2

Force on a Cu

rr

e

n

t

-

Carry

i

ng

Cond

u

ctor

1

69

21.3

T

b

e

nc

Motor

I

:z

I

21.4

Challengi

n

g

Seg

m

ent

1

73

Chapter 22

Elec

tr

o

m

ag

n

etic

In

duction

1

77

22.1

Pri

nci

pl

es

of

E

l

ec

t

romag

n

eti

c In

d

u

ctio

n 1

77

22.2

T

he A.C.

G

enera

t

or 179

2

2

.

~

Tr

an

s

f

o[

lllf

~

[ and

POll"er

'Iransmisaion

1

81

22.4

C

h

a

ll

e

ng

i

ng S

egme

n

t 1

84

All~~ers

and Worke

d

Salutians

1

89

Q

ua

tit

y

L

e

n

g

t

h

S

y

m

bo

l

I

,

h

...

U

nit

k

m

,

I

n

,

e

m

,

nun

A

r

ea

A

m

2 ,

e

m

-Volume

V

m

:l,

e

m

"

W

e

ight

W

N*

Ma

s

s

m, M

kg

,

g

,

mg

T

i

m

e

I

h,

min

,

S,

m

s

P

erio

d

"

T

s

Density"

p

g

/

cm

'

,

k

g/

rn

"

Speed

"

1.1" l'

k

rn

/h

,

m

i

s,

c

m

/

s

Acceleration+

_a

_mi

_s

_'

Acc

el

e

rati

o

n

o

f f

r

ee fa

ll

s

r

n

/

s

'

, N

/k

g

Fo

rc

e"

F

,

P

N

Mo

m

e

n

t

o

f fo

r

ce

*

N

m

W

o

r

k don

e

W

,

E

J

*

,

kW

h

*

E

n

e

r

gy

E

J

P

ow

e

r

P

\"'1

*

P

r

e

ss

u

r

e

p

,

P

Pa

*

,

N/

m

z

Atmo

s

p

h

e

r

i

c pr

e

ss

u

r

e

u

se of rni

li

b

ar

Tempe

ra

t

u

r

e

H

ea

t ca

p

a

c

i

ty

{J,

T

C

°

C

,

K

J/

o

C

,

I

/K

Sp

e

ci

fic

h

ea

t

ca

p

a

c

i

t

y

c

J

/

(g

°C

)

,

J

/

(g K)

L

at

e

n

t

h

e

a

t

L

J

Sp

ecific

la

te

n

t h

e

at

I

J

/

kg

,

J

/

g

F

r

e

qu

e

cy

_.f

_H

_z

II-SUMMA

R

Y

O

F

K

E

Y QU

Ai

~'

r

rrIES

,

SYMB

O

LS AN

D

l

JNI

T

S

Wa

ve

l

e

n

g

th

,

m

,

cln

F

o

c

a

l

l

e

n

g

t

h

_.f

In

,

e

rn

An

g

le of i

n

cid

e

n

c

e

I

d

e

gree

(0)

Angles

of

r

efle

ct

io

n

,

r

e

f

r

a

ctio

n

r

d

eg

r

ee

(0)

Cr

i

tical an

g

l

e

c

d

e

g

r

ee

(0)

P

o

t

e

ntia

l

diff

e

r

e

n

ce

*

/

v

o

l

tag

e

V V*,

m

v

Current"

I

A, IliA

C

h

a

r

ge

q,

Q

C

,

A

S

e

.

m

.

r

r

-

-

E

V

r

e

s

i

s

t

an

ce

R

Q

Physical Quantities, Units and

~~

.

r~~~/

~

m

~

e

~

as~u

~

re~m~en~t

_

s~

>-

1

.

1

B

ase

Q

u

antiti

es

, U

ni

ts

a

n

d P

r

efix

es

1. John, who has a mass of 50 kg. height of 1.54 In, is able to run a distance of I km in a time of 5 min 12 s. His average speed was calculated to be 3.21 rals:

(a) Write down all the physical quantities and their respective SI units for the situation

above. (5) Physical Quantities SI units

(b) Which of the quantities above

are

considered

a

s

base quantities?

[2J

(c) What other base quantities are there besides those in (b) above?

[4J (d) Which prefix has been used in the situation above? State how many times is the factor

of

this prefix over its base unit.

[

2J

2. Ali said, "I found out that the speed of light in space is 3 x 10" In/s. This means that light can travel a distance of 3 x 10" m in a time interval of just 1 second!"

