Machine Design and Shop Practice (Problems and Elements)
MACHINE DESIGN AND SHOP PRACTICE PROBLEMS ELEMENTS (with answers and solutions 1.
This radial radial distance distance in a gear is is measured measured between between the addendum addendum and and dedendum dedendum circle, circle, and is the sum of the the addendum addendum and the dedendum !ow do "ou call this distance a) #ddendum b) $hole depth c) $or%ing depth d) Space width #nswer& b) $hole depth
'.
$hat is the the polar polar section section modulus modulus of a solid solid shaft shaft with with a diamete diameterr of 11. 11. mm a) '*.+ cm b) '*.+ cm c) '+.* cm
d) '+.* cm-
#nswer& c) '+.* cm
Solution& .
Z j=
J 2 J π 3 π = = D = ( 10.16 )3=205.9 cm 3 c D 16 16
This minimum minimum distance is measured between the nondri/ing side of a tooth tooth and the ad0acent side of the mating mating tooth. t is the amount b" which the width of a tooth space e2ceeds the thic%ness of the engaging tooth measured on the pitch circle. $hat is this distance a) 3ircular pitch b) $hole depth c) 4ac%lash d) Space width #nswer& c) 4ac%lash
-.
$ith $ith the water interr interruptio uptions ns pre/ailin pre/ailing g in "our town, "ou ha/e been been as%ed to design an upright upright c"lindr c"lindrical ical water water tan% meters in diameter and meters high, /ented, and to be filled completel" with water. Determine the minimum thic%ness thic%ness of the tan% plate if the stress is limited to - Mpa. a) . mm b) -.- mm c) +.+ mm d) 5.5 mm #nswer& b) Thic%ness, t 6 -.- mm
kPa Solution& p= ρ gh=( 1000 ) ( 9.8066 ) ( 6 )=58 839.6 Pa=58.8396 kPa pD ( 58.8396 ) ( 6 ) t = = =0.00441 m = 4.41 mm 2 s t 2 ( 40 000 ) +.
$hat is the algebrai algebraicc difference difference between between the the ma2imum ma2imum limit limit and the correspondi corresponding ng basic si7e si7e a) 8undamental de/iation b) 9pper de/iation c) :ower de/iation d) Tolerance #nswer& b) 9pper De/iation
.
# steel steel shaft 1.;+ 1.;+ inches in diamete diameterr transmits transmits - !p at 15 rpm. rpm. #ssumin #ssuming g a modulus of rigidit rigidit" " of 1' 2 1 psi, find the torsional deflection of the shaft in degrees per foot length. a) .; b) .; c) . d) .1
Solution&
;.
θ T 32 T = = = L JG πD 4 G
32
(
63 000 Hp
n 4
π D G
) [ 32
=
63000 ( 40 ) 1800
]
π ( ( 1.75 ) ( 12 x 10 6 ) 4
= 0.00013 radian =0.0073
$hat is the algebrai algebraicc difference difference between between the the minimum minimum limit limit and the correspond corresponding ing basic basic si7e a) 8undamental de/iation b) 9pper de/iation c) :ower de/iation d) Tolerance #nswer& c) :ower De/iation 1
Machine Design and Shop Practice (Problems and Elements)
5.
# helical helicalcoil coil spring spring has a mean coil coil diameter diameter of 1 inch and a wire dia diamete meterr of 1?5 inch. Determi Determine ne the cur/e correc correction tion factor of the spring. a) 1.1-b) 1.-c) 1.11-d) 1.1-1#nswer& 3ur/e 3orrection 8actor, @ c 6 1.11-4 C −1 0.615 + C 4 C − 4 1 .184 .184 K c = = = =1.1144 K s 2 C + 1 1.0625 2 C Solution&
K w
*.
This This is either either the upper upper or the lower lower de/iatio de/iation, n, dependi depending ng on which which is closer closer to the basic si7e. si7e. !ow do "ou call call this this de/iation a) 8undamental de/iation b) 9pper de/iation c) :ower de/iation d) Tolerance #nswer& 8undamental de/iation
1. # /ise is eAuipped eAuipped with a 1inch single sAuare thread, thread, with - threads per inch. The The frictional radius of the collar collar is .+ inch. The coefficient of friction for both the collar and threads is .'. !ow much e2ternal torAue must be applied to produce a force of ' lb against the 0aws of the /ise a) *.; inlb b) .*; inlb c) ;.* inlb d) *.; inlb #nswer& c) ;.* inlb
>ut !andle
8 6 ' lb
Solution&
p = 8or the thread pitch,
1
1
>umber of Threads per nch
=
4
= 0.25
inch
8or the minor diameter, D i 6 Do B p 6 1 B .'+ 6 .;+ inch
8or the mean or pitch diameter of the screw,
Dm
=
Do
+ Di 2
=
1 + 0.75 2
= 0.875
inch
8or the lead angle, l=
�: � �p � � o -1 -1 � 0. 25 -1 = tan 0. 0909 09095 5 = 5.197 197 �= tan � �= tan � � �0.875p � �pD m � �pD m �
tan -1 �
Sol/ing for the torAue reAuired to o/ercome the collar friction,
Tc
=
f8Dc 2
=
( 0.2 ) ( 200 ) ( 0.5 )
= 20
2
in � lb
Sol/ing for the torAue reAuired to o/ercome the thread friction,
Ts
=
8Dm �tan l + f � � �= 2 � 1 - f tan l �
(
200 0 .875 875 2
) �0.09 09 09 5 + 0 .2 � lb � �= 25.93 in � 1 - 0.2 ( 0 .9095 ) � � '
Machine Design and Shop Practice (Problems and Elements)
Sol/ing for the total torAue, T 6 Ts C Tc 6 '+.* C ' 6 -+.* inches
ans.
