As Newtons Laws and Momentum Questions

8/10/2019 As Newtons Laws and Momentum Questions

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AS Newtons laws of motion and momentum

1. The net force acting on a body is zero. Which of the following quantities must also have zero

magnitude for this body?

A. Momentum B. Velocity

. !"eed #. Acceleration(1)

2. A trolley of mass $.% &g is "ulled along a horizontal table by a force of %.'(.

f o r c e % . ' (

The frictional force acting on the trolley is '.%'(.

The acceleration of the trolley is

A. '.)' m s*+

. B. '.)) m s*+

.

. ).' m s*+

. #. ).) m s*+

.(1)

3. An elevator ,lift- is used to either raise or lower sac&s of "otatoes. n the diagram/ a sac& of

"otatoes of mass $' &g is resting on a scale that is resting on the floor of an accelerating

elevator. The scale reads $+ &g.

$ ' & ge l e v a t o r

s c a l e

The best estimate for the acceleration of the elevator is

A. +.' m s*+downwards. B. +.' m s*+u"wards.

. $.+ m s*+

downwards. #. $.+ m s*+

u"wards.(1)

4. A frictionless trolley of mass mmoves down a slo"e with a constant acceleration a. A second

similar frictionless trolley has mass +m. The acceleration of the second trolley as it moves down

the slo"e is

A..

+

$a

B. a.

. +a. #. 0a.(1)

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5. A light ine1tensible string has a mass attached to each end and "asses over a frictionless "ulley

as shown.

" u l l e y

s t r i n g

m a s s m

m a s s M

The masses are of magnitudesM and m/ where m 2M. The acceleration of free fall isg. The

downward acceleration of the massM is

A.

( )( )mM

gmM

+

. B.

( )

M

gmM

.

.

( )( )mM

gmM

+

. #. ( )mMMg

+ .(1)

6. A frictionless trolley of mass mmoves down a slo"e with a constant acceleration a. A second

similar frictionless trolley has mass +m. The acceleration of the second trolley as it moves down

the slo"e is

A.

.

+

$a

B. a.

. +a. #. 0a.(1)

7. A bloc& on a frictionless horizontal table is attached by a light/ ine1tensible string to an ob3ect 4

of mass mthat hangs vertically as shown below.

M

" u l l e y

4

m a s s m

The "ulley has zero friction and the acceleration of free fall is g. The acceleration of the bloc&

and ob3ect 4 is

A. g. B..g

Mm

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.

.gMmm+ #.

.gm

Mm+

8. The diagram below shows five wooden bloc&s 3oined by inelastic strings. A constant force

accelerates the bloc&s to the right on a frictionless horizontal table.

W 5 6 7 a c c e l e r a t i n gf o r c e

t a b l e

n which string is the tension the greatest?

A. W B. 5

. 6 #. 7(1)

9. A general e1"ression for (ewton8s second law of motion is

F9 t

p

:

:

What condition is a""lied so that the law may be e1"ressed in the formF = ma?

A. The mass mis constant. B. The acceleration ais constant.

. The forceF is constant. #. The direction of the forceF is constant.(1)

10. A constant force of magnitudeFacts on a body. The gra"h shows the variation with time tof the

momentumpof the body.

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+ '

''

$ ' '

; '

< '

0 '

+ ' '

$ ; '

$ < '

$ 0 '

$ + '

t = s

p = & g m s * $

$ + ) 0 % < > ; ? $ '

The magnitude of the forceFis

A. $''' (. B. +'' (.

. +' (. #. '.'% (.(1)

11. A bloc& of massMis held at rest on a horizontal table. A heavy chain is attached to the bloc&

with "art of the chain hanging over the table. The bloc& and the chain can slide without friction.

t a b l e

b l o c &

c h a i n

The bloc& is released. Which oneof the following gra"hs best re"resents the variation with time

tof the s"eed vof the bloc& as it moves on the table?

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A . v

'

B . v

'' t ' t

. v

'

# . v

'' t ' t

(1)

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12. A sphere of mass m strikes a vertical wall and bounces off it, as shown below.

m o m e n t u m p

m o m e n t u m p

B

A

w a l l

The magnitude of the momentum of the s"here 3ust before im"act ispBand 3ust after im"act is

pA.The s"here is in contact with the wall for time t. The magnitude of the average force e1ertedby the wall on the s"here is

A.

( )

t

pp AB *

. B.

( )

t

pp AB +

.

.

( )

mt

pp AB *

. #.

( )

mt

pp AB +

.(1)

13. A ball of weight Wis dro""ed on to the "an of a to" "an weighing balance and rebounds off the

"an.

" a n

' ' . ' '

At the instant that the ball has zero velocity when in contact with the "an/ the scale will read

A. zero. B. a value less than Wbut greater than zero.

. W. #. a value greater than W.

(1)

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14. A block of mass mis pulled along a horizontal, frictionless surface by a force of

magnitudeF. The force makes an angle with the vertical.

F

b l o c &

The magnitude of the acceleration of the bloc& in the horizontal direction "roduced by the force

Fis

A..

m

F

B..

sin

m

F

..

cos

m

F

#..

tan

m

F

(1)

15. A small boat in still water is given an initial horizontal "ush to get it moving. The boat gradually

slows down. Which of the following statements is true for the forces acting on the boat as it

slows down?

A. There is a forward force that diminishes with time.

B. There is a bac&ward force that diminishes with time.

. There is a forward force and a bac&ward force both of which diminish with time.

