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April 2012





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ةلولحم نيرامتو حرش تاركذم


ديدعلل ةقباس تاناحتما

هاندأ داوملا نم


ىلع

اناجم ةحاتم

نيروكذملا نيعقوملا

هاندأ

لعجا
كءاقدصأ

كنم نيبيرق
،

لعجا نكل
كئادعأ

أ
برق
.






Chapter 5


APPLYING
NEWTON’S LAWS

April 2012





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= 0






= 0
,





= 0


Solving
N
ewton’s
F
irst
L
aw

P
roblems
:


1.

Draw a very simple sketch of
the physical situation.


2.


Draw a free
-
body diagram for each body that is in equilibrium.


3.


Ask yourself what is interacting with the body by touching it or in any




other way.


4.


Do not show in the free
-
body diagram any forces exerted
by
the body on



any other body.


5.



Choose a set coordinate axes and include them in your
free b
o
dy






diagram.


6.


Find the components of each force along each of the body’s coordinate





axes.


7.


Set the algebraic sum of all
x
-
components of force equal to zero.

In a


separate equation, set
algebraic sum of all
y
-
components
.


8.




If there are two or more bodies, repeat all of the above steps for each




body.


9.




Make sure that
yo
u have as many independent equations as the number





of
unknown quantities.






لولأا
فملا مملست مل اذامل :
امدلنع رلرمل لظ
ناللنلا اا؟تدللجو
ايندلللاو
ن
اراوللتم أللقولا ناللك :
لولأا اللليل
:

ابلللصلا للا ا؟ممللست ملللل اذاللملو
ا

أارلللللللللل

ص دلللللللللق دوللللللللل نلا ألللللللللناك : نالللللللللنلا
ا




5
.1)
Using Newton’s First Law:
Particles in Equilibrium

April 2012





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Solution
:
























Solution
:





















(





)





















































































(









)


(





)














































للا ا؟توللص كللتجوك عتللس نللمل :لولأا
: نانلا اأابااتنلاا
هي عوس يذلا حررممل
لولأا ا تولللص
اكتوللللص عتلللس نلللملو :
هرر ت مل ام اذه : نانلا
تجوك

!دعب






Example 5.1:
(One
-
dimensional equilibrium:
T
ension in a massless rope
)



A gymnast with mass









kg suspends herse
l
f from
the lower end of a
hanging rope
. the upper end of the rope is attached to the g
y
mnasium ceiling
.

W
hat
is
the

gymnast's weight? What force (
magnnitude and directi
on) does the rope exert
on her
? what is the tension at the top of
the rope
? Assume that the mass of the rop
e

itself is negligible .


















(



)
(



)




























































(





)
































(









)















Example 5.2:
(One
-
dimensional equilibrium:
T
ension in a rope with mass
)



Suppose
that in Example 5.1, the weight of the rope is not negligible but is 120 N.
Find the tension at each end of the rope.


April 2012





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Solution
:



































Solution
:







Example
5
.
3
:

(
Two
-
dimensional

equilibrium
)



In
F
ig. 5.3a, a car engine with weight
w

hangs from a chain that is linked at ring
O

to two other chains, one fastened to the ceiling and the other to the wall. Find the
tension in each of the three chains in terms of
w
. the weights of the ring and chains
are negligible.





















































(



)















(



)




























Example
5
.
4
:

(
An inclined plane
)



A car of weight
w

rest on a slanted ramp leading to a car
-
transporter trailer
(
F
ig.

5.4a). Only

a cable running from the trailer to the car prevents the car
from rolling backward off the ramp. (
T
he car

s brakes are off and its
transmission is in neutral.)
F
ind the tension in the cable and the force that the
tracks exert on the car

s tires
.











































(





)















(





)




مللأا فرعي لا نم حورجلا نم رخسي
.

April 2012





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Solution
:






























(







)



















































اذاللللم رايللللس كلللل أيرتللللرا وللللل :لوكللللا
ايرلللللمع لللللصن : لللللجوكلا ا ني عتلللللس

ن
انسف :لوكلا
،

نيترايس كل يرتروس
ا






Example
5
.
5
:

(
Tension over a frictionless pulley
)



Blocks of granite are to be hauled up a



slope out of a quarry, and dirt is to
be dumped into the quarry to fill up old holes. To simplify the process, you
design a system in which a granite block on a cart with steel wheels (weight



,
including both b
lock and cart) is pulled uphill on steel rails by a d
ir
t
-
filled
bucket (weight



, including both dirt and bucket) dropping vertically into the
quarry (
F
ig.