11. $hat is the difference between the ma2imum and minimum si7e limits of a part a) #llowance b) Tolerance c) De/iation
d) 4asic si7e
#nswer& b) Tolerance 1'. # helicalcoil spring has a mean coil diameter of 1 inch and a wire diameter of 1?5 inch. Determine the $ahl factor of the spring. a) 1.1-5 b) 1.15c) 1.-15 d) 1.51#nswer& b) $ahl 8actor, @ w 6 1.15C =
D m d
1 =
=
1
8
8
Solution&
K w =
4 C −1 0.615 4 ( 8 ) −1 0.615 + = + =1.184 C 4 C − 4 8 4 ( 8 )− 8
1. t is the capacit" of a material to absorb energ" when it is deformed elasticall" and then, upon unloading, to increase this energ". $hat is this capacit" of a material a) esilience b) Toughness c) igidit" d) Ductilit" #nswer& a) esilience 1-. # helicalcoil spring has a mean coil diameter of 1 inch and a wire diameter of 1?5 inch. Determine the /alue of 4ergstrassar factor of the spring. a) 1.1;' b) 1.;1' c) 1.'1; d) 1.';1 #nswer& a) 4ergstrassar 8actor, @ 4 6 1.1;'C =
D m d
1 =
=
1
8
8
Solution&
K B =
4 C + 2 4 ( 8 ) + 2 = =1.1724 4 C −3 4 ( 8 )−3
1+. !ow do "ou call the strain energ" per unit /olume reAuired to stress a material from an unloaded state to the point of "ielding a) Modulus of roughness b) Modulus of elasticit" c) Modulus of rigidit" d) Modulus of resilience #nswer& d) Modulus of esilience 1. 3ompute the tooth thic%ness of a 1-.+o spur gear with diametral pitch of +. a) .'1- inch b) .1-1 inch c) .-1- inch
d) .1- inch
#nswer& b) Tooth thic%ness, t 6 .1-1 inch
t = Solution&
1.5708 1.5708 = = 0.31416 inch 5 pd
1;. !ow do "ou call a structural member designed to support loads perpendicular to its longitudinal a2is a) 3antile/er beam b) 4eam c) /erhanging beam d) 3olumn #nswer& b) 4eam 15. 3ompute the speed of the gear mounted on a +'.+ mm diameter shaft recei/ing power from a dri/ing motor with '+ !p. a) ' 15' rpm b) ' ;1 rpm c) ' '+ rpm d) ' -1 rpm #nswer& c) The speed, > 6 ''+ rpm
Machine Design and Shop Practice (Problems and Elements)
80 P 80 ( 250) =2 264. 92 rpm = 3 = 52.5 3 D 25.4 Solution& 8rom PSME 3ode&
( )
1*. t is a load applied trans/ersel" to longitudinal a2is of member. !ow do "ou call this load a) 4ending load b) 3ombined load c) Distributed load d) 3"clic load #nswer& a) 4ending load '. $hat is a load distributed o/er an entire area a) 4ending load b) 3ombined load
c) Distributed load
d) 3"clic load
#nswer& c) Distributed load '1. 3ompute the wor%ing strength of 1 inch bolt which is screwed up tightl" in pac%ed 0oint when the allowable wor%ing stress is 1 psi. a) lb b) *+ lb c) * lb d) 5 lb #nswer c) The wor%ing strength, $ 6 * lb
Solution& 8rom machiner"Fs !andboo%, page 11-*&
[
]
! = s t ( 0.55 d 2− 0.25d ) =( 13 000 ) 0.55 ( 1 )2−0.25 ( 1 ) = 3 900 "#
''. t is a design approach where no catastrophic loss can occur as a result of a component failure. $hat is this design approach a) 8ailsafe design approach b) 8ault free anal"sis approach c) Manifest danger approach d) edundanc" approach #nswer& a) 8ailsafe design approach '. t is the condition of a machine element when it is completel" inoperable, cannot perform its intended function adeAuatel", or is unreliable for continued safe use. $hat do "ou call this condition a) 8ailsafe condition b) 8ailure condition c) 3ritical condition d) Sal/age condition '-. 3ompute the nominal shear stress at the surface, in MPa, for a + mm diameter shaft that is sub0ected to a torAue of .-5 %>m. a) 1.*+ b) '1.+ c) 1*.+ d) '+.1' #nswer& Shear Stress, s s 6 1*.+ MPa
ss = Solution&
16 T
16 ( 0.48 )
π D
π ( 0.050 )3
= 3
=19 556.96 kPa =19.56 $Pa
'+. !ow do "ou call a statistical data used to identif" the most li%el" failure modes a) 8inite element anal"sis b) 8ault free anal"sis c) 8ailure anal"sis
d) andom anal"sis
#nswer& b) 8ault free anal"sis '. # hollow iron pipe to be designed as a column has an outside diameter of '- mm and is sub0ected to a force of 5 @>. 8ind the pipe thic%ness if the compressi/e stress is limited to 1 MPa. a. +.5+ mm b. .5+ mm c. ;.5+ mm d. 5.5+ mm #nswer& b) Pipe thic%ness, t 6 .5+ mm
-
Machine Design and Shop Practice (Problems and Elements)
√
Di= D 2% −
Solution& nside Diameter,
√
4 ( 80 ) 4 & = ( 0.24 )2 − = 0.2263 m −226.3 mm πs π ( 16 000 )
D % − D i 240 − 226.3 t = = = 6 . 8 5 mm Thic%ness of the Pipe,
2
2
';. t is a computational method used for sol/ing comple2 shapes, such as those found in machiner"G replaces the comple2 shape with a set of simple elements interconnected at a finite set of a specific purpose. $hat is this computational method a) 8inite element anal"sis b) >umerical method of anal"sis c) 8ault free anal"sis d) S"nthesis #nswer& a) 8inite element anal"sis '5. # uniform beam 1' meters long is fi2ed at one end. t has a uniform weight of + %g?m along its length. # load of ' %gs. is suspended on the beam - m from the free end. The moment at the fi2ed end is a. ; %gm b. . %gm c. %gm d. -5 %gm $ 6 + (1') 6 %g
#nswer& a) ; %gm
8 6 ' %gs
Solution& 4ending Moment,
$ =6 ( 600 )+ 8 ( 20 )=3 760 kg⋅m m 5m '*. $hen a hot part is cooled suddenl" b" Auenching, there is momentaril" a high temperature gradient that induces a stress gradient. Some metal parts under certain conditions crac% as a result. !ow do "ou call this phenomenon a) Thermalshoc% failure b) Thermal fatigue c) !oning d) Huenching #nswer& a) Thermalshoc% failure . # 'o straighttooth be/el pinion ha/ing 1- teeth and a diametral pitch of teeth?inch dri/es a -'tooth gear. The two shafts are at right angles and in the same plane. 8ind the pitch angle of the pinion. a) 15.-o b) 'o c) 1-.+o d) '.+o #nswer& a) Pitch angle of the pinion 6 15.-o
' = tan− 1 Solution&
( ) () T p T g
= tan
−1
14 % = 18.4 42
1. !ow do "ou call the diameter of the imaginar" c"linder that bounds the crest of an e2ternal thread and the roots of an internal thread a) Mean diameter b) Stress diameter c) Minor diameter d) Ma0or diameter #nswer& d) Ma0or diameter '. # 'o straighttooth be/el pinion ha/ing 1- teeth and a diametral pitch of teeth?inch dri/es a 'tooth gear. The two shafts are at right angles and in the same plane. The pinion is to transmit 15 rpm and transmitting + hp. Determine the pitch diameters of the gears. a) '. inches and +. inches b) .' inches and .+ inches c) +. inches and . inches d) '. inches and '. inches #nswer& a) '. inches and +. inches
+
Machine Design and Shop Practice (Problems and Elements)
D1 Solution&
=
T1
=
Pd
1-
=
)
D'
'.,, inches
=
�T � �,' � D1 � ' �= ( '.,, ) � �= +.,) inches �1- � �T1 �
. t is a measure of the change in length of a material sub0ected to a change in temperature. !ow do "ou call this propert" of the material a) Toughness b) 3oefficient of thermal e2pansion c) Thermal conducti/it" d) Electric esisti/it" #nswer& b) 3oefficient of thermal e2pansion -. # 1inch diameter shaft has a single disc weighing ;+ lb mounted midwa" between two bearings 'I apart. 8ind the lowest critical speed in rpm. >eglect the weight of the shaft. #ssume that the modulus of elasticit" is 2 1 psi. a) '5 rpm b) '5 rpm c) '5 rpm d) '5 rpm $ 6 ;+ lb
Solution& D 6 1 inch
E 6 2 1 psi
=
pD
Moment of nertia,
-
)-
p =
( 1)
: 6 ' inches 1I
-
)-
=
(.(-*1 in.
wcr =
+;)Eg $ :,
Sol/ing for the lowest critical speed,
> cr =
,( wcr
=
,( ( '1,.,* )
p
=
1I
-
( +;) ) ( ,( 2 1() ) ( (.(-*1) ( ,'.')
=
( ;+) ( '( )
,
=
'1,.,* rad ? s
' (,;.)5 rpm
p
+. $hat is a condition where one surface is comparati/el" free of stress a) ctahedral plane b) 4ia2ial or Plane stress c) Strain plane
d) Principal normal stress
#nswer& b) 4ia2ial or Plane stress . # fl"wheel weighing -+; %g has a radius of ;+ mm. !ow much energ", in >m, does the fl"wheel loss from rps to '.5 rps a) 5 b) 1+ c) 1-;d) 5 #nswer& c) 8l"wheel Energ" 61-;Solution&
( 1 =2 π ( 0.375 ) ( 3 )=7.069 m / s
) K* =
<'
m ( ( 21 − ( 22 ) 457 [ ( 7.069 )2− ( 6.597 )2 ] 2
=
2
=
' p ( (.,; +) ( '.5 ) = ).+* ; m ? s
= 1 473.91
⋅m
;. !ow do "ou call the circle on a gear that corresponds to the contact surface of the friction wheel a) #ddendum circle b) oot circle c) Pitch circle d) 4ase circle #nswer& c) Pitch circle 5. # triple threaded worm has a pitch diameter of inches. The wheel has '+ teeth and a pitch diameter of + inches. Material for both the wheel and the wheel is phosphor bron7e. Determine the heli2 angle of the gear. a) 11.1o b) 1.11o c) 11.1o d) 1.1o #nswer& Jear !eli2 angle 6 11.1o
Machine Design and Shop Practice (Problems and Elements)
Pc
=
pD g
p =
Tg
( +)
'+
=
(.)'5, inch
Solution& 3ircular pitch of the worm gear, $here, Pc 6 Pa 6 pitch of the worm Sol/ing for the lead, : 6 > t Pa 6 (.'5) 6 1.55-* inches
l=
�: � 1.55-* � -1 � o = 11.,1 �= tan � � � ,p � �pDw �
tan -1 �
Sol/ing for the lead angle of the worm,
8or the heli2 angle, and considering that the shafts angle is * o, g 6 l 6 11.1o
ans.