#. There is a forward force and a bac&ward force that are always equal and o""osite.(1)

16. Mandy stands on a weighing scale inside a lift ,elevator- that accelerates vertically u"wards as

shown in the diagram below. The forces on Mandy are her weight W and the reaction force from

the scaleR.

l i f t

s c a l e

a c c e l e r a t i o n

The reading of the scale is

A. R@ W. B. W.

. R. #. R* W.(1)

17. A truc& collides head on with a less massive car moving in the o""osite direction to the truc&.

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#uring the collision/ the average force e1erted by the truc& on the car isFTand the average

force e1erted by the car on the truc& isF. Which oneof the following statements is correct?

A. FTwill always be greater in magnitude thanF.

B. FTwill always be equal in magnitude toF.

. FTwill be greater in magnitude thanFonly when the s"eed of the car is less than the

s"eed of the truc&.

#. FTwill be equal in magnitude toFonly when the s"eed of the truc& is equal to the s"eed

of the car.

(1)

18. A roc&et accelerates vertically u"wards by e3ecting highs"eed gases vertically downwards as

shown in the diagram below. At the instant shown the weight of the roc&et is Wand the

magnitude of the force the roc&et e1erts on the gases is T.

d i r e c t i o n o f a c c e l e r a t i o n

g a s e s

The magnitude of the net force on the roc&et is

A. W. B. T.

. T@ W. #. T W.(1)

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19. Two spheres of masses m1and m2are moving towards each other along the same

straight-line with speeds v1and v2as shown.

The s"heres collide. Which of the following gives the total change in linear momentum of the

s"heres as a result of the collision?

A. ' B. m$v$@ m+v+

. m$v$ m+v+ #. m+v+ m$v$(1)

20. Two trolleys 4 and C/ are connected by a rubber band. They are at rest on a horizontal surface.

The mass of C is twice that of 4. The trolleys are "ulled a"art so that the band is stretched and

are then released.

The ratioCtrolleyofonacceleratiinitialofmagnitude

4trolleyofonacceleratiinitialofmagnitude

is

A. 0

$

. B. +

$

.

. $. #. +.(1)

21. A roc&et is fired vertically into the air. When the roc&et reaches its ma1imum height/ the roc&ete1"lodes.

What change/ if any/ occurs in the momentum and in the &inetic energy of the roc&et during the

e1"losion?

momentum ineti! ene"#$

A. increases increases

B. increases constant

. constant increases

#. constant constant(1)

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22. A fan and a sail are mounted vertically on a cart that is initially at rest on a horizontal table as

shown in the diagram below.

f a n a i r

s a i l

When the fan is turned on an air stream is blown towards the right and is incident on the sail.

The cart is free to move with negligible resistance forces.

After the fan has been turned on the cart will

A. move to the left and then to the right. B. remain at rest.

. move towards the right. #. move towards the left.(1)

23. A ball of massMhits a wall at s"eed Vnormal to the wall. t rebounds with s"eed vnormal to

the wall as shown below.

w a l l

M

V

v

l e f t r i g h t

What is the magnitude of the change in momentum of the ball and the direction of the force that

the wall e1erts on the ball?

!%an#e in momentum di"e!tion of fo"!e

A. M,V* v- to the right

B. M,V* v- to the left

. M,V@ v- to the right

#. M,V@ v- to the left

(1)

24. A net force of magnitudeFacts on a body for a time t"roducing an im"ulse of magnitude Y.

Which of the following is the magnitude of the rate of change of momentum of the body?

A. F B. Ft

. Y #. Yt

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(1)

25. The diagram below shows a trolley of mass 0.' &g moving on a frictionless horizontal table with

a s"eed of +.' m s*$

. t collides with a stationary trolley also of mass 0.' &g.

0 . ' & g 0 . ' & g

+ . ' m s* $

Which of the following diagrams shows a "ossible outcome?

+ . ' m s * $

+ . ' m s * $

+ . ' m s * $' . ' m s* $

' . ' m s* $

' . ' m s* $

0 . ' & g

0 . ' & g

0 . ' & g

0 . ' & g

0 . ' & g

0 . ' & g

0 . ' & g

0 . ' & g

A . B .

. # .

(1)

26. Two ob3ects collide inelastically. Dor this system of two ob3ects

A. only momentum is conserved.

B. only &inetic energy is conserved.

. both momentum and &inetic energy are conserved.

#. neither momentum nor &inetic energy are conserved.(1)

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27. Two s"heres of masses m$and m+are moving towards each other along the same straightline

with s"eeds v$and v+as shown.

" o s i t i v e d i r e c t i o n

m $ v $ v + m +

The s"heres collide. Which of the following gives the total change in linear momentum of the

s"heres as a result of the collision?

A. ' B. m$v$@ m+v+

. m$v$ m+v+ #. m+v+ m$v$(1)

28. Two s"heres 5 and 6 are moving towards each other along the same straight line with momentaof magnitudeP5andP6res"ectively. The s"heres collide and move off with momentap5and

p6res"ectively/ as illustrated below.

5 56 6

P pP p1 16 6

B e f o r e c o l l i s i o n A f t e r c o l l i s i o n

Whichone of the following is a correct statement of the law of conservation of momentum forthis collision?

A. P5@P69p5@p6 B. P5*P69p5@p6

. P5*P69p5*p6 #. P5@P69p5*p6(1)

29. The engine of a roc&et e3ects gas at high s"eed/ as shown below.

h i g h s " e e d

g a s

r o c & e t

d i r e c t i o n o f

m o t i o n o f r o c & e t

The roc&et accelerates forwards because

A. the momentum of the gas is equal but o""osite in direction to the momentum of the

roc&et.