5.5a). How must the weights



and



be related in order for the
system to move with constant speed? Ignore friction in the pulley and wheels
and the weight of the cable
.


April 2012





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Solving
N
ewton’s
S
econd

L
aw

P
roblems
:

1.


Draw a simple sketch of the situation.


2.


For each body you identified, draw a free
-
body diagram that




shows all the forces acting
on

the body.

3.


Label each force with an algebraic symbol for the force
'
s



magnitude.

4.

Choose your
x
-

and y
-
coordinate axes for each body, and show


them

in its free
-
body diagram.

5.

In addition to Newton's second law,











indentify any other



equations you might need.











أللليأر دللل ل للمأ :اللل؟ملأ ريرللصلا
اللي :ملأا ،امللستبم لرللاي للبأ

هاا

ن
ادو ن هنم بم أ نأ أيسن د ل
ا






5
.
2
)
Using Newton's Second Law:



Dynamics of Particles



April 2012





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Solution
:










































































(

)
(



)















Solution
:


































(

)

(



)

(

)












سردملا
ا صاعلا ه ام :
:ذيممتلا
ااااا ءاوه
هنكل

!!
ن
ادج لجعتسم






Example
5
.
6
:

(
Straight
-
line motion with a constant force
)



An iceboat is at rest on a perfectly frictionless horizontal surface. A wind is
blowing (along the direction of the runners) so that 4.0 s
after the iceboat is
released
,

it attains a velocity of 6.0 m/s (about 22 km/h, or 13 mi/h). What
constant horizontal force



does the wind exert on the iceboat? The mass of
iceboat and rider is 200 kg.


Example
5
.
7
:

(
Straight
-
line motion with friction
)



Suppose a constant horizontal friction force with magnitude 100 N opposes the
motion of the iceboat in Example 5.6. In this case, what constant force



must the
wind exert on the iceboat to cause the same consta
nt


-
acceleration













April 2012





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Solution
:


































Solution
:














Example
5
.
8
:

(
Tension in an elevator cable
)



An elevator and its load have

a total mass of 800 kg (Fig. a). The elevator is
originally moving downward at 10.0




; it slows to a stop with constant
accele牡tion in a distance o映 25.0 m. Find the tension
T

in the supporting
cable while the elevator is being brought to rest.


















(




)


(

)



(


)


(



)































(






)








(

)
(








)


























(



)




















Example
5
.
9
:

(
Apparent weight in an accelerating elevator
)



A 50.5
-
kg woman stands on a bathroom scale while riding in the elevator in
Example 5.8
.
What is the reading on the scale?


















(




)











(


)
(





)






















هيخأب ريثك ءرملا
.

April 2012





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Solution
:


































































Solution
:













نلللللمل أللللبجع:ءامكفلا دلللللفأ لاللللق
لاو رال؟نلا لا أارم ه؟جو لسري
رم نسلا ا ولو هبمق لسري
ا






Example
5
.
10
:

(
Acceleration down a hill
)



A toboggan loaded with vacationing students (total weight) slides down a long,
s
now
-
covered slope. The hill slopes at a constant angle



and the toboggan is so
well waxed that the牥 is vi牴u
ally no 晲fction. What is its accele牡tion?

Example
5
.
11
:

(
Two bodies with the same
acceleration
)



You push a 1.00
-
kg food tray through the cafeteria line with a constant 9.0
-
N
force. As the tray moves, it pushes on a 0.50
-
kg carton of milk (
F
ig. a).