(a) Identify and write down from what ALisaid, all the base physical quantities and their respective SI units. (2)

(b) Rewrite the distance of 3 x IU' m using the prefixes kilo-, mega- and giga-.

[3J 3 x 10" nl

=

kin

=

Min

=

Gm (c) Convert 3 x (i) km/s, 10" nl/s into: (21

(ii) km/h, [21

Chapter I

1

3. Alice calculated the density of a solid metal box by first measuring the mass and volume of

the box. The results are as follows:

Ma

ss

=

300

g

Volume

=

60

e

m'

Density =

5

glcm'

(a) Out of the three physical quantities above, which are not considered as base quantities? [2)

(b) Convert for all three quantities above, into their respective SI units.

[

6

]

Mass : 300

g

-

_

Volume:

60

e

m

'

-

_

Density: 5 g/cm? - _

>

1

.

2

Errors in Measurements

1. (a) Write down the tWO types of errors that may be present during measurement. (2)

(b) State which of the errors above can be reduced by taking a larger number of

m

e

a

s

ur

e

ment

s

and averaging? [I]

2. State the main type of error for each of the tWO cases below. Explain your choice of answer

and describe how in each case, the error can be reduced.

(a) Bala and Billy have a digital stopwatch each. Both measures the time taken for a marble

to roll down a l-m ramp and the results are 3.57 s and 3.42 s respectively.

Type of error: _

Explanation and description on how to reduce error:

[I)

[2]

(b) A glass cylinder has a length specified by the manufacturer as 15.0 cm. Bill wanted to

measure and confirm this length. He used a metre rule, unaware that it has a defective scale at the zero mark. His measurement result is 14.8 cm.

Type of error: _

Explanation and description on how to reduce error:

[1]

[2]

Copyrighted

,

3. Bob is trying (0 determine the period of a 1.2 m long pendulum. He first measures the time interval for 10 complete oscillations with a digital stopwatch. He then carries out an averaging

to determine the period of oscillation. Suggest two ways in which he can make the results more accurate. [2]

,

,

,

,

I , clamp r , I ,1=1.2nl r ,

,

/

.. "'

. ,;" \ \ ...... I

>-

1

.3

L

e

n

g!

h

Meas

u

re

m

e

nts with

C

ali e

r

s and

M

i

c

romet

e

r

1. Write down the readings for the following measurements below. The following pairs of

cal ipers have no zero error. (a) 20 30 Reading

=

[I] (b) Reading = [I] 2. Write down the readings for the measurements below. This pair of calipers has no zero error. (a) 1111111111111111111[111111 em

o

5 10 Illllllllll 4 5 Reading =---lIJ (b)

1IIIIIIIIIIIIIIfllllllili

em

7 8

Reading

=

[I]

1,

3

.".;;,.----'

3. A pair of faulty calipers is found to have a zero error of +0.03 cln when the jaws are fully

closed. This pair of calipers is used to measure the depth of a beaker.

1111111111111111111111111

em

9 10

(a) Write down the measurement made with this pair of faulty calipers. (I)

(b) Write down the actual depth of the beaker. [1]

(c) State the pan of the vernier calipers used to measure the depth of the beaker. [I] 4. A pair of faulty calipers is found to bave a zero error of -0.01 ern when tbe jaws are fully closed. This pair of calipers is used to measure the diameter of a syringe.

o

5 10 1 I

I

II

I

I

I I

I

1 111111111[1111111111111111 em 3 4

(a) Write down the measurement made with this pair of faulty calipers. [1)

(b) Write down the actual diameter of the syringe. [1]

(c) Describe what you would do to obtain a more accurate diameter of the syringe. (2)

S. Write down the two measurements below made with a micrometer. Assume that the micrometer has no zero error. (a) (b) ~,=".-~n 10

'

~

lM,§--J5

o Reading = [1] _{Reading = ---[1]}

4

Understanding Physics through Problem Solving

'---'

6. The diagrams below shows four measurements of a diameter of a non-uniform iron rod made with a micrometer. ~l=:--~n3S 30

W

I-_

~_'

2

5

Measurement 1 Measurement 2 Measurement 3 Measurement 4

(a) Record the readings of all four measurements in the table below.

Measurement No. I

2 3

4

Initial measurements Corrected measurements

14]

(b) A student checks the micrometer and finds that it has a zero error of -0.02 mm, Correct

all four earlier measurements and record them in the table above. l4]

(c) Calculate the average diameter of the iron rod.

(d) State the type of error present in this situation.

[21

[

I

I

7. A faulty micrometer screw gauge with an error of -0.02 nun when the jaws are fully closed is

used to measure the external diameter of a test tube.