B. the gas "ushes on the air at the bac& of the roc&et.

. the change in momentum of the gas gives rise to a force on the roc&et.

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#. the e3ected gas creates a region of high "ressure behind the roc&et.(1)

30. An ob3ect of mass mis initially at rest. An im"ulseIacts on the ob3ect. The change in &inetic

energy of the ob3ect is

A..+

+

m

I

B..

+

m

I

. I+m. #. +I

+m.

(1)

31. A stationary metal "late is hanging freely on a string. A steel ball/ travelling horizontally/ hits

the "late. The s"eed of the ball after the collision is less than before/ but still in a horizontal

direction/ as shown below.

b e f o r e c o l l i s i o n

a f t e r c o l l i s i o n

s t r i n g

m e t a l " l a t e

Which oneof the following gives a correct statement/ with a valid reason/ about the ty"e of

collision between the ball and the "late?

&$'e of !ollision eason

A. inelastic The s"here has changed its momentum during the collision.

B. inelastic The s"here has lost &inetic energy during the collision.

. un&nown The change in momentum of the "late during the collision is un&nown.

#. un&nown The &inetic energy of the "late after the collision is un&nown.

(1)

32. The momentum of a system is conserved if

A. no e1ternal forces act on the system.

B. no friction forces act within the system.

. no &inetic energy is lost or gained by the system.

#. the forces acting on the system are in equilibrium.

(1)

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33. A small ball moves with speed v towards another identical ball ! along a line "oining

the centres of the two balls. #all ! is at rest. $inetic energy is conserved in the collision.

4 C a t r e s t

v

Which oneof the following situations is a "ossible outcome of the collision between the balls?

4 C

4 C

4 C

4 C

A . B .

. # .

v v

v ) v

00

v 9 ' v

v v

+ +

(1)

34. A constant force is a""lied to a ball of mass m. The velocity of the ball changes from v$to v+.

The im"ulse received by the ball is

A. m,v+@ v$-. B. m,v+* v$-.

. m,v++@ v$

+-. #. m,v+

+* v$

+-.

(1)

35. A ball of mass +.' &g falls vertically and hits the ground with s"eed >.' ms*$

as shown below.

> . ' m s * $

* $

) . ' m s

before after

The ball leaves the ground with a vertical s"eed ).' ms*$

.

The magnitude of the change in momentum of the ball is

A. zero. B. ;.' (s.

. $' (s. #. +' (s.(1)

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36. A ball of mass mfalls from rest on to a horizontal "late and bounces off it. The magnitudes of

its velocity 3ust before and 3ust after the bounce are v$and v+res"ectively. The variation with

timet of the velocity v of the ball is shown below.

v

v

v

'' t t t t

$

$ + )

+

The magnitude of the net force on the ball is given by which oneof the following?

A. $

$

tmv

B.-*, +)

+

ttmv

.

( )

( )$+

+$

tt

vvm

#.

( )

( )$+

+$

tt

vvm

+

(1)

37. An astronaut in outer s"ace is holding a hammer and drifting at constant velocity. The astronaut

throws the hammer in the o""osite direction to that in which she is drifting.

What change/ if any/ occurs in the total &inetic energy and the total momentum of the astronaut

and hammer?

&otal ineti! ene"#$ &otal momentum

A. unchanged increased

B. unchanged unchanged

. increased increased

#. increased unchanged

(1)

38. Eoe is standing on the surface of a frozen "ond and he throws a ball horizontally. onsideringEoe and the ball together/ which oneof the following correctly describes the change in the

magnitude of the momentum and the change in the &inetic energy of Eoe and the ball

immediately after the ball is thrown?

a#nitude of momentum of *oe and +all ,ineti! ene"#$ of *oe and +all

A. (o change ncreases

B. ncreases ncreases

. (o change (o change

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#. ncreases (o change

(1)

39. A stone on a string is moving in a circle as shown below.

4

C

v

v

y * d i r e c t i o n

x * d i r e c t i o n

At "oint 4/ the stone of mass mhas s"eed vin theydirection. A quarter of a revolution later/ the

stone at "oint C has s"eed vin thexdirection.

What is the change/ in theydirection onl$/ of the magnitude of the momentum of the stone?

A. zero B. mv

. mv+ #. 2mv

(1)

40. When a body is accelerating/ the resultant force acting on it is equal to its

A. change of momentum. B. rate of change of momentum.

. acceleration "er unit of mass. #. rate of change of &inetic energy.(1)

41. Which of the following quantities are conserved in an inelasti! collision between two bodies?

&otal linea" momentum of t%e +odies &otal ineti! ene"#$ of t%e +odies

A. yes yes

B. yes no

. no yes

#. no no

(1)

42. Two bloc&s having different masses slide down a frictionless slo"e.

Which of the following correctly com"ares the accelerating force acting on each bloc& and also

the accelerations of the bloc&s down the slo"e?

A!!ele"atin# fo"!e A!!ele"ation

A. Fqual Fqual

B. Fqual #ifferent

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. #ifferent Fqual

#. #ifferent #ifferent

(1)

43. A ball of mass m/ travelling in a direction at right angles to a vertical wall/ stri&es the wall with

a s"eed v$. t rebounds at right angles to the wall with a s"eed v+. The ball is in contact with the

wall for a time :t. The magnitude of the force that the ball e1erts on the wall is

A. t

vvm

++$

. B. m,v$@ v+-:t.

. t

vvm

+$

. #. m,v$* v+-:t.

(1)

44. A ball is held at rest at "oint 5 and is then released. t dro"s on to a flat horizontal surface andrebounds to a ma1imum height at "oint 6.