*. This material is the most popular allo" spring steel for conditions in/ol/ing higher stresses than can be used with the high carbon steels and for use where fatigue resistance and long endurance are neededG this is also good for shoc% and impact loads. a) 3hrome silicon b) 3hrome /anadium c) harddrawn wire d) iltempered wire #nswer& b) 3hrome
>ote& Ma2. 3hain Pitch in Practice&
2
( )
( )
pmax≤
900 n
pmax =
3
900
1000
2 3
=0.932 in
Since 3 5, p 6 1 inch e2ceeds the ma2imum and 3 ; does not e2ist, and then use 3 . -1. These are gears with teeth formed on conical surfaces and are used mostl" for transmitting motion between intersecting shafts. !ow do "ou call these gears a) Spur gears b) !elical gears c) 4e/el gears d) $orm gearings #nswer& c) 4e/el gears -'. # single sAuare thread power screw is to raise a load of ; %>. The screw has a ma0or diameter of mm and a pitch of mm. The coefficient of thread friction and collar friction are .1 and .1 respecti/el". f the collar mean diameter is * mm and the screw turns at rpm, find the a2ial linear speed of the screw. a) + mm?s b) mm?s c) ; mm?s d) +.+ mm?s #nswer& b) mm?s Solution& 8or the linear speed of the screw, < n 6 n (:) 6 ( rpm)( mm?re/) 6 mm?min 6 mm?s -. # double thread #3ME screw dri/en b" a motor at - rpm raises the attached load of * %g at a speed of 1 m?min. The screw has a pitch diameter of mmG the coefficient of friction on threads is .1+. The friction torAue on the thrust bearing of the motor is ta%en as ' K of the total input. Determine the lead angle. a) 1'.-+o b) 1-.'+o c) 1+.-'o d) 1.-+'o #nswer& a) 1'.-+o
( 10 L= = =0.025 m= 25 mm n 400 Solution& 8or the lead,
;
Machine Design and Shop Practice (Problems and Elements)
+ =tan
−1
8or the lead angle,
( ) ( )
L −1 25 % =tan =12.465 36 π πDm
--. $hat !p can a 1inch diameter short shaft transmit at 5 rpm a) !p b) 15 !p c) 1 !p
d) ;.1 !p
#nswer& c) 1 !p
D3
( 1 )3 ( 380 )
38
38
P= Solution&
=
=10
Hp
-+. # spur pinion rotates at rpm and transmits '+ %$ to a mating gear. The pitch diameter of the pinion is 1 mm, and the pressure angle is 'o. Determine the tangential load, in >. a) ; b) ;* c) * d) *5
( )( ) ( ) [
& t = Solution&
2 30 P D π n
=
2 0.10
30 ( 25 000 )
π ( 600 )
]
=7 957.75
-. # bearing that primaril" guides the motion of a machine member without specific regard to the direction of load application. a) =ournal bearing b) 3learance bearing c) Juide bearing d) Thrust bearing #nswer& c) Juide bearing
47. A multiple-disk clutch, composed of three plates with a small diameter of 150 mm and large diameter of 200 mm, is designed to transmit 100 k at !000 rpm at a coe"cient of friction of 0.5. #etermine the spring force needed to engage the clutch. b) '-'5 > c) +- > d) 5 > a$ '5' > #nswer& 5 >
T = %olution&
30 P 30 ( 100 ) = = 0.3183 k ⋅m= 318.3 ⋅m π n π ( 3000 )
[
T =, ⋅ P⋅r , ⋅ ,s =, ⋅ P⋅
( D + d )
P =
4
]
⋅ ,s
4 T
, ⋅( D + d )⋅ ,s
=
4 ( 318 300 ) 0. 5 ( 200 + 150 ) ( 2 )
= 3 637.71
4'. A wire rope lifts a load of 10 kips at a ma(imum speed of 1000 feet per minute, attained in 5 seconds starting from rest. )he rope has a metallic cross sectional area of 0.4 in 2. #etermine the ma(imum tensile stress on the rope in ksi. a$ '.' b) '+. c) ';. d) '.#nswer& c) ma2imum tensile stress 6 ';. MPa
a= Solution&
( 1 − ( % t
=
( 1000 / 60 )− 0
= 3.33
,ps -
( )
& =! L 1+
5 11/ 034.16 =27 585. 4 psi=27.6 ksi .t = 0. 4
(
)
3.33 a =( 10 000 ) 1+ =11 034.16 "# 32.2 g
-*. $hat is the bursting steam pressure of a hemispherical steel shell with a diameter of 1 inches and made of .+m thic% steel plate, if the 0oint efficienc" is ; K and the tensile strength is psi a) - ' psi b) - ' psi c) ' - psi d) ' - psi 5
Machine Design and Shop Practice (Problems and Elements)
#nswer& b) -' psi
p=
4 t s" * j
Solution&
D
( = 4
)
63.5 in ( 60 000 "# / in- ) ( 0.70 ) 25.4
100 in.
$here, p 6 bursting pressure, psi t 6 shell thic%ness, inches
= 4 200 psi
sl 6 shell stress, psi D 6 shell diameter, inches
E 0 6 0oint efficienc"
s L=
pD 4 t * j
>ote& 8or the longitudinal stress of the thinwalled c"linder, and the stress for spherical tan%& +. # c"linder ha/ing an internal diameter if +5 mm and e2ternal diameter if *1-.- mm is sub0ected to an internal pressure of * MPa and an e2ternal pressure of 1- MPa. Determine the hoop stress at the inner surface of the c"linder. a) *.11 MPa b) *1.1 MPa c) *11. MPa d) 1*.1 Mpa #nswer& a) *.11 MPaa
s ti=
(
)
pi r 2% + r 2i −2 p % r 2% r 2%−r 2i
( 69 $Pa ) =
[(
914.4 mm 2
(
Solution&
) +( 2
)] ( ) −( )
508 mm 2
2 914.4 mm 2
2
914.4 −2 ( 14 $Pa ) mm 2
508 mm 2
)
2
2
sti 6 *.11 Mpa $here, sti 6 ma2imum tangential or hoop stress at the inside pi 6 internal pressure, Mpa po 6 e2ternal pressure, Mpa
ri 6 inside radius, mm ro 6 outside radius, mm 2
s t% =
2 pi r i − p%
>ote& 8or the ma2imum tangential or hoop stress at the outside,
(r
2
r2
%+ i
)
r 2% −r 2i
+1. $hat length of a sAuare %e" is reAuired for a -in diameter shaft transmitting 1 hp at 1 rpm The allowable shear and compressi/e stresses in the %e" are 1+ %si and %si, respecti/el". a) '.1 inches b) '.5 inches c) .' inches d) -.' inches #nswer& a) '.1 inches
T = Solution& Transmitted torAue,
63000 Hp
n
=
63000 ( 1000 ) 1000
= 63 000
in⋅"#
D #≈ / ,%r good proportion 4 @e" width, 2 ( 63 000 ) 2 T L= = =2 .1 inch0s s #D 15 000 1 4 ( ) ( ) s @e" length based on shear, L= @e" length based on compression, Therefore, use : 6 '.1 inches
4 ( 63 000 ) 4 T = =2 .1 s c t D 30 000 ( 1 ) ( 4 )
+'. $hich of the following are the compositions of stainless steel ' a) 15 K chromium and 5 K nic%el b) 15 K nic%el and 5 K chromium c) 15 K chromium and 5 K phosphor bron7e d) 15 K bron7e and 5 K /anadium
*
Machine Design and Shop Practice (Problems and Elements)
#nswer& a) 15 K chromium and 5 K nic%el +. The root diameter of a double sAuare thread is .++ inch. The screw has a pitch of .' inch. 8ind the number of thread per inch. a) .' threads?inch b) 1 threads?inch c) + threads?inch d) '.+ threads?inch #nswer& TP 6 + threads per inch Solution&
TP1 = The number of threads per inch,
1 1 = =5 thr0ads /inch p 0.2