(a) Write down the measurement shown on

the micrometer. _ _[1]

(b) Write down the actual diameter of the

test tube. _{_ [IJ}

8. A faulty micrometer screw gauge with an error of +0.02 mm when the jaws are fully closed

was used to 111eaSUrtehe diameter of a washer.

(a) Write down the measurement shown on

the micrometer. _ _[II

(b) Write down the actual diameter of the

washer. _

_[ll

Chapter I

....

5

...

_

...

,

,

-

,

,

,

•

I

,

, ,

I ,

,

,

J' » , ,

,

,

,

,

,

:>

1

.

4 Time Measurem

e

ts and the Pendulum

1. The diagram below shows a simple pendulum setup in a school laboratory. The average time taken for the bob to move from

Q

to R is 0.4 s.

(a) Define the period of an oscillation.

[

u

r r

"

,

,

,

,

_,

clamp I

,

,

_,

(b) What is the period of the pendulum? [1] _,,

,

,

, , ,

,

P"-" ,

-

, R Q

(c) The pendulum experiment allows us to calculate an approximate value of Earth's gravitational acceleration with a simple formula.

length of pendulum bob in metre

Gravitational acceleration = 41t2X

square of period of osci llation in seconds

(i) The length of pendulum in this experiment is 0.65 m. On the diagram above,

IIIark the length of the pendulum. [1]

(ii) Using the value found in (b) and length of pendulum as 0.65 m, calculate the

gravitational acceleration of Earth in nl/s2. (2]

(iii) How must the length of the pendulum be adjusted to increase the period of the

pendulum? [I]

(iv) A student proposes to use a bob that is heavier in order to lengthen the period of the

pendulum. Explain if the proposal is valid. [2]

2. The diagram below shows a setup of a simple pendulum suspended from a clamp.

The pendulum bob is moved about 5° to J and released, causing the bob to oscillate between

positions J and L. The bob takes an average of 0.60 s to move from J to K and to L.

(a) What is the period of the pendulum above? [I)

(b) What is the time taken for the pendulum

,

,

"

,

_,

,

,

,

,

I clamp to make 2.5 oscillations? [I] L-_ ;6::...J Understanding Physics through Problem Solving

,

,

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,

-

-I -: L K Copyrighted material

(c) Marcus lengthens the pendulum and proceeded to measure the rime taken for the

pendulum to make 20 oscillations. Marcus uses a digital stopwatch. The process

is repeated four more times and the results are as follows:

35.26

s

36.23

s

34.83

s

34.94

s

36.02

s

(i) Calculate the new period of the pendulum by averaging. Show your workings

clearly. [2]

(ii) Calculate the frequency of oscillation of the pendulum. 12]

(iii) Explain why the determination of the period of oscillation is more accurate by calculating the average of 20 oscillations and not from one single oscillation?

[I)

(iv) The method used in (i) and (ii) is useful to minimise what type of error? [I]

1. The diagram below shows a box acted upon by two

forces.

(a) State the resultant magnitude and direction of the

box due to the two forces. [2] 51'1

~

b

I

ox 8N (b) The 8-N force is now reversed. State the resultant magnitude and direction of the box due to this change. The 5-N force remains the same, [2]

2. A vector of size 6 units, points directly north while another vector of size 8 units, points east.

Draw a parallelogram to determine the vector addition of these two vectors. Use a scale of

Chapter I

7

3. Force is a vector quantity. Two forces of 6 N each acts on an object.

(a) Describe how it is possible to produce a zero resultant force from the two forces. (2)

(b) Describe how it is possible to produce a resultant force of 12 N from the two forces. [2]

(c) Draw a vector diagram to show how a resultant force of 6 N may be obtained from the

two forces of 6 N each. Label the 6-N forces and the resultant force clearly.

[2J

4. The diagram below shows two forces of 30 Nand 40 N acting on a crate. JON

crate

Draw a parallelogram to determine the resultant force of these tWOforces. Use a scale of

I ern : 5 N. State the magnitude and direction of the resultant force. [5)

5. Which of the following diagram correctly shows the addition of the 3-N and 4-N forces?

A

B

c

D

SN 51'1 51'1 51'1 3N IN 3N 3N 4N 41'1 41'1 41'1

r

1

>-

1

.

6 Chall

e

n

g!

n

g S~

m

e

nt

1.

A pair of calipers has a zero error of +0.2 mrn. Alan uses it to measure the length of a cubic

dice. The reading is 12.6 mm. Recognising the error in the calipers, Alan makes adjustments

to his reading and recorded the length of one side of the dice as 12.8

mm

.