" o i n t 5

" o i n t 6

b e f o r e a f t e r

Which oneof the following gra"hs best shows the variation with time tof the momentumpof

the ball as it moves between "oint 5 and "oint 6?

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A . B .

. # .

p

t'

'

p

t'

'

p

t'

'

p

t'

'

(1)

45. The velocity of a body of mass mchanges by an amount vin a time t. The im"ulse given to

the body is equal to

A. mt. B..

t

v

..

t

vm

#. mv.

(1)

46. Which of the following quantities are conserved in an inelastic collision in an isolated system of

two ob3ects?

-inea" momentum of s$stem ,ineti! ene"#$ of s$stem

A. 6es 6es

B. 6es (o

. (o 6es

#. (o (o

(1)

47. The velocity of a "article is changing. The rate of change of the momentum of the "article is

equal to the

A. acceleration of the "article. B. net force acting on the "article.

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. wor& done on the "article. #. change in &inetic energy of the "article.(1)

48. A toy cannon is mounted vertically on a cart. The cart is moving along a straightline with

constant s"eed. A s"ring inside the cannon shoots a ball vertically u"wards.

c a n n o n

c a r t

(o resistance forces act on the cart and on the ball. Which oneof the following statements is

true about the "osition where the ball will land?

A. The "osition de"ends on the s"eed of the cart.

B. The ball will land behind the cannon.

. The ball will land inside the cannon.

#. The ball will land in front of the cannon.(1)

49. A body of weight +Whangs vertically from a string attached to a body of weight W. Weight Wis

released and both bodies fall vertically.

W

+ W

Air resistance may be neglected. What is the tension in the string during the fall?

A. 7ero B. W

. +W #. )W(1)

50. The gra"h below shows the variation with time tof the magnitude of the net forceFacting on a

body moving along a straightline.

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F

'' t

The shaded area re"resents

A. the total wor& done byF.

B. the change in the &inetic energy of the body.

. the change in the momentum of the body.

#. the change in the velocity of the body.(1)

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51. A particle moves under the influence of a forceF. The graph below shows the variation

of the forceFwith the distance dmoved by the particle.

F

' ' d

The shaded area is equal to

A. the average value ofF. B. the im"ulse "roduced byF.

. the wor& done byF. #. the "ower "roduced byF.(1)

52. The gra"h below shows the variation with loadFof the lengthLof a s"ring.

F

'' L L L

F

F

+

$

$ +

Which of the following e1"ressions gives the force "er unit e1tension ,the s"ring constant- of

the s"ring?

A. $

$

L

F

B. +

+

L

F

.

( )

+

$+

L

FF

#.

( )

$+

$+

LL

FF

(1)

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53. !and falls vertically on a conveyor belt at a rate of m&g s*$

.

s a n d

b e l tv

n order to &ee" the belt moving at constant s"eed vthe horizontal force that must be e1erted on

the belt is

A. mv. B .mv+$

. mv+. #.

.+

+

$ mv

(1)

54. A roc&et is moving through s"ace. The roc&et engine e3ects a mass mof e1haust gases in time t.The s"eed of the e1haust gases/ relative to the roc&et/ is vas shown below.

e 1 h a u s t g a s e s / s " e e d v

r o c & e t

d i r e c t i o n o f m o t i o n

o f r o c & e t

Which of the following e1"ressions is the magnitude of the force e1erted on the roc&et by the

e1haust gases?

A. mv B. mv+

. mvt #. tmv

(1)

55. Two unequal masses M and m are 3oined by a light ine1tensible string. The string "asses over a

light frictionless "ulley as shown.

M m

" u l l e y

The masses accelerate when released.

Which diagram is the correct freebody diagram for the two masses?

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MM m m M m M m

A . B . . # .

(1)

56. An ob3ect of massMis sus"ended from a s"ring. The e1tension of the s"ring is e. The same

ob3ect is sus"ended from an identical s"ring on the Moon where the acceleration of free fall is

less than that on Farth. Which of the following is correct?

ass of t%e o+e!t on oon /tension of s'"in# on oon

A. M e

B. less thanM less than e

. M less than e

#. less thanM e

(1)

57. An im"ulseIacts on a body of mass mthat is initially at rest. What is the distance moved by the

body in a time tafter the im"ulse has been delivered?

A. m

It

B. t

Im

. m

I

#. It(1)

58. This question is about momentum and energy.

,a- #efine impule !" a "!#$eand state the relation between im"ulse and momentum.

definition

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

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

relation

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

.....................................................................................................................................(2)

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,b- By a""lying (ewton8s laws of motion to the collision of two "articles/ deduce that

momentum is conserved in the collision.

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

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

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

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

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

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

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

.....................................................................................................................................(5)

,c- n an e1"eriment to measure the s"eed of a bullet/ the bullet is fired into a "iece of

"lasticine sus"ended from a rigid su""ort by a light thread.

+ 0 c m

s " e e d Vb u l l e t

" l a s t i c i n e

The s"eed of the bullet on im"act with the "lasticine is V. As a result of the im"act/ the

bullet embeds itself in the "lasticine and the "lasticine is dis"laced vertically through a

height of +0 cm. The mass of the bullet is %.+G$'*)

&g and the mass of the "lasticine is

'.); &g.

,i- gnoring the mass of the bullet/ calculate the s"eed of the "lasticine immediately

after the im"act.

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

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

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

...........................................................................................................................(2)

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,ii- #educe that the s"eed Vwith which the bullet stri&es the "lasticine is about

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59. Momentum

,a- !tate the law of conservation of momentum.