+-. # single sAuare thread power screw is to raise a load of ; %>. The screw has a ma0or diameter of mm and a pitch of mm. The coefficient of thread friction and collar friction are .1 and .1 respecti/el". f the collar mean diameter is * mm and the screw turns at rpm, find the combined efficienc" of the screw and collar. a) 1+.' K b) 1'.+ K c) 1.+' K d) 1+.*; K #nswer& b) 1'.+ K
h= Solution& 8or the depth of the thread, 8or the mean diameter of the screw,
+ = tan 8or the lead angle,
−1
() () 1 1 p= 2 2
D m = D % − h= 36 − 3= 33 mm
( )
( )
( )
tan + (1 − , tan + ) ( 100
)
Di
( )
, c D c tan + + , + ( 1− , tan + ) D m
Dm Do
( tan 3 .3125 %) ( 1 −0.13 tan3.3125 % ) ( 100 )
0=
p
L p 6 % −1 −1 = tan = tan = 3.3123 33 π πD m πD m
0= Sol/ing for the Efficienc",
$ 6 ; >
( 6 )=3 mm
%
tan3.3125 + 0.10 +
[
0.10 ( 90 ) 33
] (
=12.53 %
1−0. 13 tan 3. 3125
)
++. Determine the power capacit" of a cone clutch under uniform pressure and assuming the following conditions& ma0or diameter 6 '+ mmG minor diameter 6 ' mmG length of conical elements in contact 6 1'+ mmG rotational speed 6 5; rpmG coefficient of friction 6 .G and allowable pressure 6 ; %Pa. a) '+.;- !p b) '-.;+ !p c) ';.-+ !p d) '-.+; !p #nswer& a) '+.;- !p
r , = Solution&
2 3
8riction radius, Surface #rea of contact,
( ) ( )[ r 3% −r i3 r 2% −r 2i
=
2 3
( 125 ) ( 125 )
3
−( 100 )
3
2
−( 100 )
2
]
=112.96
mm
2 , =2 πr , # =2 π ( 0.11296 ) ( 0.125 )=0.0887 m
8orce normal to the surface of contact,
2
& n = p2 , = ( 70 ) ( 0.0887 )= 6.209 k 1
Machine Design and Shop Practice (Problems and Elements)
P= Power 3apacit",
π n T , 30
=
πn
(,
30
& n r , ) =
π ( 870 ) 30
( 0.30 ) ( 6.209 ) ( 0.11296 )=19.2 k! =25.74 Hp
+. Three e2tension springs are hoo%ed in series that support a single weight of 1 %g. The first spring is rated at - %>?m and the other two springs are rated %>?m each. Determine the eAui/alent stiffness of the three springs. a) 1.;1 %>?m b) + %>?m c) '.;1 %>?m d) .;1 %>?m #nswer& a) 1.;1 %>?m
1 Solution&
k 0
=
1
+
1
+
1
k 1 k 2 k 3
=
1 1 1 1 1 3 + 4 7 + + = + = = 4 6 6 4 3 12 12
12 k 0 = = 1.71 k / m 7
+;. These springs are made from one or more flat strips of brass, bron7e, steel or other materials loaded as cantile/ers or simple beam. a) Torsion springs b) :eaf springs c) Jarter springs d) Drawbar springs #nswer& b) :eaf Springs +5. # flat belt is inches wide and 1? inch thic% and transmits ' !p. The center distance is 5 ft. The dri/ing pulle" is inches in diameter and rotates at ' rpm such that the loose side of the belt is on top. The dri/en pulle" is 15 inches in diameter. The belt material is .+ lb?in and the coefficient of friction is .. Determine the belt net tension. a) '1 lb b) '1 lb c) 1' lb d) 1' lb #nswer& b) '1 lb
Solution&
& = & 1 − & 2=
(
)()
2 T 2 63 000 Hp 2 63 000 ( 20 ) = = =210 "# 6 2 000 D D n
( )
( m= π D n= π
ther Solution&
& = & 1 − & 2=
6 ( 2 000 )=3141.59 ,pm 12
33 000 Hp ( m
=
33 000 ( 20 ) = 210 "# 3141.59
+*. # pulle" mm in diameter transmits - %$ at + rpm. The arc of contact between the belt and pulle" is 1++ o, the coefficient of friction between belt and pulle" is .+ and the safe wor%ing stress of the belt is '.1 MPa. Determine the belt tensions ratio, neglecting the effect of centrifugal force. a) '.+;5 b) '.5+; c) +.'5; d) +.;5' & 1
Solution&
& 2
(
0 . 3 5 155
= 0 = ( 0) ,θ
( )=2.578
) π
180
#nswer& a) '.+;5 . This refers to the space between ad0acent coils when the spring is compressed to its operating length. a) 3oil clearance b) Pitch c) :ead d) Deflection #nswer& a) 3oil clearance
1. Select a deepgroo/e ball bearing to carr" a radial load 8 2 6 5 lb and a thrust load 8 7 6 ; lb at 1;+ rpm. The ser/ice is 5 hr?da", but it is not continuousG design for ' hr. The operation is smooth with little /ibrationG the outer ring rotates. Determine the design life in mr with no more than 1 K failure. a) '1 mr b) '1 mr c) '1 mr d) 1' mr 11
Machine Design and Shop Practice (Problems and Elements)
#nswer& b) '1 mr
B 10=( Hrs ) ( 60 min s / hr ) ( rpm )= Solution&
(20 000 ) ( 60 ) ( 1 750 ) 6
= 2100
10
mr
'. Determine the !p lost when a collar is loaded with ' lb, rotates at + rpm, and has a coefficient of friction of .1+. The outside diameter of the collar is - inches and the inside diameter is ' inches. a) .;1- !p b) .;1- !p c) .-;1 !p d) .-;1 !p #nswer& b) .;1- !p
,Hp = Solution&
T , n
=
63000
, ! r , n 63000
=
0.15 (2000 "# ) ( 1.56 inch0s ) ( 50 rpm ) 63000
r , = $here,
2 3
( ) [ r 3% −r i3 r 2% −r 2i
=
2 3
( 2 ) (3 )
− (1 )
3
3
2
2
− (1 )
=0.3714
]
=1.56 inch0s
. n a lathe machine, it is the diameter of the largest wor%piece it can rotate in a chuc% or between centers without hitting the bed. a) 3huc% diameter b) Swing c) Distance between centers d) Spindle diameter #nswer& b) Swing -. $hat load in > must be applied to a '+ mm round steel bar '.+ m long (E 6 '; Jpa) to stretch the bar 1. mm a) -' > b) +' 5- > c) + > d) > #nswer& b) The load, +' 5- > Solution& The load,
& =
[
()
1.3 2 * π 2 = D * = L L 4 2. 5 ( 1000 )
] ( ) (
π 2 0.025 ) ( 207 000 000 000 )=52 837.66 4
+. This is a general term that refers to the mating of c"lindrical parts such as bolt or a holeG it is used onl" when the internal member is smaller that the e2ternal member. !ow do "ou call this a) 3learance b) nterference c) #llowance d) Tolerance #nswer& a) 3learance . # +mm diameter shaft is to transmit 1' %$ power at a speed of + rpm, determine the mean diameter of the pin, under double shear, for a material ha/ing a safe unit stress of - >?mm '. a) 11.5 mm b) 1'.5 mm c) 1.5 mm d) 1.5 mm Pin Shaft #nswer& b) Diameter of the pin 6 1'.5 mm
T = Solution&
Transmitted TorAue, Pin Shearing 8orce, Pin Mean Diameter,
30 P 30 ( 12 000 ) = =229.183 ⋅m= 229 183 ⋅mm πn π ( 500 )
& s=
ss=
2 T
=
2 ( 229 183 )
D 50 4 & s & s 2 2s
=
2 π d
= 2
= 9 167 . 32
2 & s
π d2
1'
T
Machine Design and Shop Practice (Problems and Elements)
d=
√
2 & s
=
π ss
√
2 ( 9 167.32 )
π ( 40 )
=12.08
mm