He then proceeds to

calculate the volume of the dice and writes down the result as 2 097

mrn

"

,

(a) State the three errors made by Alan. (3)

(b) Which of the quantities above is a derived quantity? [l]

2.

Two forces act at right angles at a point

0

as shown below.

What is the resultant of the forces shown? Qr - - - R Magnitude A 15 N B 15 N C 21 N D 21 N Direction

OQ

PR

OQ

PR 91'1 p 12 N

o

[ )

3. Two forces are combined and cause a resultant force.

(a) State the one factor that affects the magnitude of the resultant force. [l)

(b) State the range of the magnitude of the resultant when forces of magnitude 3 Nand 4 N

are combined. [1.1

4. James, starting at a point P, walks due North for one hour at a constant speed of 4.0 km/h and

then, at the same constant speed, walks 4.0 km due East, finishing at a point Q. In the

same total time but at a different constant speed, Jo walks directly from P to Q. Determine

(a) the total distance walked by James. [2)

-'-_

...

(b) by drawing. the distance walked by Jo,

(c) the velocity of Jo.

5. The reverse bungee is II new and excinng form of

fairground ride first introduced in

19

9

9.

Passengers

b

o

ard

a spherical cage. and arc then released vertically

upwards into the sky. The cage is pulled upwards by a

pair of elastic cords mounted on the side of the cage. The

diagram shows the forces acting on the spherical cage.

Each force has a size of 40 kN each.

B

y

means of II scale drawing, determine the magnitude

and direction of the resultant force exerted by both elastic

cords on the spherical cage.

10

Underxtendiug 1)I,y:..ic!1o Ihl'ou~h Problem Solving

"---'

[5)

l2

J

B

Kinematics

1. (a) How is displacement different from distance? 12]

(b) Which of (he quantities above is a vector? II]

(c) Kathy throws a ball upward into the air and caught it

at the same position when the ball returns to Earth. Mid-point of downward motion

4m

Evaluate the following statements below, making the

neccessary corrections to statements that are false.[5] Point ofthrowing

b.1l

(i) The distance travelled by the ball is

8

rn

.

True I False (ii) The displacement of the ball at the point that it is caught is +4 111. True I False (iii) The height reached by the ball is equal to the total distance travelled. True I False (iv) The displacement of the ball at the highest point is +4 m. True I False (v) When the ball is mid-way on its downwards motion, its displacement is ·2 111. True

I

False 2. The diagram on the right shows a spring suspended from a retort stand. A bob is hung below the spring, causing the spring to be extended to the neutral position shown. The bob is then pulled downwards to position J which is 8 cm below the neutral position and then released. This causes the bob to oscillate between positions J and K repeatedly. bob neutral \ position - - - - - - - -

-!

K one complete up 1.I11c1 <10\\'11 oscitlation J (a) What is the displacement of the bob when it is at position J? [I] (b) What is the displacement of the bob when it is at position K? [I] (c) What is the total distance moved if the bob rnakes one complete oscillation from the neutral position? [I] (d) What is the displacement of the bob when it has make one

complete oscillation measured from the neutral position? [IJ

3. (a) Define speed and state its SI unit. (2)

(b) Differentiate between average speed and instantaneous speed. [2]

(c) Write down the formula used to calculate average speed. [J

I

(d) Is there a formula to calculate instantaneous speed? _

[

I

I

(e) A car starts from rest and travels 11 distance

of 600 rn in 15 s. A fter which its slows down and travels another distance of 600 m in 25 s. Calculate the average speed of the car. 4. (a) Define velocity and state its SI unit. (2) (b) Differentiate her-ween average speed and average velocity. [2] (c.) Explain when average speed is the same as average velocity. [1] (d) Evaluate the following statements below about speed and velocity, making the necessary corrections to statements that are false. [3] (i) Speed and velocity has the same magnitude but could be of different direction. True

I

False (ii) The quantity speed can be a negative value. True / False

(iii) The quantity velocity can be a negative value. Tnle / False

5. (a) The speedometer of a vehicle shows a reading of 50 km/h. Cross out the statements that are wrong. [3]

D

The instantaneous speed of the vehicle is 50 km/h.

D

The average speed of the vehicle is 50 km/h.

D

The total distance travelled in the last one hour is 50 km. ..._

12

..I Understanding Physics through Problem Solving Copyrighted material

(b) A van moves at <Inaverage speed of 50 krn/h. Cross out the statements that are wrong.

o

The instantaneous speed of the van cannot be less than 50 km/h.