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

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

...................................................................................................................................(2)

,b- An ice hoc&ey "uc& collides with the wall of an ice rin&. The "uc& is sliding along a line

that ma&es an angle of 0%to the wall.

w a l l

i c e r i n &

d i r e c t i o n o f " u c &b e f o r e c o l l i s i o n

d i r e c t i o n o f " u c &a f t e c o l l i s i o nr

0 % 0 %

The collision between the wall and the "uc& is "erfectly elastic.

,i- !tate what is meant by an elati$ $!llii!%.

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

.........................................................................................................................(1)

,ii- #iscuss how the law of conservation of momentum a""lies to this situation.

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

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

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

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

(2)

,c- The diagram below is a scale diagram that shows the vector re"resenting the momentum

of the "uc& before collision.

!caleK $.' cm 9 '.$' ( s

28


29/61

By adding a""ro"riate vectors to the diagram/ deduce that the magnitude of the change in

momentum of the "uc& as a result of the collision is '.>$ ( s.(4)

,d- The s&etchgra"h below shows the variation with time tof the forceFe1erted by the wall

on the "uc&.

F

'

' t

The total contact time is $+ ms. Fstimate/ e1"laining your reasoning/ the ma1imum force

e1erted by the wall on the "uc&.

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

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

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

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

...................................................................................................................................(3)

(&otal 12 ma"s)

60. This question is about momentum and energy.

,a- #efine impule !" a "!#$eand state the relation between im"ulse and momentum.

definitionK

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

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

relationK

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

.....................................................................................................................................(2)

29


30/61

,b- By a""lying (ewton8s laws of motion to the collision of two "articles/ deduce that

momentum is conserved in the collision.

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

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

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

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

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

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

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

.....................................................................................................................................(5)

,c- n an e1"eriment to measure the s"eed of a bullet/ the bullet is fired into a "iece of

"lasticine sus"ended from a rigid su""ort by a light thread.

+ 0 c m

s " e e d Vb u l l e t

" l a s t i c i n e

The s"eed of the bullet on im"act with the "lasticine is V. As a result of the im"act/ the

bullet embeds itself in the "lasticine and the "lasticine is dis"laced vertically through a

height of +0 cm. The mass of the bullet is %.+G$'*)

&g and the mass of the "lasticine is

'.); &g.

,i- gnoring the mass of the bullet/ calculate the s"eed of the "lasticine immediately

after the im"act.

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

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

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

...........................................................................................................................(2)

30


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,ii- #educe that the s"eed Vwith which the bullet stri&es the "lasticine is about

$


32/61

,ii- #educe that the u"ward force that the e3ected water e1erts on the roc&et is

a""ro1imately +.' (. F1"lain your wor&ing by reference to (ewton8s laws of

motion.

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

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

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

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

.........................................................................................................................(4)

,iii- alculate the time delay between o"ening the nozzle and the roc&et achieving lift

off.

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

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

.........................................................................................................................(2)

(&otal 10 ma"s)

62. ollisions

A large metal ball is hung from a crane by means of a cable of length %.; m as shown below.

c r a n ec a b l e

% . ; m

w a l l

m e t a l b a l l

n order to &noc& down a wall/ the metal ball of mass )%' &g is "ulled away from the wall and

then released. The crane does not move. The gra"h below shows the variation with time tof the

s"eed vof the ball after release.

32


33/61

v

=

m

s*

$

' . ' ' . + ' . 0 ' . < ' . ; $ . ' $ . + $ . 0

t = s

) . '

+ . '

$ . '

' . '

The ball ma&es contact with the wall when the cable from the crane is vertical.

,a- Dor the ball 3ust before it hits the wall/

,i- state why the tension in the cable is not equal to the weight of the ballL

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

.........................................................................................................................(1)

,ii- by reference to the gra"h/ estimate the tension in the cable. The acceleration of free

fall is .; m s*+

.

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

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

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

.........................................................................................................................(3)

33


34/61

,b- Hse the gra"h to determine the distance moved by the ball after coming into contact with

the wall.

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

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

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

...................................................................................................................................(2)

,c- Dor the collision between the ball and the wall/ calculate

,i- the total change in momentum of the ballL

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

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

.........................................................................................................................(2)

,ii- the average force e1erted by the ball on the wall.

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

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

.........................................................................................................................(2)

,d- ,i- !tate the law of conservation of momentum.

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

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

.........................................................................................................................(2)

,ii- The metal ball has lost momentum. #iscuss whether the law a""lies to this

situation.

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

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

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

.........................................................................................................................(2)

34


35/61

,e- #uring the im"act of the ball with the wall/ $+%of the total &inetic energy of the ball is

converted into thermal energy in the ball. The metal of the ball has s"ecific heat ca"acity

0%' E &g*$

I*$

. #etermine the average rise in tem"erature of the ball as a result of

colliding with the wall.

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

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

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

...................................................................................................................................(4)

(&otal 18 ma"s)

63. ollisions

A large metal ball is hung from a crane by means of a cable of length %.; m as shown below.

n order to &noc& down a wall/ the metal ball of mass )%' &g is "ulled away from the wall and

then released. The crane does not move. The gra"h below shows the variation with time tof the

s"eed vof the ball after release.

v

=

m

s*

$

' . ' ' . + ' . 0 ' . < ' . ; $ . ' $ . + $ . 0

t = s

) . '

+ . '

$ . '

' . '

35


36/61

The ball ma&es contact with the wall when the cable from the crane is vertical.