T
he
tray and carton slide on a horizontal surface that is so greasy that friction can
be

neglected. Find the acceleration of the tray and carton and the horizontal
force that the tray exerts on the carton.








































































(



)
(



)






























(





)







April 2012





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Solution
:
























لإا حبصي نيتسلا نس ا
ناسن
اولأا أاوا دعب نكلو
ن
ابار
ان






Example
5
.
12
:

(
Two bodies with the same magnitude of acceleration
)



(
Figure
. a)

shows an air
-
track glider with mass



moving on a level,
晲fctionless ai爠 t牡ck

k in the physics lab. The glide爠 is connected to a lab
weight with mass



by a light, 晬exible, nonst牥tching st物ng that passes ove爠
a small 晲fctionless pulley. Find the

accele牡tion o映each body and the tension
in the st物ng.


































(








)











































For m
1
:

























For m
2
:


April 2012





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Whenever two bodies interact by direct contact (touching) of their surfaces,
we describe the interaction in terms of contact forces.

The normal force is
one example of a contact force.




The perpendicular component vector is the
normal force, denoted by





. The
component vector parallel to the surface (and p
erpendicular to





) is the
friction force,
denoted by



. If the surface is frictionless, then




is zero
but there is still a normal force.

The direction of the
friction force is always such as to oppose relative
motion of the two surfaces.

The kind of friction that acts when a body
slides over a surface is called a
kinetic friction force














is a constant called the
coefficient of kinetic
friction




is a pure
number,
without

units
.











ذيملاتلا :رظانلا
، سردملا روس قوا نم نوك ي
مدنااي روسلا مد؟ن :سردملا اكيأر ا لفلا ام

ا






5
.
3
)
Frictional Forces

Kinetic and Static Friction









April 2012





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Solution
:























Solution
:







(



)




s
o











نظي بضارلا
أ
نأ عي تسي هن
هيمع رد ي امم رنكأ لع ي

ا






Example
5
.
13
:

(
Friction in horizontal motion
)



You are trying to move a 500
-


c牡te ac牯ss a level 晬oo爮 To sta牴 the c牡te
moving, you have to pull with a 230
-


ho物zontal 景牣e. Once the c牡te

b牥aks
loose


and sta牴s to move, you can keep it moving at constant velocity with
only 200



what a牥 the coe晦fcients o映static and kinetic 晲fction?









(


)






























Before the crate starts to move
:









(

(


)

)




so
(


)















(


)

















After
the crate starts to move
:









(



)



so


















(


)

















Example
5
.
14
:

(
Static friction can be less than the maximum
)



In
E
xample 5.13, what is the friction force if the crate is at rest on the surface
and a horizontal force of 50


is applied to it?


April 2012





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Solution
:



















Coefficient of rolling friction



,

is the horizontal force needed for constant speed
on a flat surface divided by the upward normal force exerted by the surface. Typical
values of




are 0.002 to 0.003 for steel wheels on steel rails and 0.01 to 0.02 for
rubber tires on concrete.












Solution
:








(





)
(




)







:لولاا
لاوكلا ا ظفلا ليمق انأ
ا
: نانلا
ااذامل
:لولأا
لأ
!أتام لولأا تأرما ن
ينانلاو
تف أمت مل ا
نلآا
ا






Example
5
.
15
:

(
Minimizing kinetic friction
)



In
E
xample 5.13, suppose you try to move the crate by trying a rope around it
and pulling upward on the
rope at an angle of 30


above the ho物zontal. How
ha牤 do you have to pull to keep the c牡te moving with constant velocity?
††
Is this easie爠 o爠 ha牤e爠 than pulling ho物zontally? Assume





and




















(





)



































(

)









(



)


























(


)



















Rolling Friction

Example
5
.
18
:

(
Motion with rolling friction
)



A typical car weighs about 12,000 N (about 2700 lb). If the coefficient of
rolling friction is



= 0.015, what ho物zontal 景牣e is needed to make the ca爠
move with constant speed on a level 牯ad? Neglect air

牥sistance.


April 2012





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Solution
:





















(




)



(

)































(


)
(


)



























(





)
(




)


























،ركاذت أنأو عايذملا عمست لا :هنبلا دلاولا
عمسأ انأ :دلولا
بأ اي ا عايذملا

ا

5
.
4
)
Dynamics of
C
ircular

Motion

motion

Example
5
.
20
:

(
Force in uniform circular motion
)



A sled with a mass of 25.0 kg rests on a horizontal sheet of essentially
frictionless ice. It is

attached by a 5.00
-
m rope to post set in the ice. Once given
a push, the sled revolves uniformly in a circle around the post (Fig.