[

4

]

o

The instantaneous speed of the van cannot be more than 50

k

rn/h

,

o

The van may reach an instantaneous speed of 100 km/h.

o

The van may reach an instantaneous speed of 0 km/h.

6. Evaluate the following statements below about an object moving with a negative velocity,

making [he necessary corrections to statements that are false. 14]

(a) The moving object is decelerating at a uniform rate. True / False

(b) The moving object is decelerating at a non-uniform rate. True / False

(c) The moving object is moving at a constant speed. True

I

False

(d) The moving object is moving at zero acceleration. True! False

7

.

(a) Define acceleration and state its SI unit. [2J

(b) Is acceleration a vector or scalar

q

ua

r

u

it

y?

Why'! [2]

(c) Write down the equation used to calculate acceleration of an object. [I]

(d) A football was moving at a speed of 0.5 rn/s when it was given a kick. The time taken for

the impact is 0.2 s. Irs new speed is 5.5 nl/s. Calculate the acceleration of the football. [2]

(e) A motorcycle accelerated away from rest at a traffic light with a magnitude of 2.4 rn/s:. Calculate the lime taken for it to reach a speed of 18 Ill/s. (2)

Chapter 2

, , _·· ,

·

8. Evaluate the following statements below about acceleration. Correct the statements which are

~se. [~ (a) (b) When an object accelerates, its velocity increases. When an object accelerates, its speed may be increasing. True

I

False True

I

False

(c) Deceleration is a scalar quantity. True

I

False

(d) When an object decelerates, it is slowing down. True I False (e) An object first accelerates at 2 m/s2.It then decelerates at 2 In/s2,

This must mean that the object is now moving in a direction

opposite to that when it was moving with an acceleration of 2

m

/s

2

.

True

I

False

(f) Mathematically, deceleration

=

-

acceleration. True

I

False

9. A van takes 20 s to travel the first 80 m, another lOs to travel a further 70 m. It

then decelerates at a rate of 3 m

/s

2

to come to a complete stop in 2.5 s.

(a) Calculate the average speed of the van in the first 30 s of its motion. [2]

(b) Calculate the instantaneous speed of the van at lime of 30 s. [2)

G

r

a

hi

e

al

a

nal

ysis

of motion

dim . -I. _,,_ ....&.-.- _. ... _~ ··

.

..

.

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I.. The graph on the right shows a distance-time graph of

_.

•

.

, ·;

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a moving object. Analyse the graph and evaluate

the 100 , , _{. ·}

_-

.-

.. .. _· .. ri. following statements as true or false. [10] _. (a) Object has travelled a distance of75 m in 3,0 S. 50

;/

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_{· ·} ,-" True

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False

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lis (b) Object has travelled a distance of 100 m in 5.0 s. True I False

o

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1

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.\

.

" . · · _-,_ _· , , , , (c) Object is not stationary from 0 to 4.0 s. True I False (d) Object is not stationary from 4.0 to 6.0 s. True/False

Understanding Physics through Problem Solving

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(e)

(

0

Speed of object Speed of object from from 0 to 4.0 s is constant. 0 to 4.0 s cannot be calculated by dividing True

I

False Tru~

l

Fal~e 50 m by 2 s.

(g) Speed of object from 4.0 to 6.0

s

is non-zero. True f Fals~ (h) Speed of object from 4.0 to 6.0 s can be calculated by dividing Tru~

L

False

100 m by 2

s.

(i) The slope of a distance-time graph gives us the speed of the object. True / False

(j) Object is moving at constant speed between 0 to 4.0

s

and is at rest True

I

False from 4.0 to 6.0

s.

2. The distance-time graph below shows the speed trend of a jogger.

Distance/km -,

.

; ,.- ~. "f: • '. .,....~ + - ,.

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.i ...- :"-., +--':---'':---'---'----'--''-;..._ ..._..-.I...._ _.J Time/min

o

5 10 15 20 25 311 35 40

(a) From the graph. what is the total distance travelled by the jogger? _ [1]

(b) How many times did the jogger stopped running? Explain which pan of the graph

suggests this to you? [2]

(c) Write down the times at which the jogger is at his fastest run. Without making any

calculations, explain how you deduce your answer, (2)

(d) Calculate the speed (in m/s) of the jogger when he is at his slowest run. [2]

-I ._. _, .••.•.. _,., .' ._... , _'._''''_

\ ... ~.