,a- Dor the ball 3ust before it hits the wall/

,i- state why the tension in the cable is not equal to the weight of the ballL

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

.........................................................................................................................(1)

,ii- by reference to the gra"h/ estimate the tension in the cable. The acceleration of free

fall is .; m s*+

.

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

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

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

.........................................................................................................................(3)

,b- Hse the gra"h to determine the distance moved by the ball after coming into contact with

the wall.

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

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

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

...................................................................................................................................(2)

,c- alculate the total change in momentum of the ball during the collision of the ball with

the wall.

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

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

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

(2)

,d- ,i- !tate the law of conservation of momentum.

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

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

.........................................................................................................................(2)

36


37/61

,ii- The metal ball has lost momentum. #iscuss whether the law a""lies to this

situation.

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

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

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

.........................................................................................................................(2)

,e- #uring the im"act of the ball with the wall/ $+%of the total &inetic energy of the ball is

converted into thermal energy in the ball. The metal of the ball has s"ecific heat ca"acity

0%' E &g*$

I*$

. #etermine the average rise in tem"erature of the ball as a result of

colliding with the wall.

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

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

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

...................................................................................................................................(4)

(&otal 16 ma"s)

64. This question is about collisions and radioactive decay.

,a- ,i- #efine li%ea# m!me%tum a%d impule.

inear momentumK ..........................................................................................

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

m"ulseK ..........................................................................................

..........................................................................................(2)

,ii- !tate the law of conservation of momentum.

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

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

...........................................................................................................................(2)

,iii- Hsing your definitions in ,a-,i-/ deduce that linear momentum is constant for an

ob3ect in equilibrium.

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

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

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

37


38/61


39/61

...........................................................................................................................(2)

The halflife of the decay of radon++' is %% s.

,d- ,i- F1"lain why it is not "ossible to state a time for the life of a radon++' nucleus.

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

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

...........................................................................................................................(2)

,ii- #efine (al")li"e.

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

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

...........................................................................................................................(2)

A sam"le of radon++' has an initial activityA'.

,iii- On the a1es below/ draw a gra"h to show the variation with timet of the activityA

for timet 9 ' to timet 9 $;' s.

A

A '

'' 0 ' ; ' $ + ' $ < ' + ' '

t =(2)

39


40/61

%iv& 'se your graph to determine the activity, in terms ofA(, of the sample of radon at timet

) 12( s. Also, estimate the activity, in terms ofA(, at timet ) **( s.

Activity at timet 9 $+' s K PPPPPPPP................................................

Activity at timet 9 ))' s K PPPPPPPPP............................................(2)

(&otal 25 ma"s)

65. This question is about the collision between two railway truc&s ,carts-.

,a- #efine li%ea# m!me%tum.

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

.....................................................................................................................................(1)

n the diagram below/ railway truc& A is moving along a horizontal trac&. t collides with a

stationary truc& B and on collision/ the two 3oin together. mmediately before the collision/ truc&

A is moving with s"eed %.' ms*$

. mmediately after collision/ the s"eed of the truc&s is v.

BA

% . ' m s * $

m m e d i a t e l y b e f o r e c o l l i s i o n

m m e d i a t e l y a f t e r c o l l i s i o n

BA

v

The mass of truc& A is ;'' &g and the mass of truc& B is $+'' &g.

,b- ,i- alculate the s"eed v immediately after the collision.

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

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

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

...........................................................................................................................(3)

,ii- alculate the total &inetic energy lost during the collision.

40


41/61

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

...........................................................................................................................(2)

,c- !uggest what has ha""ened to the lost &inetic energy.

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

.....................................................................................................................................(2)

(&otal 8 ma"s)

66. This question is about an e1"eriment designed to investigate (ewton8s second law.

n order to investigate (ewton8s second law/ #avid arranged for a heavy trolley to be

accelerated by small weights/ as shown below. The acceleration of the trolley was recorded

electronically. #avid recorded the acceleration for different weights u" to a ma1imum of ).' (.

Qe "lotted a gra"h of his results.

h e a v y t r o l l e ya c c e l e r a t i o n

" u l l e y

w e i g h t

,a- #escribe the gra"h that would be e1"ected if two quantities are "ro"ortional to one

another.

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

.....................................................................................................................................(2)

41


42/61

%b& +avids data are shown below, with uncertainty limits included for the value of the

weights. +raw the best-fit line for these data.

$ . 0 '

$ . + '

$ . ' '

' . ; '

' . < '

' . 0 '

' . + '

' . ' '' . ' ' ' . % ' $ . ' ' $ . % ' + . ' ' + . % '

w e i g h t = (

a c c e l e r a t i o n= m s * +

,c- Hse the gra"h to

,i- e1"lain what is meant by aytemati$error.

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

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

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

...........................................................................................................................(2)

,ii- estimate the value of the frictional force that is acting on the trolley.

...........................................................................................................................(1)

,iii- estimate the mass of the trolley.

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

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

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

...........................................................................................................................(2)

(&otal 9 ma"s)

67. This question is about conservation of momentum and conservation of energy.

42


43/61

,a- !tate (ewton8s third law.

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

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

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

(1)

,b- !tate the law of conservation of momentum.

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

.....................................................................................................................................(2)

The diagram below shows two identical balls A and B on a horizontal surface. Ball B is at rest

and ball A is moving with s"eed Valong a line 3oining the centres of the balls. The mass of each

ball isM.

A B

v

B e f o r e c o l l i s i o n

#uring the collision of the balls/ the magnitude of the force that ball A e1erts on ball B is FAB

and the magnitude of the force that ball B e1erts on ball A isFBA.

,c- On the diagram below/ add labelled arrows to re"resent the magnitude and direction of

the forcesFABandFBA.