;. This is a lubrication condition where nonconformal surfaces are completel" separated b" lubricant film and no asperities are in contact. !ow do "ou call this lubrication condition a) Elastoh"drod"namic lubrication b) 4oundar" lubrication c) !"drod"namic lubrication d) !"drostatic lubrication #nswer& a) Elastoh"dod"namic lubrication 5. # 1' mm cast iron pulle" is fastened to 11'.+ mm shaft b" means of a '5.1 mm sAuare %e" 1;+ mm long. The %e" and shaft ha/e a shearing stress of 1- psi. Determine the force acting at the pulle" that will shear the %e". a) 1 1+ lb b) 11 + lb c) 11 + lb d) 1 +1 lb #nswer& a) The force acting on the pulle" 6 1 1+ lb
& p= Solution&
2 T
D p
2 =
(
s s #LD 2
D p
$here,
)
= s s #L
T =
( )
s s #LD 2
(
28.13 D = ( 14 000 ) D p 25.4
→ T%r450
)( )( 175 25.4
)
112.5 = 10 014.74 "# 1 200
#as0d %n sh0ar / in⋅"#
*. # ;+mm diameter shaft is transmitting + %$ at + rpm. # flange coupling is used and has bolts, each 15 mm in diameter. 8ind the reAuired diameter of the bolts circle based on an a/erage shearing stress of ';.+ MPa. a) '-+ mm b) '+- mm c) -+' mm d) -'+ mm #nswer& a) 4olt 3ircle diameter 6 '-+ mm
D B = Solution&
8 T
π s s d 2 nB
=
8 ( 30 ) P
π 2 d 2 s s n nB
=
8 ( 30 ) ( 350 )
π 2 ( 0.018 )2 ( 27 500 ) ( 650 ) ( 6 )
= 0.245 m = 245
mm
2
>ote&
π s s d DB n n B 30 P T = = πn 8 TorAue 4ased on Shear,
;. !ow do "ou call the flattened end of a shan%, and intended to fit into a dri/ing slot in the soc%et a) !andle b) Tang c) elief d) Tip #nswer& b) Tang ;1. f a slee/e bearing has an outside diameter of 5.1 mm and a length of +.5 mm, the wall thic%ness is ?1 inch. The bearing is sub0ected to a radial load of + %g. $hat is the bearing pressure, in psi a) *- psi b) -* psi c) -* psi d) *- psi #nswer& c) 4earing pressure 6 -* psi
(
2 B = L D = Solution&
8or bearing or pro0ected area,
50.8 25.4
in .
)[
38.1 25.4
in . −2
! ( 500 kg ) ( 2.205 "# / kg ) p= = =490 psi 2 2.25 in B 4earing pressure,
1
( ) 3
16
]
in =2.25 in -
Machine Design and Shop Practice (Problems and Elements)
;'. This material is the most popular allo" spring steel for conditions in/ol/ing higher stresses than can be used with the high carbon steels and for use where fatigue resistance and long endurance are neededG this is also good for shoc% and impact loads. a) 3hrome silicon b) 3hrome /anadium c) harddrawn wire d) iltempered wire #nswer& b) 3hrome
h= Solution& 8rom
2.157 2.157 = =0.089875 inch pd 24
;-. # parallel helical gear set was a 1;tooth pinion dri/ing a -tooth gear. The pinion has a righthand heli2 angle of o, a normal pressure angle of ' o, and a normal diametral pitch of + teeth?in. 8ind the a2ial circular pitches. a) 1.'+ inches?toothb) 1.'+ inches?tooth c) 1.+' inches?tooth d) 1.'+ inches?tooth #nswer& a) #2ial circular pitch 6 1.'+ inches?tooth Pc = Solution&
Pcn
=
cos
Pa =
(.)'5,' cos,( Pc
o
=
tan
=
(.;'++' inch ? tooth
(.;'++' tan ,(o
= 1.'+))
inches ? tooth
;+. 8or an #merican Standard Screw Threads, what does ' 9>3 designate a) Si7e , ' threads per inch, coarse thread b) inches basic diameter, ' threads per inch, coarse thread c) Si7e , ' threads per inch, fine thread d) ' inches basic diameter, threads per inch, coarse thread #nswer& a) Si7e , ' threads per inch, coarse thread
>ote& stands for the designated si7e, ' stands for the number of threads per inch, 9>3 stands for 3oarse threads
;. Determine the PoissonFs ratio of a material whose modulus of elasticit" is ' JPa and whose modulus of rigidit" is 5 JPa. a) . b) .'+ c) .5 d) .'' #nswer& b) PoissonFs ratio 6 .'+
G= Solution&
* 2 ( 1 +6 )
E 6 'JPa,
J 6 5JPa&
;;. # steel has a 4!> 6 . $hat is its appro2imate ultimate strength in %si a) %si b) 1+ %si c) ;+ %si
∴ 6 =0.25
d) ' %si
#nswer& b) 9ltimate Strength 6 1+ %si Solution& Su .+(4!>), %si ;5. f the angular deformation of a solid shaft should not to e2ceed 1 o in a length of 1.5 m and the allowable shearing stress is 5 MMa, what is the diameter of the shaft #ssume that the shaft material has J 6 ;; 2 1 %Pa. a) '''.- mm b) '-.'' mm c) '.-' cm d) '-.'' cm 1-
Machine Design and Shop Practice (Problems and Elements)
#nswer& a) Shaft diameter 6 '''.- mm
32
Solution&
TL 32 T L θ= = 4 = JG πD G
( ) πD3 ss 16
L
=
π D4 G
D =
2 s s L
2 s s L
θG
2 ( 83 000 ) ( 1 .8 )
=
D G
1
%
( )( π
180
%
77 x 10
= 222.34 6
mm
)
;*. !ow do "ou call the process of producing the residual compressi/e stress of machine parts, which is performed b" directing the a high /elocit" stream of hardened balls or pellets at the surface to be treated. a) >itriding b) Shot blasting c) Peening d) Tempering #nswer& b) Shot blasting 5. Determine the !p lost when a collar is loaded with ' lb, rotates at + rpm, and has a coefficient of friction of .1+. The outside diameter of the collar is - inches and the inside diameter is ' inches. a) .;1- !p b) .;1- !p c) .-;1 !p d) .-;1 !p #nswer& b) 8rictional !orsepower 6 .;- !p ,Hp =
Solution&
T , n 63000
=
, ! r , n 63000
=
0.15 (2000 "# ) ( 1.56 inch0s ) ( 50 rpm ) =0.3714 63000
( ) [ 3
3
]
3 3 2 r % −r i 2 (2 ) − ( 1 ) r , = = = 1.56 inch0s 3 r 2 −r 2 3 (3 )2− ( 1 ) 2 % i
$here,
51. t is a process that produces residual compressi/e stress on the machine part, which uses a series of hammer blows on the surface. a) >itriding b) Shot blasting c) Peening d) Tempering #nswer& c) Peening 5'. Two shafts . m between centers carr" pulle"s 1.' m in diameter and .*1 m in diameter respecti/el", connected b" a crossed belt. t is desired to put the belt on as an open belt. !ow long a piece must be cut of it a) . mm b) mm c) . mm d) . mm #nswer& :ength to be cut off 6 . mm Solution& 8or the length of an open belt connection,
L% =
π 2
( D + D ) 1
2
( D − D ) + 2 C + 2
2
1
4 C
()
=
π 2
( 1200− 910) ( 1200 +910 )+ 2 ( 3600 )+ 4 ( 3600)
2
=10 520.22
mm
8or the length of belt for crossed belt connection, 2
Lc=
π
( D
2
1
+ D2
)
( D − D ) + 2 C + 2
4 C
1
()
=
π 2
( 1200+ 910) ( 1200 + 910) +2 ( 3600 ) + 4 ( 3600 )
2
=10 823.55
mm
Sol/ing for the difference of lengths,
)L = Lc− L % =10 823. 55 −10 520. 22=303.33 mm 5. t is a surfacehardening process for allo" steels in which the material is heated to *+ o8 in a nitrogen atmosphere, t"picall" ammonia gas, followed b" slow cooling. a) Huenching b) >itriding c) Shot blasting d) Peening 1+
Machine Design and Shop Practice (Problems and Elements)