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(e) Calculate the average speed (in In/s) of the jogger throughout the whole journey. [2]

(I) The jogger started and ended his run at the same point. State and explain, whether there

is anything from the graph that suggests this information. [2)

3.

A

tennis ball was thrown vertically upwards. It travelled upwards for

8

m

,

stopped, travelled

back downwards and caught at the point that it was thrown. The time taken for ball 10 reach its highest point is I s. It takes another I

s

for it to drop back to the point it was caught.

(a) Evaluate the following statements about the distance and displacement of the ball. Make corrections to the statements that are false. [7] (i) The total distance travelled by the ball is

8

m. True / PaIse (ii) At the highest point, the distance travelled and the displacement

of the ball is the same, True / False

(iii) The displacement of the ball at the point it was caught is 16 m. True

L

False (iv) The displacement of the ball at the highest point is

8

m. True

I

False (v) The displacement of the ball halfway downwards is -4 m, _True I false

(vi) The total distance travelled and displacement of the ball at the

point it was caught is the same. True

I

False (vii) Both quantities: distance and displacement. are vector quantities. True I False

(b) On the graphs below sketch the distance-rime and displacement-time graph of the

motion.

₍

₄

_]

(i) distance-lime graph

.

-, ., -, . 1-. -. "'T-' (ii) displacement-time graph -r -.,..- _.-.; I·.. •·· ,-t··.. -- .. ·· -~--- _.. ..,.•---<.~. .. ....

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.-Understanding Physics through Problem Solving

I

·

· .

(c) Calculate the average speed of the baU throughout the whole motion. (2]

(d) Calculate the velocity of the ball

(i) when it just leaves the hand, and (ii) just before it was caught. [41

4

.

Albert standing at

a platform

10m above ground throws a ball vertically upwards. The motion

of the ball is plotted in the graph below. displacement/m 10

/

.

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<,

_..

..

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.

. .

.

. .

.

.

.

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(a) State the rime at which the ball reaches the maximum height. [I) (b) State the approximate time at which the ball hits the ground.

[

11

(c) Stale the total distance travelled by the ball. [I] (d) State the displacement. of the ball at the end of the motion. [I) (e) State the time at which the speed of the ball is 0 In/s.

[

11

(I) Describe the speed of the ball from 0 to 3

s

.

[2] Chal)lC(2

1

7

..I

,

5. Joseph conducted an experiment to investigate the speed of a remote control car. The data from the data-logger is as shown below. Speed in rols 0.0 0.4 0.8 1.2 1.6 2.0 2.0 3.0 4.0 5.0 0.0

Ttm

e

in

s

0 2 4 6 8 10 12 14 16 J8 20 (a) Plot the speed-lime trend of the car in the graph below. [2] . ... , .

-

, ..

.

....

.

, .,. ,. , ; . " .

._.

_

_

.

.

'

.

I ' -. ,

.

-:' ' , .,

.

;, .•. .' " • , '.. I _ .. I

.

:,,1 .... ~ .•• , , , , _ •• n •..•• , ... . _ , • I "'" , ... _., . ..

- -

.

...

.

L-_...L._....L_--' .L...._...L.._...!. L-_...L._....L_--'_-+'tillleiS From the graph,

(b) determine the speed of the car when the time is 15.0 seconds. (c) which time(s) suggest to you that the car is stationary? (1] (1) (d) write down the times when the car (i) accelerates, (ii) decelerates. (e) calculate the acceleration of the car from 14.0 to 18.0 s.

(

0

calculate the acceleration of the car from 18.0 to 20.0 seconds.

18

Understanding Physics through Problem Solving ---[1]

(1)

(

2)

[2

]

(g) calculate the total distance travelled by the car.

l

2J

(h) calculate the average speed of the car. [2]

6. (a) Write down the equation used to calculate acceleration. _ (I]

(b) A toy car moves down a slope from rest, It travels 3.6 In in the first 3 seconds. Determine

the acceleration of the toy car with the aid of graphical analysis. Assume that the

acceleration is constant. [2] 7. The graph on the right shows the speed of two cars over a period of time. :<

wi'

I

car J

c

.

K ,,.,

/

V

1

"

,,"

1

,

,

,

o

timcls

From the graph, evaluate the following statements below for true or false. Make the

neccessary correction for statements that are false.

[

11

(a) Car J accelerates at the same rate as car K. True

I Fa

lse

(h) Car J and car K always travel at steady speed. True {False

(c) Car J stalls at a faster speed chan car K. True {False (d) Car J overtakes car K just as car K is about to stall moving. True {False (e) Cars J and K start at the same time. True {False

'.'._

.-·

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··

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.