5.31a). If
the sled makes five complete revolutions every minute,
F
ind the force
F

exerted
on it by the rope.


April 2012





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Solution
:





























رولللللضف لللللمع نولللللجوكتملا ترلللللفي
تامرمل ا ،م؟ئاقدصأ نارق ألا ف
ا

Example
5
.
21
:

(
The conical pendulum
)



An inventor proposes to make a pendulum clock using a pendulum bob with
mass


at the end o映a thin wi牥 o映length L. Instead o映swinging back and
景牴h, the bob moves in a ho物zontal ci牣le with constant speed


, with the
wi牥 making a constant angle
𝛽

with the ve牴ical di牥ction. This system is
called a conical pendulum because
the suspending wi牥 t牡ces out a cone.
Find the tension
F

in the wire and the period
T

(the time for one revolution of
the bob) in terms of

𝛽

.

1


𝛽






















𝛽




𝛽







𝛽





















𝛽










𝛽












𝛽






F牯m
and


1

2

1

2

April 2012





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Solution
:























Solution
:







Example
5
.
22
:

(
Rounding a
flat curve
)



The sports car is rounding a f
l
at, unbanked curve with radius


. I映
the coe晦fcient o映static 晲fction between ti牥s and 牯ad is



, what is
the maximum speed



at which the d物ve爠 can take the cu牶e
without sliding?












































(



)
(



)
(

)















































Example
5
.
23
:

(
Rounding a banked curve
)



For a car traveling at a certain speed, it is possible to bank a curve at just the
right angle so that no friction at all is needed to maintain the car's turning
radius. Then car can safely round the curve even on wet ice. (Bobsled racing
depends on this s
ame idea.) Your engineering firm plans to rebuild the curve
in Example 5.22 so that a car moving at speed


can sa晥ly make the tu牮
even with no 晲fction. At what angle
𝛽

should the cu牶e be banked?






𝛽















𝛽

















𝛽
















𝛽







F牯m and ,



1

2

1

2

هتاذ نع هروصتل ساكعنا ءرملا
ا







April 2012





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Solving Physics exercises






















Solution
:


(

)







































































































(

)
(



)











(

)



مل ليق
ا مومسم أتام كتامف نإ :لوك
لا ا
!ا؟ناسل أضع ديكوتلاب :






Problem

5
.
4
:


An adventurous archaeologist crosses between two rock cliffs
by
slowly going hand over hand along a rope stretched between
the
cliffs. He stops to rest at the middle of the rope (Fig. 5.42). The
rope
will break if the tension in it exceeds 2.50

1



N, and ou爠
he牯


mass is 90.0 kg. ⡡⤠ I映 the angle


is 10.0°, 晩nd the tension in
the
牯pe. ⡢⤠What is the smallest value the angle


can have i映 the
牯pe
is not to b牥ak?














(

)
(



)

(






)
















April 2012





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أـطخ

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Solution
:

(

)



































(

)
(



)














(

)

















































لللجوكلا أللللاق
الللنأ :
ن
ادلللج لللليابلاو لللنرلا اللل؟جوكل
:لليدوم رلار نالباي رايلس ل أيرترا كنأ أممف
نأ نيللممعت اللمكا ،الل؟يمع ظااللف كوللجرأ :الل؟باجوا
! ريالأا رت لا ا ادج أع ترا اهراعسأ أارايسلا






Problem

5
.
8
:


A large wrecking ball is held in place by two
light

steel cables (Fig.
5.43). If the mass
m
of the wrecking ball is 4090 kg, what are
(a)
the tension




in the cable that makes an
angle o映 40° with the
ve牴ical and ⡢⤠ the
tension



in the ho物zontal cable?


April 2012





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,












Solution
:


(

)

























(

)
(



)












(

)
























(

)





















ااامنيللسلا رول؟مج نيللب نلم دلفاو
ديعلس ليا؟ن هل ممي لا اذه

-

للكا
ديعس ناك دفاو
ا

؟تنا امدنع
ا






Problem

5
.
13
:



A solid uniform 45.0
-
kg ball of diameter 32.0 cm
is supported against a vertical frictionless wall
using a thin 30.0
-
cm wire of negligible mass, as
shown in
(
Fig. 5.47
)
.