#nswer& b) >itriding 5-. # 'tooth motor sproc%et, running at 1' rpm, dri/es a blower at a speed ratio of -&1. 9sing the largest permissible chain si7e and the largest permissible center distance of 5 pitches, what length of chain in pitches is reAuired to connect the sproc%ets a) ' pitches b) '1' pitches c) '1 pitches d) '' pitches #nswer& b) 3hain length 6 '1 pitches 2
Solution&
t 1+ t 2 ( t 2− t 1) = 212. pitch0s L c = + 2 C p + 2 40 C p
5+. $hich of the following gases is t"picall" used in nitriding process of surface hardening a) >itrogen gas b) 3arbon dio2ide c) #mmonia gas d) !"drogen gas #nswer& c) #mmonia gas 5. # '%$ motor, running at 1' rpm, dri/es a - mm diameter pulle" at a belt tension ratio of '.-. f the beltFs tight side tension is onl" 1' >, determine the transmission efficienc". a) 5;.*; K b) 5-.+5 K c) 5+. K d) 5.++ K #nswer& a) Transmission Efficienc" 6 5;.*; K
T %5t ( π n ) 7= Solution&
P%5tp5t Pinp5t
=
30
P inp5t
=
( ) ( ) π n
D
30
2
& n0t
P inp5t
=
( ) ( ) ( π n
D
30
2
& 1 − & 2 ) =
Pinp5t
(
1200 π 30
)( ) ( 0.40 2
1200−
20 000
1200 2.4
)
=0.8797
5;. # righthanded singlethread hardenedsteel worm has a catalog rating of '.'+ %$ at + rpm when meshed with a -5 tooth caststeel gear. The a2ial pitch of the worm is '+ mm, normal pressure angle is 1-.+ o, and the pitch diameter of the worm is 1 mm. The coefficient of friction is .5+. Determine the shafts center distance. a) '-1 mm b) 1-' mm c) -1' mm d) 1'- mm #nswer& a) 3enter distance 6 '-1 mm
.p00d 8ati%/ .8 = Solution&
Tan + =
9w 9g
=
nw ng
=
T g D g cos + =
Pitch diameter of the gear, 3enter Distance,
D g
T w D w sin + D w tan +
L p 25 = = = 0.07958 πD w πD w π (100 ) D g =
=
( )
→
+= 4 . 5 5%
( ) ( ) ( )( ) ( )( )
T g T g T g p p 48 D w tan + = D w = = 1 T w T w πD w T w π
25
π
= 381.97
mm
D w + D g 100 + 381.97 = = 241 mm C = 2
2
55. $hich of the following is the benefit in using nitriding as a surfacehardening process for allo" steels a) mpro/ement of endurance strength, + K or more b) mpro/ement of endurance strength, less than + K c) mpro/ement of endurance strength, more than + K d) 5 K impro/ement on the endurance strenght #nswer& a) mpro/ement of endurance strength, + K or more 5*. # 'o straighttooth be/el pinion ha/ing 1- teeth and a diametral pitch of teeth?inch dri/es a -'tooth gear. The two shafts are at right angles and in the same plane. 8ind the pitch angle of the pinion. a) 15.-o b) 'o c) 1-.+o d) '.+o 1
Machine Design and Shop Practice (Problems and Elements)
#nswer& a) Pitch angle 6 15.- o
' = tan−1 Solution&
( ) () T p T g
=tan
14
−1
42
=18.4
%
*. # triplethread worm has a lead angle of 1;o and a pitch diameter of '.'5' inches. 8ind the center distance when the worm is mated with a wheel of -5 teeth. a) .;' inches b) ;.' inches c) .'; inches d) ;.' inches #nswer& a) 3enter Distance 6 .;' inches
D g = Solution&
( ) T g
T w
( )(
48 % 2.2802 ) tan17 =11.154 inch0s 3
D w tan + =
D w + D g 2.2802+ 11.154 C = = =6.72 inch0s 2
2
*1. # doublethread worm has a pitch diameter of inches. The wheel has ' teeth and a pitch diameter of + inches. 8ind the gear heli2 angle. a) -.*o b) *.-o c) .-*o d) .*-o #nswer& b) Jear heli2 angle 6 *.- o −1
+ =tan
[( )( ) ] T w D g Tg
Solution&
D w
−1
= tan
[ ( )] 2
5
20
3
=9 . 4 6
%
*'. # tooth pinion turning at rpm dri/es 1'tooth gear of 1-.+o in/olute full depth pressure angle. Determine the rpm of the dri/en gear. a) rpm b) -+ rpm c) ;+ rpm d) * rpm #nswer& d) * rpm
n g = n p Solution&
( ) ( ) T p
T g
= ( 300 )
36
120
= 90
rpm
*. f two parallel shafts are connected b" c"linders in pure rolling contact and turning in the same direction, and ha/ing a speed ratio of '.;+, what is the 3enter distance of the two shafts assuming that the diameter of the smaller c"linder is '' cm a) 15.'+ cm b) 1*.'+ cm c) '.'+ cm d) 1;.'+ cm #nswer& b) 3enter Distance 6 1*.'+ cm Solution&
Diameter of the bigger c"linder,
3enter distance,
D 2 = .8 ( D 1 )= 2.75 ( 22 )= 60.5 cm
D 2− D 1 60.5 −22 C = = = 19.25 cm 2
2
*-. n estimating the actual endurance strength of steel parts, one of the factors to be considered is the material factor, which of the following is the recommended material factor for cast steel a) .; b) .5 c) .;+ d) 1. #nswer& a) Material factor for cast steel 6 .; *+. !ow do "ou call the le/el of stress that the part will be permitted to see under operating conditions 1;
Machine Design and Shop Practice (Problems and Elements)
a) Lield stress
b) Endurance stress
c) Design stress
d) 9ltimate stress
#nswerG c) Design Stress *. $hich of the following column formulas is applicable to cast iron columns a) EulerFs formula b) =.4.=ohnsonFs formula d) Secant formula d) Straight line formula #nswer& d) Straight line formula o
#ns. D. Straight line formula. 3ast iron columns are usuall" designed on the basis of
[ ]
L 0 P =9000− 40 2 k
o
→
a .traight "in0 ,%rm5"a
$here the slenderness ratio :e?% should not e2ceed ;.
*;. $hich of the following ferrous metals has the lowest carbon content a) 3arbon steel b) $rought iron c) 3ast iron
d) S#E -1-
#nswer& b) $rought iron o
$rought iron usuall" contains less than .-K 3G steel usuall" has less than '.+K 3G cast iron has more than 1.;K 3G S#E -1- has appro2imatel" .-K 3.
*5. Two e2tension coil springs are hoo%ed in series that support a single weight of 1 %g. The first spring is rated at - %>?m and the other spring is rated at %>?m. Determine the total deflection of the springs. a) -5. mm b) -5. mm c) -5. mm d) -.5 mm #nswer& a) Spring Deflection 6 -5. mm
3 t =3 1+3 2= Solution&
( )
k 1+k 2 & & + = & = ( 100 kg ) ( 9. 8066 / kg ) k 1 k 2 k 1 k 2
[ ] 4 +6
( )
=408.6
4 6
mm
**. f the ultimate shear strength of a steel plates is -' psi, what force is necessar" to punch a .;+ inch diameter hole in a .'+ inch thic% plate a) 1 5+ lb b) + 51 lb c) 1 +5 lb d) 15+ lb #nswer& a) Punching force 6 1 5+ lb Solution&
& =s 5 2 s= s 5 ( πd t )=( 42000 "# / in - ) ( π ) ( 0.75 in ) ( 0.625 in ) =61 850.1 "#
1.f stiffness is the main criterion in selecting a material, which of the following is the most economical choice a) S#E 1 b) S#E 1' c) S#E 1+ d) #S 1, hard stainless steel o
#ns. 4. S#E 1' plain carbon steel. #ll of the abo/e materials are steel with practicall" eAual modulus of elasticit". The three other materials are allo" steels that are relati/el" more e2pensi/e.