.

.

8. Wilson, standing at the second storey of a building which is 10 m above ground, throws a ball

vertically upwards. The speed of the ball when it leaves the hand is 10 m/8 and the speed is

17.3 m/5 just before it hits the ground, The motion of the ball is plotted in the graph below. (a) What is the height reached by the ball? [I] (b) _{What is the total distance travelled by} the ball?

III

(c) Write down the gravitational acceleration of Earth? disptacemenvm IO~---r~~~--,----.---.---,

.

_.

...

_;,

y/ ~

_{.,. . ,_ ,}

,

_f\:

:::::::;.:::.

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" '''.' .- ••.••.•••••.... " ...r....' ... \ ! ' ••• n_ ••. ;.. ...,! ~..;. [I] _I 0 ~.--,-_"_~_~.,,_ :;_.•_-'-._._. _.,

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(d) Sketch the

(i) distance-time graph of the motion, (li) speed-rime graph of the motion

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;.

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.

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_, ' i .;. (iii) velocity-time graph of the motion • . ;

(iv) acceleration-rime graph of the motion

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20

... Undeoranding Physics through Problem Solving

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V

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.

9. The diagram below shows the velocity-time graph of two cars A and B rnoving along a

straight road in the same direction.

40~~.-~-r~~~~~ -r ~ ~c·rr,~B

.... .

...

.

.

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2 4 _{6 10} 12 14

(a) Describe the motion of cars A and B at time 0 s. (2)

(b) At time t = 8

s,

what is the acceleration of,

0) car A. _ _{(ii) car}

_B

_,

_~

_{_}

₍₂₎

(c) Jerry said, "From the graph, it looks like car B overtakes car A at 8 s. This is because the

speed ofB is now more than that of A." Is what Jerry said true? Explain and justify your answer by showing the appropriate calculations. (2)

10. A small marble is given an initial push up a ramp. It moves up the frictionless slope and down

again. The time taken for this to happen is 1.2 s. (a) Sketch a velocity-rime graph 10

represent the motion of the marble

in 1.2 s, (You may take the upward

motion along the ramp as positive)

(b) Sketch a distance-time graph

to represent the motion of the

marble in 1.2 s.

....

.

>-

2.3 Free

f

a

ll

1. Evaluate the following statements about free-faJl on Earth in the absence of air resistance for

true or false. Make necessary corrections to the statements which are false. [4)

(a) Any object falling freely will always increase its speed at a rate of

10 m/s every second. True

I

False

(b) Any object falling freely will always fall at a constant speed of 10

In

/s

.

True / False

Cc) A feather and a pebble dropped from the same height will reach the

ground at exactly the same time. True / False

(d) Any object thrown verticaJly upwards will accelerate at +10 m/s2. True

I

False

2. A ball is thrown vertically upwards at a speed of 8

In/

s

.

It then falls back to Earth. Ignoring the

effect of air resistance. evaluate the following statements for true or false. [3]

(a) The size of acceleration of the ball throughout its motion is the same. True / False

(b) The acceleration of the ball is -10 m/s2 upwards and 10 111/Sd2ownwards. True I

False (c) The speed of the ball as it passes the point of throwing is 8 m/s. True I

False

3. Which graph represents the motion of an object in free fall reaching terminal velocity?

A B

c

D

o

.

+-..:::::=

=-

lime/s

o

+---

--+

rimers

o

+

---

-4

timels [ ]

4

.

The diagram on the right shows the changes of the speed of an object with time, as the object falls

24

_r

.

-

r

K

...

-

-

.·

.,

..

.

.-

-

....

,.

~

.

~

..

-

,

.

.

-

"

.

~

.

-'

~~

free Iy through the air. ,- :,'

..

.;.

.

.

.

,

, .•_~. -I • o._ . I.. _ ....' -r •

.

.~

' .._ (a) Write down [he speed of the object when its acceleration is 16 ., - - ,~.; "r":'" ;.,~ .~ - .

_'!

/-

'~"

r+ , ..i !" 1'''1 "t. 'I > ,

~:

!

;--;:-1

:T++ ~~•••~- ~:::.::

(i) at its maximum value, [1] 8 -. I , , . . ; J. "

.

-

,.

.