(a) Make a free
-
body diagram for the ball and
use it to find the tension in the wire.

(b) How hard does the ball push against the wall?

April 2012





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,















Solution
:


(a)



For

block

B
:














































(
b
)


For

block

A
:














































(
c
)


























(
d
)






















and



















































اذإ

؟ا ناتأرما أسما؟ت
كان

نلان أرما مع رماؤم

!







Problem

5
.
14
:


Two blocks, each with weight
w
, are held in
place on a frictionless
incline (Fig.
5.48). In
terms of
w

and the angle


of the incline,
cal
culate the tension in (a) the rope
connecting the blocks and (b) the rope that
connects block A to the
wall. (c) Calculate the
magnitude of the force that the incline exerts
on each block. (d) Interpret your answers for
the cases


= 0 and



= 90°.


April 2012





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net
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,












Solution
:

(a)




















































(

)
(



)













(
b
)

















































(



)
























(






)
(







)















Problem

5
.
16
:


A
125
-
kg (including all the contents) rocket has an engine
that
produces a constant vertical force (the



)

of 1720 N. Inside
this
rocket, a
15.5
-
N electrical power supply rests on the floor.
(a)
Find the acceleration of the rocket. (b) When it has reached an
altitude of 120 m, how hard does the floor push on the power sup
-

ply?

(
Hint
:

Start with a free
-
body di
agram for the power supply.)


نأ ملل؟لا روللي عللنمت نأ عي تللست نلل
نأ عي تلست كنكلو كسأر قوا قمفت
كسأر ا شرعت نأ نم ا؟عنمت
ا






April 2012





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,

































Solution
:


(a)

The free
-
body diagrams for the bricks and counterweight


are given in (Fig. 5.19).

(
b
)

Bricks
:

































































Counterweight
:





























































(





)


(





)





(










)


(






)
(



)
















(
c
)






















(



)

(

)
(







)



















رساتو برافت نأ لضاأ

ن
ادبأ برافت لاأ نم
ا






Problem

5
.
19
:



Figure 5.19

Atwood
's
Machine.
A
15.0
-
kg load of
bricks hangs

from one end of a rope that
passes over a small, frictionless
pulley.


A
28.0
-
kg counterweight
is suspended from
the other end
of the rope, as shown in Fig. 5.51.
The system is released from rest.


(a)
Draw two
free
-
body dia
grams, one for the
load of bricks
and one for the counterweight



(b)
What is the magnitude of the
upward
acceleration of the load
of bricks?

(c) What is the tension
in the rope while the
load is mov
ing? How does the tension com
-

pare to the weight of the load of bricks? To
the weight of the

counterweight?



April 2012





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,




















Solution
:


(a)







































(





)














(
b
)



























(
c
)











means









(


























)


(
d
)









































(




)










(

)
(








)












(

)











(

)
(







)

















(

)


الللم؟م كعادلللبإ لللا رمتلللسا
كتاقا اإ نع سانلا ثدفت
ا

Problem

5
.
24
:


Apparent Weight.

A 550
-
N physics student stands on a
bathroom
scale in an 850
-
kg (including the student) elevator that is supported by a
cable. As the elevator starts moving, the scale reads
450 N. (a) Find the
acceleration of the elevator (magnitude and
direction).

(b) What is the acceleration if the scale reads 670 N?

(c) If the scale reads zero, should the student worry? Explain.

(d) What is the tension in the cable in parts (a) and (c)?


April 2012





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Solution
:


(a)







































































(
b
)































,























(

)
(



)











(
c
)


(i)


















(





)

























(



)
(



)












(ii)




































(



)
(



)












، فيصنلا بم ي ضعبلا
رملأا نم هغارا دعب نكل
ا





Problem

5
.
31
:


A crate of 45.0
-
kg tools rests on a horizontal floor. You exert
a gradually
increasing horizontal push on it and observe that the crate just begins to
move when your force exceeds 313 N. After
that you must reduce your
push to 208 N to keep it moving at a
steady 25.0 cm/s.

(a) What are the coefficients of static and kinetic
friction between the crate
and the floor?