11.$hich of the following materials can easil" be machined a) #S 31' b) #S 3111' c) #S 31
d) #S 311
#nswer& b) #S 3' o
#ns. b. 3111'. This is a freecutting steel with a higher sulfur content for ease in machining
1'.ood is an ****** material+ that is, its mechanical properties are uniue and independent in three
mutuall perpendicular directionslongitudinal, radial, and tangential. a$ sotopic b) #nisotropic c) /rthotropic d$ An of these 15
Machine Design and Shop Practice (Problems and Elements)
Answer& c$ /rthotropic material 1.# stepped torsion shaft has diameters of 1 mm and 1' mm and a fillet radius of ' mm. The shaft is sub0ected to a torAue of 1'.+ >m. 8ind the ma2imum induced stress caused b" the fillet. 3onsider a stress concentration factor of 1.'+. a) .5- MPaa b) -.+ MPa c) 5.- MPa d) -+. MPa #nswer& b) -.+ MPa Solution& Sol/ing for the a/erage induced shear stress in the shaft
ss =
1) T pd
,
=
1) ( 1'.+ )
p ( (.(1' )
=
,
,)5-1-''.(1 Pa = ,).5- MPa D 6 1 mm
Sol/ing for the ma2imum induced shear stress, ss ( ma2 )
=
% ts ss
=
( 1.'+) ( ,).5- )
=
r 6 ' mm d 6 1' mm
-).(+ MPa
1-.# steam engine that has a stro%e of 1' inches has an o/erhung cran% of 11 inches. The ma2imum tangential force, P, on the cran% ma" be assumed as ;+ lb. #ssuming an allowable stress in shear as -- psi, determine the cran%shaft diameter. a) -.;; inches b) .;; inches c) '.;; inches d) 1.;; inches #nswer& a) 3ran%shaft Diameter 6 -.;; inches
4
Solution&
T = P⋅ 8 =( 7500 ) ( 6 )= 45 000 in⋅"#
Sol/ing for the torAue,
Sol/ing for the bending moment, $ =( 7500 ) ( 11) =82 500 in⋅"#
D =
[( ) π ss
][ 1
√ $ + T 2
11I 3ran%shaft
Sol/ing for the shaft diameter, 16
I
#
3ran%pin
2
3
=
16
π ( 4400 )
]
1
√ ( 45 000 )2 + ( 82 500 )2 3 = 4.77} {
¿
1+. )he principal raw materials used in steelmaking are iron ore, coal, and **********. a$ 3o%e b) imestone c) Slag d) 8lu2 #nswer& b) :imestone 1. )he steel part is heated to a temperature of 001150 degrees 3 in an atmosphere of ammonia
gas and dissociated ammonia for an e(tended period of time that depends on the case depth desired. a$ >itriding b) 3arburi7ing c) 3ase hardening d) 3"aniding Answer& a$ itriding 1;.Determine the !p lost when a collar is loaded with ' lb, rotates at + rpm, and has a coefficient of friction of .1+. The outside diameter of the collar is - inches and the inside diameter is ' inches. a) .;1- !p b) .;1- !p c) .-;1 !p d) .-;1 !p #nswer& b) .;1- !p
,Hp = Solution&
T , n 63000
=
, ! r , n 63000
=
0 . 1 5 ( 2000 "# ) ( 1.56 inch0s ) ( 50 rpm ) 63000
1*
= 0.3714
Machine Design and Shop Practice (Problems and Elements)
r , =
2 3
$here,
( ) [ r 3% −r i3 r 2% −r 2i
=
2 3
( 2 ) (3 )
3
3
− (1 ) − (1 )
2
2
]
=1.56 inch0s
15. )he primar application of high-speed steels is to tools used for the working of metals **********. b) at high cutting speeds a$ that are too hard c$ that are too soft d) at slow cutting speeds #nswer& b) #t high cutting speeds 1*.# parallel helical gearset consists of a 1*tooth pinion dri/ing a +;teeth gear. The pinion has a lefthand heli2 angle of 'o, a normal pressure angle of 1-N o, and a normal diametal pitch of 1 teeth?inch. f the pinion is to transmit + !p at a speed of 1;+ rpm. Determine the center distance of the two gears. a) '.' inches b) . inches c) -.- inches d) '. inches #nswer& c) -.- inches
Pdn = Solution&
P d
=
T p
=
T g
cos : D p cos : D g cos :
T p 19 D p = = = 2.02 inch0s P dn cos : 10cos 20% Pitch diameter of the pinion, T g 57 Dg = D p = 2.02 = 6.06 inch0s T p 19 Pitch Diameter of the gear,
( ) ( )
D p + Dg 2.02 + 6.06 C = = =4.04 inch0s 2 2 3entertocenter distance, 11.n gearing, this is the ratio of the arc of action to the circular pitch. a) Speed ratio b) #rc ratio c) 3ontact ratio
d) Jear ratio
#nswer& c) 3ontact ratio 111. # single sAuare thread power screw is to raise a load of ; %>. The screw has a ma0or diameter of mm and a pitch of mm. The coefficient of thread friction and collar friction are .1 and .1 respecti/el". f the collar mean diameter is * mm and the screw turns at rpm, find the a2ial linear speed of the screw. a) + mm?s b) mm?s c) ; mm?s d) +.+ mm?s #nswer& b) mm?s Solution& 8or the linear speed of the screw,
112.
8l"wheel arms are usuall" of elliptical crosssection, the strength of the arms should eAual OOOOOOOOOthe strength of the shaft in torsion. a) Threefourths b) nehalf c) Twothirds d) nefourth #nswer& a) Threefourth
11.This allo" (nickel, iron, chromium, cobalt is a nonmagnetic, corrosion resistant material suitable for sub7ero temperatures and temperatures up to about ;+ degrees 8., pro/ided that torsional stresses are %ept below ;+, pounds per sAuare inch. t is precipitationhardened to produce hardnesses of -5 to + oc%well 3 and is used in watch and instrument springs. a) Elin/ar b) Monel c) nconel d) D"na/ar '
Machine Design and Shop Practice (Problems and Elements)
Ans. #naar+ source& 6achiners hand8ook 11-.To ensure an adeAuate factor of safet" in the design of a shaft with standard %e"wa", the %e" width should be about& a) ne half of the shaft diameter b) ne fourth of the shaft diameter c) ne eighth of the shaft diameter d) ne third of the shaft diameter #nswer& b) nefourth of the shaft diameter >ote& nefourth of shaft diameter, as a guide in %e" selection for both sAuare and flat rectangular %e"s.
115.
$hat is the propert" of matter that causes it to resist an" change in its motion or state of rest a) Momentum b) @inetic Energ" c) nertia d) Section modulus #nswer& c) nertia
119.
This is defined as the cutting time to reach a predetermined wear, called the tool wear criterion. a) $ear duration b) 3"cle time c) Tool life d) :ife c"cle #nswer& c) Tool life
117. hich of the following :-codes refers to rapid traerse in ;; machining< a$ J b) J1 c) J' d) J Answer& a$ :00 11'.