.,

--- /-., -;. , '. _ ..-- -.,..,. t-· " -,.-,_ , _• (ii) at its minimum value. [I] ::lO'---.1.4--.!.S--1.L2--IL6--2LO- timels (b) Write down the minimum value of the acceleration of the object. [1] (c) Describe the motion of the object from time 0 to 20 s, making reference to the term 'terminal velocity', [2]

'--_

5. A man is in a gondola of a hOI air balloon, ascending at a rate of 12

I

n

/s

.

As the gondola

passes through a point that is 500 111 above ground, he leans over the edge and releases a coin.

(a) Sketch a velocity-time graph of the first 4 s of the motion of the coin. On the graph, label

clearly the time when the coin is at zero speed.

14]

(b) Make use of the graph to calculate,

0) velocity of the coin after 4 s,

[

2

1

(ii) height of the coin above ground after 4 S.

[

2

1

6. A (ennis ball thrown upwards vertically falls back to earth. Which of the following

acceleration-rime graph is correct?

ABC D

acceleration acceleration acceleration nccelcrauou

o

+

_

..:::::

==-.,.

lime 0 time 0 time 0 time

l

]

1. A plane carrying some parachutist starts moving along a runway, in the process of taking off. The table below shows the variation of rime with the distance travelled by the aircraft as it moves down the runway. Time/s

0

1 2 3 4 5 Distance/Ill

0

I

₈

24 52 95 (a) State and explain, (i) if the speed of the plane is increasing. decreasing or remaining constant, (2J

(ii) if the acceleration of the plane is increasing, decreasing or remaining constant. [2]

(b) When the plane reaches an appropriate altitude, a parachutist steps off from the plane.

The parachute opens SOllletime after the start of the fall.

Explain why the initial vertical acceleration of the parachutist is about

10

m/s1. [2]

2. A model rocket is launched from rest. Its engine delivers a constant acceleration of 8.2 m

Is

'

for

a full 5.0 S, after which the fuel is used up. Assuming that the rocket was launched vertically

and that air resistance is not significant, (a) sketch a velocity-time graph in the space on the right to show the variation of velocity to time of the rocket motion from launch until it returns to Earth. [2J (b) find the maximum altitude reached by the rocket. [2] (c) find the total time the rocket is in flight. (2)

'-----'

24

ljnderstundiug Physics through Problem Solving

3. An RSAF pilot is training with his F-16 Fighting Falcon in a secluded desert in the USA. To

pass his training, he must control his aircraft such that it can maintain a stable line of flight. This is necessary so that the launched missile is able to hit a stationary target sonle distance away. His aircraft has a speed of Mach 1.2. When the aircraft is :; km away frorn the target,

the pilot presses the launch button and the missile speeds away from his aircraft at a speed of Mach 1.8 relative to the aircraft. Assume that air resistance is not significant and the condition is windless.

missile F 16 fighling Falcon

(Mach speed refers to how many times the aircraft is travelling faster than the speed of sound. Speed of sound is assumed to be 340 nl/s in this situation.)

(a) Calculate the time taken for the missile to hit the target.

1

2

J

(b) After passing the firsttest, the pilot flies back to base. He flies his aircraft forward at an additional Mach 0.1 per second, but all the while decreasing altitude at a uniform rate for

the next five seconds. Describe the acceleration of the aircraft in both the horizontal and vertical directions in this five seconds.

14]

(c) The aircraft speed is now Mach 1.7. Estimate the lime taken in minutes for him 10 return

to base which is 96 km from his current position, State any assumptionsmade. [21

(d) The pilot is preparing to land his plane with an approach speed of 80 m/s. Upon touch

down, he applies the brakes which quickly slow the plane down to a stop in just 5.0 s.

Calculate the distance the plane travelled on the runway before it comes to a complete

stop. [2]

-4. A toy car initially travelling at a speed of 0.5 ID/s, accelerated to a speed of 3.5

m/

s

.

The

distance covered by the car during this acceleration is 8 m. Determine the acceleration of the

toy car by method of graphical analysis. (5)

5. A traffic stunt is planned for an action movie. The stunt involves the main character being

thrown horizontally away from the top of a moving car that crashes into a railing and landing inside an open-top truck filled with mattresses as it passes by underneath. The diagram below

shows a sketch of the planned stunt with some other important data. main character spot to ruin for is exactly 2 m from back of truck ,,

-

-

--

-

-

-5m

,

J 80 kmIh 30 kmlh ~ critical distance

As the stunt coordinator, you will need to determine the critical distance between the back of

truck and the point of impact. This distance is crucial such that the mechanics of the motion will not result in the main character landing on the road in front or behind the truck!

(Assume that air resistance is not significant and that the speed of the main character after

being thrown off the car is 80 krn/h.) (6]