(b) What push must you
exert to give it an acceleration of 1.10 m/




⡣⤠ Suppose you we牥
performing the same experiment on this crate but
were doing it
on th
e moon instead, where the acceleration due to
gravity is
1.62 m
/


.
(i) What magnitude push would cause it to
move?
(ii) What would its acceleration be if you maintained the push in

pa牴 ⡢⤿


April 2012





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,












The normal force has magnitude






































(



)

























ن
اجضان رمنلا نوكي امدنع
ه ست دفاو سمل
ا





Problem

5
.
32
:


An 85
-
N box of oranges is being pushed across a horizontal
floor. As it
moves, it is slowing at a constant rate of 0.90 m/s each
second. The
push force has a horizontal component of 20 N and a
vertical
component of 25 N downward. Calculate the coefficient of
kinetic
friction between the box and floor.



Problem

5
.
33
:


You are lowering two boxes, one on top of the
other, down
the ramp shown in Figure 5.53 by
pulling on a rope parallel to the
surface of the
ramp. Both boxes move together at a constant
speed
of 15.0 cm/s. The coefficient of kinetic
friction between the ramp
and the lower box is
0.444, and the coefficient of static friction
between the two boxes is 0.800. (a) What force
do you ne
ed to exert to accomplish this? (b)
What are the magnitude and direction of the
friction force on the

upper box?



(

)




















[
(





)

[



]





)
]
(

)
(



)


















(

)



























































































































(







)















(

)
(



)












April 2012





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,


























(a)














with








applied to block B gives,












,


































with





applied to block A gives,














































































(
b
)

Block (A)
:

























Block (
B
)
:





















































































(





)










































The acceleration is upward and block B slows down.

كنكل ،أممع امب دعست لا دق
أممع اذإ لاإ دعست نل
ا






Problem

5
.
36
:




5.36.

Consider the system shown in

Fig.
5.54. Block
A

weighs
45.0 N and
block
B

weighs 25.0 N. Once block
B

is set
into down
ward motion, it descends at a
constant speed.

(a) Calculate the coefficient of kinetic
friction between block
A

and the tabletop.

(b) A cat, also of weight 45.0 N, falls
asleep on top of block
A.

If
block
B

is now
set into downward motion, what is its
acceleration
(magnitude and direction)?

April 2012





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Solution
:










































































































































































































































































































كللللسوما دلللليرت كوللللنبلا

،


دلللليرت لللللودلاو
كتايف

،
لبا م لابو نيننلاا ديرت أرملاو

!






Problem

5
.
37
:



(

)






(





)








(

)












Two crates connected by a rope lie on

a horizontal surface
(Fig.
5.55). Crate
A

has
mass



, and crate
B

has mass



. The
coefficient of kinetic friction between each
crate and the surface is



. The crates are pulled
to the right at constant velocity by a hori
zontal
force






. In terms of



,


, and


, calculate
(a) the magni
tude of
the force




and (b) the
tension in the rope connecting the
blocks.
Include the free
-
body diagram or diagrams
you used to
determine each answer.


April 2012





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Solution
:










Solution
:


(a)





















































































(

)

(



)
(

)







(
b
)


























































(

)



















ءالللللل اأ بالللللكترلا للللليرفلا
عادبلإاو قمامل ئيبلا راوت
ا






Problem

5
.
50
:


A flat
(unbanked) curve on a highway has a radius of
220.0 m. A
car rounds the curve at a speed of 25.0 m/s. (a) What is
the minimum
coefficient of friction that will prevent sliding?


( b) Suppos e t he hi ghwa y i s i c y a nd t he c oe f f i c i e nt of f r i c t i on
be t we e n t he t i r e s a nd pa ve me nt i s o nl y o ne
-
t hi r d wha t yo u f o u nd
i n
pa r t ( a ). Wha t s ho u l d be t he ma xi mu m s pe e d o f t he c a r s o i t c a n r o u nd
t he c u r v e s a f e l y?


April 2012





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,
























Solution
:





























































































































































































(




)



(



)
(



)


(

)








































أومت تف
ن
لا لجرلا لظي
وجا خار أتام اذإا ،همأ
ا





Problem

5
.
53
:


In another version of
the
"
Giant Swing
"

the seat is con
nected to two cables as
shown
in Fig.
5.58, one of which is
horizontal. The seat swings in
a
horizontal circle at a rate of
32.0 rpm
(
rev/min). If the
seat weighs
255 N and


a

825
-
N
person is sitting in it, find the
tension in each cable.