A B# u r i n g t h e c o l l i s i o n

(3)

The balls are in contact for a time :t. After the collision/ the s"eed of ball A is @vAand the s"eed

of ball B is @vBin the directions shown.

A BA f t e r t h e c o l l i s i o n

v A v B

As a result of the collision/ there is a change in momentum of ball A and of ball B.

,d- Hse (ewton8s second law of motion to deduce an e1"ression relating the forces acting

during the collision to the change in momentum of

43


44/61

,i- ball B.

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

...........................................................................................................................(2)

,ii- ball A.

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

...........................................................................................................................(2)

,e- A""ly (ewton8s third law and your answers to ,d-/ to deduce that the change in

momentum of the system ,ball A and ball B- as a result of this collision/ is zero.

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

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

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

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

.....................................................................................................................................(4)

,f- #educe/ that if &inetic energy is conserved in the collision/ then after the collision/ ball A

will come to rest and ball B will move with s"eed V.

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

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

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

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

.....................................................................................................................................(3)

(&otal 17 ma"s)

68. This question is about momentum and the &inematics of a "ro"osed 3ourney to Eu"iter.

,a- !tate the law of conservation of momentum.

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

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

.....................................................................................................................................(2)

44


45/61

A solar propulsion engine uses solar power to ionize atoms of enon and to accelerate

them. As a result of the acceleration process, the ions are e"ected from the spaceship with a speed of

*.( 1(/m s

01.

1 e n o n i o n ss " e e d 9 ) . ' G $ ' m s

0 +* $s " a c e s h i "m a s s 9 % . 0 G $ ' & g

,b- The mass ,nucleon- number of the 1enon used is $)$. #educe that the mass of one ion of

1enon is +.+ G $'*+%

&g.

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

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

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

.....................................................................................................................................(2)

,c- The original mass of the fuel is ;$ &g. #educe that/ if the engine e3ects >> G $'$;

1enon

ions every second/ the fuel will last for $.% years. ,$ year 9 ).+ G $'>s-

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

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

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

.....................................................................................................................................(2)

,d- The mass of the s"aceshi" is %.0 G $'+&g. #educe that the initial acceleration of the

s"aceshi" is ;.+ G $'*%

m s*+

.

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

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

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

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

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

.....................................................................................................................................(5)

45


46/61

The gra"h below shows the variation with timet of the acceleration aof the s"aceshi". The

solar "ro"ulsion engine is switched on at timet 9 ' when the s"eed of the s"aceshi" is $.+ G $')

m s*$

.

a = G $ ' m s* %

>

* +

t = G $ ' s

$ ' . '

? . %

? . '

; . %

; . '' . ' $ . ' + . ' ) . ' 0 . ' % . ' < . '

,e- F1"lain why the acceleration of the s"aceshi" is increasing with time.

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

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

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

.....................................................................................................................................(2)

,f- Hsing data from the gra"h/ calculate the s"eed of the s"aceshi" at the time when the

1enon fuel has all been used.

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

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

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

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

.....................................................................................................................................(4)

46


47/61

,g- The distance of the s"aceshi" from Farth when the solar "ro"ulsion engine is switched on

is very small com"ared to the distance from Farth to Eu"iter. The fuel runs out when the

s"aceshi" is a distance of 0.> G $'*$$

m from Eu"iter. Fstimate the total time that it would

ta&e the s"aceshi" to travel from Farth to Eu"iter.

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

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

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

.....................................................................................................................................(2)

(&otal 19 ma"s)

69. This question is about a balloon used to carry scientific equi"ment.

The diagram below re"resents a balloon 3ust before ta&eoff. The balloon8s bas&et is attached to

the ground by two fi1ing ro"es.

b a l l o o n

b a s & e t

f i 1 i n g r o " e f i 1 i n g r o " e

% ' % '

g r o u n d

There is a forceFvertically u"wards of +.$% $')( on the balloon. The total mass of the

balloon and its bas&et is $.% $'+&g.

,a- !tate the magnitude of the resultant force on the balloon when it is attached to the ground.

...................................................................................................................................(1)

47


48/61

,b- alculate the tension in eit%e"of the fi1ing ro"es.

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

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

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

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

...................................................................................................................................(3)

,c- The fi1ing ro"es are released and the balloon accelerates u"wards. alculate the

magnitude of this initial acceleration.

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

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

...................................................................................................................................(2)

,d- The balloon reaches a terminal s"eed $' seconds after ta&eoff. The u"ward forceF

remains constant. #escribe how the magnitude of air friction on the balloon varies during

the first $' seconds of its flight.

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

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

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

...................................................................................................................................(2)

(&otal 8 ma"s)

70. inear momentum

,a- #efine

,i- li%ea# m!me%tumL

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

.........................................................................................................................(1)

,ii- impule.

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

.........................................................................................................................(1)

48


49/61

%b& plain whether momentum and impulse are scalar or vector uantities.

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

...................................................................................................................................(1)

,c- By reference to (ewton8s laws of motion/ deduce that when two "articles collide/momentum is conserved.

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

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

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

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

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

...................................................................................................................................(5)

A rubber ball of mass %' g is thrown towards a vertical wall. t stri&es the wall at a horizontal

s"eed of +' m s*$

and bounces bac& with a horizontal s"eed of $; m s*$

as shown below.

s " e e d b e f o r e = + ' m s* $

s " e e d a f t e r = $ ; m s* $

The ball is in contact with the wall for '.';' s.

,d- ,i- alculate the change in momentum of the ball.

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

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

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

.........................................................................................................................(2)

ii- alculate the average force e1erted by the ball on the wall.