April 2012





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-
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,























Solution
:

(a)



































(



)
(

)











(
b
)








































































(

)
(






)
(






)
























(



)








نولو ي نمل أ تمت لا
عي تست نل كنإ ،كل
ا





Problem

5
.
57
:


An airplane flies in a loop (a circular path in a vertical plane)
of radius 150
m. The pilot

s head always points towa牤 the cente爠
o映 the loop. The
speed o映 the ai牰lane is not constant; the ai牰lane
goes slowest at the top o映
the loop and 晡stest at the bottom.

⡡⤠ At
the top o映 the loop, the pilot 晥els weightless. What is the speed o映
the ai牰lane at this point?

⡢⤠At the bottom o映 the loop, the speed
if the airplane is 280 km/h. What
is the apparent weight of the
pilot
at
this point? His t牵e weight is 700 N.


April 2012





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ينورتكللاا ديربلاب وأ




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Solution
:


(
a)


























































(















)










(








)

(
b
)









































(















)










(








)

(
c
)

The largest








(








)

The smallest





(








)


كتجوك قوذ ا نع ت لا
ا؟تارايتاا دفأ أنوا
ا








Problem

5
.
65
:



A block with mass



is placed on an inclined
plane with
slope angle


and is connected to a
second hanging block with mass



by a cord
passing over

a small, frictionless pulley (Fig.
5.62).
The coefficient of static friction is



and
the coefficient of kinetic
friction is


.


( a ) F i n d
t h e ma s s



f o r w h i c h b l o c k



mo v e s u p
t h e
p l a n e a t c o n s t a n t s p e e d o n c e i t i s s e t i n mo t i o n.

( b ) F i n d t h e
ma s s



f o r w h i c h b l o c k





mo v e s d o w n t h e p l a n e a t c o n s t a n t
s p e e d o n c e i t
i s s e t i n m o t i o n.

( c ) F o r w h a t r a n g e o f v a l u e s o f



w i l l t h e b l o c k s
r e m a i n a t r e s t i f t h e y a r e r e l e a s e d f r o m r e s t?


April 2012





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Solution
:

(a)


















































































































[







































(
b
)














(



)
(

)








































































(



)





























ريص لا ديلا مع للاد ليو لا ناسملا
ا






Problem

5
.
66
:


(a) Block A in Fig. 5.63 weighs 60.0 N. The
coefficient of
static friction between the block and
the surface on which it rests is
0.25. The weight w
is 12.0 N and the system is in equilibrium. Find
the
friction force exerted on block A.
(b) Find the
maximum
weight w for which the system will
remain in equilibrium
.


April 2012





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Solution
:

(a)









































































































(
b
)

For block A
:






















































(



)
(



)


















































For block
B
:








































هنلأ ضاملا بفن نفن
هانهركل داع ولو بهذ
ا





Problem

5
.
67
:



Block
A

in Fig.
5.64
weighs
1.20 N and
block
B

weighs
3.60 N. The coefficient
of kinetic friction between all surfaces is

0.300. Find the magnitude of the horizontal
force





necessa特 to
drag block
B

to the
left at constant speed (a) if A rests on
B

and
moves with it (Fig. 5.64a) and (b) if
A

is held at rest (Fig. 5.64b).


April 2012





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أـطخ

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-
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,



















Solution
:










𝛽














𝛽

(


)





𝛽






















𝛽






(

)
(



)

































ا
ردارت امدنع سانلا كبفي نأ مع لمع
هممستت امدنع كنوبفي امك كبصنم
ا






Problem

5
.
98
:


You are riding in a school bus. As the bus rounds a flat curve at constant
speed, a lunch box with mass 0.500 kg, suspended from
the ceiling of the
bus by a string 1.80
m

long, is found to hang at
rest relative to the bus
when the string makes an angle of
30.0°
with the vertical. In this
position the lunch box is 50.0
m

from the
center of curvature of the curve.
What is the speed


o映the bus?