49


50/61


51/61

,i- the total momentum of the system is conserved in the collisionL

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

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

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

(2)

,ii- the collision is elastic.

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

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

.........................................................................................................................(2)

,b- alculate the magnitude of the average force e1"erienced by train carriage B.

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

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

...................................................................................................................................(3)

(&otal 7 ma"s)

72. Bloc& on an inclined "lane

A bloc& is held stationary on a frictionless inclined "lane by means of a string as shown below.

s t r i n g

b l o c &

i n c l i n e d " l a n e

,a- ,i- On the diagram draw arrows to re"resent the three forces acting on the bloc&.

(3)

,ii- The angle of inclination of the "lane is +%. The bloc& has mass +.< &g. alculate

the force in the string. 6ou may assume thatg9 .; m s*+

.

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

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

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

.........................................................................................................................(2)

,b- The string is "ulled so that the bloc& is now moving at a constant s"eed of '.;% m s*$

u"

51


52/61

the inclined "lane.

,i- F1"lain why the magnitude of the force in the string is the same as that found in ,a-

,ii-.

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

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

.........................................................................................................................(2)

,ii- alculate the "ower required to move the bloc& at this s"eed.

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

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

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

(2)

,iii- !tate the rate of change of the gravitational "otential energy of the bloc&. F1"lain

your answer.

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

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

.........................................................................................................................(2)

(&otal 11 ma"s)

73. This question is about (ewton8s laws of motion/ the dynamics of a model helico"ter and the

engine that "owers it.

,a- F1"lain how (ewton8s third law leads to the conce"t of conservation of momentum in the

collision between two ob3ects in an isolated system.

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

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

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

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

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

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

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

...................................................................................................................................(4)

52


53/61

%b& The diagram illustrates a model helicopter that is hovering in a stationary position.

r o t a t i n gb l a d e s

d o w n w a r d m o t i o n o f a i r

' . > ' m' . > ' m

The rotating blades of the helico"ter force a column of air to move downwards. F1"lain

how this may enable the helico"ter to remain stationary.

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

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

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

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

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

...................................................................................................................................(3)

,c- The length of each blade of the helico"ter in ,b- is '.>' m. #educe that the area that the

blades swee" out as they rotate is $.% m+. ,Area of a circle 9 #

+-

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

...................................................................................................................................(1)

,d- Dor the hovering helico"ter in ,b-/ it is assumed that all the air beneath the blades is

"ushed vertically downwards with the same s"eed of 0.' m s*$

. (o other air is disturbed.

The density of the air is $.+ &g m*)

.

alculate/ for the air moved downwards by the rotating blades/

,i- the mass "er secondL

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

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

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

.........................................................................................................................(2)

,ii- the rate of change of momentum.

53


54/61

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

.........................................................................................................................(1)

,e- !tate the magnitude of the force that the air beneath the blades e1erts on the blades.

...................................................................................................................................(1)

,f- alculate the mass of the helico"ter and its load.

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

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

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

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

(2)

,g- n order to move forward/ the helico"ter blades are made to incline at an angle to the

horizontal as shown schematically below.

While moving forward/ the helico"ter does not move vertically u" or down. n the s"ace

"rovided below draw a free body force diagram that shows the forces acting on the

helico"ter blades at the moment that the helico"ter starts to move forward. On your

diagram/ label the angle .

(4)

,h- Hse your diagram in ,g- o""osite to e1"lain why a forward forceFnow acts on the

helico"ter and deduce that the initial acceleration aof the helico"ter is given by

a9gtan

wheregis the acceleration of free fall.

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

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

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

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

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

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

...................................................................................................................................(5)

54


55/61

%i& 3uggest why, even though the forward forceFdoes not change, the acceleration of the

helicopter will decrease to zero as it moves forward.

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

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

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

...................................................................................................................................(2)

(&otal 25 ma"s)

74. This question is about the brea&ing distance of a car and s"ecific heat ca"acity.

,a- A car of mass


56/61

,c- The same bra&ing force is a""lied to each rear wheel of the car. The effective mass of

each bra&e is %.+ &g with a s"ecific heat ca"acity of '' E &g*$

I*$

. Fstimate the rise in

tem"erature of a bra&e as the car comes to rest. !tate oneassum"tion that you ma&e in

your estimation.

estimateK

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

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

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

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

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

assum"tionK

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

.....................................................................................................................................(4)

(&otal 9 ma"s)

75. Two identical s"rings A and B each have a force constant ,force "er unit e1tension- of +.%(cm*

$. One end of each s"ring is attached to a trolley and the other ends are attached to rigid

su""orts/ as shown.

s u " " o r t t r o l l e y

s " r i n g A s " r i n g B

The s"rings are horizontal and/ when the trolley is at rest/ the e1tension of each s"ring is ).' cm.

The trolley is dis"laced $.+ cm to the right.

s u " " o r t t r o l l e y

s " r i n g B

d i s " l a c e m e n t $ . + c m

s " r i n g A

,a- alculate the magnitude of the force on the trolley due to

,i- s"ring A alone.

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

...........................................................................................................................(2)

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,ii- s"ring B alone.

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,b- The trolley is released. #etermine the initial acceleration of the trolley of mass '.>% &g.

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(&otal 5 ma"s)

76. This question is about momentum.

,a- #efine

,i- li%ea# m!me%tum.

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,ii- impule.

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,b- n a ride in a "leasure "ar&/ a carriage of mass 0%' &g is travelling horizontally at a s"eed

of $; m s*$

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As Newtons Laws and Momentum Questions