An acronm in ;; machining which means access of the machine operator to insert machining
instructions directl" into the >3 machine control s"stem /ia push buttons, pressure pads, %nobs, or other arrangements. a) 8MS b) 8M3 c) 3M d) MD #nswer& d) MD >ote& MD 6 manual data input 11*.The /ariable polarit" plasma arc (
120. hich of the following statements is /) true< a$ The terms polishingI and buffingI are sometimes applied to similar classes of wor% in different plants. b) Polishing is an" operation performed with wheels ha/ing abrasi/e glued to the wor%ing surfaces c) 4uffing is done with wheels ha/ing the abrasi/e applied loosel" d) Polishing is not so harsh an operation as buffing, and it is commonl" utili7ed to obtain /er" fine surfaces ha/ing a grainless finish.I
Answer& d$ ote& =olishing is harsher than 8u"ng. 121. >f the steel is strongl deo(idi?ed 8 the addition of deo(idi?ing elements, no gas is eoled, and the steel is technicall called *******8ecause it lies uietl in the molds. a$ Huenched b) #nnealed c) @illed d$ Tempered #nswer& c) @illed steel
122. %tainless steels generall contain at least ** per cent chromium, with or without other elements. a$ 15 b) 1 c) 1' d) 1 '1
Machine Design and Shop Practice (Problems and Elements)
#nswer& d) 1 percent
12!. hat grades of stainless steels are nonmagnetic in the annealed condition, although some ma 8ecome slightl magnetic after cold working< b) #ustenitic grades c) Martensitic grades d) #n" of these a$ 8erritic grades #nswer& b) #ustenitic grades
124. )hese steels %AB %teels 1009, 100', 1010, 1015$ are the lowest car8on steels of the plain car8on tpe, and are selected where ******** is the primar reuisite of the user. a$ Strength b) ;old forma8ilit c$ Ductilit" d) Durabilit" #nswer& b) 3old formabilit"
125. %teel is heated to a temperature a8oe the critical range, after which it is cooled in still air to produce a generall Cne pearlite structure. )he purpose is to promote uniformit of structure and properties after a hot-working operation such as forging or e(trusion. hat was the heat treatment inoled< a$ #nnealing b) ormali?ing c$ Tempering d) Stress relie/ing #nswer& b) >ormali7ing 1'.#t certain speeds called the critical speeds, a rotating shaft will become d"namicall" unstable and the resulting /ibrations and deflections can result in damage not onl" to the shaft but to the machine of which it is a part. #t what percentage of the critical speed should a shaft be safel" operated a) Plus or minus 'K b) Plus or minus + K c) Plus or minus 1 K d) #n" of these #nswer& a) Plus or minus ' K 1';.This is the most widel" used of all spring materials for small springs operating at temperatures up to about '+ degrees 8. t is tough, has a high tensile strength, and can withstand high stresses under repeated loading. a) Music wire b) !ard drawn spring wire c) il tempered spring wire d) Stainless steel spring wire 1'5.t is an acron"m in machining. This process uses an electrode to remo/e metal from a wor%piece b" generating electric spar%s between conducting surfaces. a) MJ b) JM#$ c) EDM d) 3>3 #ns. ElectroDischarge Machining (Source& Machiner"Fs !andboo%) 1'*.n die casting accurate parts made of steel, what shrin%age allowance in inches per inch is recommended a) .11 b) .'' c) . d) .-#ns. .''. (Source& Machiner"Fs !andboo%) 1.This are gears used to connect shafts that are nonintersecting and nonparallel. The" are a cross between spriral be/el gears and worm gears. a) !elical gears b) H!"oid #ears c) Planetar" gears d) 4e/el gears 11.This is a t"pe of seal used where some form of relati/e motion occurs between rigid parts of an assembl". a) Jas%et b) Distorted seal c)
Machine Design and Shop Practice (Problems and Elements)
a) Turning
b) 8acing
c) Blan'in#
d) 8inishing
1!4. An 6-code which generall refers to start spindle rotation in a clockwise direction. b) Mc) M+ d) M a$ M) #ns. Mspindle start in a cloc%wise rotation 1+.# final operation to impro/e the polish of a metal and to bring out the ma2imum luster a) 8inishing b) Surface grinding c) 4roaching d) Bu**in# 1.Machining operations with the proper application of a cutting fluid generall" has the following attributes e2cept& a) !igher cutting speeds b) !igher feed rates c) :engthened tool life d) !i#her %uttin# a%%ura%! #ns. D. The use of cutting fluids does not increase cutting accurac". 1;.# material of construction (onl" de/eloped commerciall" in the late 1*-Fs concurrentl" with 7irconium) offers the uniAue combination of wide ranging corrosion resistance, low densit", and high strength. a) Tungsten b) Titaniu$ c)
1!'. hich of the following is the lightest of all structural metals< a$ #luminum b) 3opper c) Magnesium
d$ Manganese
1*. )his process reduces internal stresses, caused 8 machining, cold working, or welding, 8 heating
the steel to a temperature 8elow the critical range and holding it there long enough to euali?e the temperature throughout the piece. a$ #nnealing b) >ormali7ing c) Tempering d) Stress Relie+in# 1-.# freecutting steel has a higher OOOOOO content than comparable carbon steels. a) Sul*ur b) 3obalt c) >ic%el
d) 3hromium
1-1.This propert" designates the steels resistance to the softening effect of ele/ated temperature. a) Hot hardness b) Machinabilit" c) Toughness d) Elasticit"
142.
9se of hard solders, sil/er solders and smelter solders which ha/e sil/er, copper, or nic%el bases and ha/e melting points abo/e 5 degrees 8 is %nown asOOOOOOO a) Soldering b) $elding c) Bra,in# d) #n" of these
1-.n bra%ing, the term bac%stop refers to a bra%e that is& a) Sel* lo%'in# in one dire%tion c) Self loc%ing in both directions
b) Self energi7ing d) #n" of these
#ns. Selfloc%ing in one direction onl" 1--.!ow do "ou call a fi2ed crane consisting of a supported /ertical member from which e2tends a hori7ontal swinging arm carr"ing a trolle" hoist or other hoisting mechanism a) -i& %rane b) Jantr" crane c) /erhead crane d) Tower crane #ns. a) =ib crane (source& PME 3ode) 1-+.This iron is also %nown as a ductile cast iron. !ow do "ou call this iron a) Malleable iron b) Nodular %ast iron c) $hite cast iron
d) Jra" cast iron
#ns. b) >odular cast iron is a ductile cast iron. 1-.t is the abilit" to deform plasticall" to compensate for irregularities in bearing assembl". !ow do "ou call this a) Plasticit" b) Con*or$a&ilit! c) Embeddabilit" d) Elasticit"
'
Machine Design and Shop Practice (Problems and Elements)
1-;.# material of construction (onl" de/eloped commerciall" in the late 1*-Fs concurrentl" with 7irconium) offers the uniAue combination of wide ranging corrosion resistance, low densit", and high strength. a) Titaniu$ b) Tungsten c) ewtonFs law of motion that describes that if a force acts to change the state of motion of the bod", the bod" offers a resistance eAual and directl" opposite to the force. a) Second law b) Third law c) 8irst law d) 9ni/ersal gra/itation #ns. b) >ewtonFs third law of motion& #ction 6 eaction 1-*.These are steels most widel" used of engineering materials. >o other material offers comparable /ersatilit" for product design. a) .rou#ht steels b) :ow carbon steels c) Medium carbon steels d) Tool steels 1+.$hich of the following steels does not readil" respond to heat treatment a) S#E 1-+ b) #S 1+ c) SAE /0 o
:ow carbon steels (.K 3 and lower) do not readil" respond to heat treatment.
1+1.$hat is an element added to steel to impro/e its machinabilit" a) 3arbon b) Sul*ur c) 3obalt o
d) S#E 1*+
d) 3hromium
8ree machining or free cutting carbon contains more sulfur than other steels.
1+'.$hich of the following information is 8#:SE regarding steel that has increased carbon content a) ts strength is increased b) ts 4!> becomes greater c) Its du%tilit! is i$"ro+ed d) ts K reduction or elongation is reduced o
The ductilit" of steel is reduced if its carbon content is increased.
1+.n manufacturing, what is the operation of cutting out flat area to some desired shape and is usuall" the first step in a series of operation a) Turning b) Blan'in# c) 8acing d) 8inishing #ns. b) 4lan%ing (Source& PME 3ode) 1+-.This is a metal 0oining process which uses a nonferrous filler metal with a melting point below that of the base metals but abo/e 58. !ow do "ou call this process a) Bra,in# b) #rc welding c) Soldering d) i/eting 1++.i/et holes are made usuall" OOOO inch larger in diameter than the nominal diameter of the ri/et. a) 1?5 & /1/2 c) d) 1?' o
Jenerall" 1?1I from MD boo%s (e.g. 4lac%) and from the Machiner"Fs !andboo%.
1+.$hich of the following eAuations?formulas does not belong to the group a) La$e3s e4uation b) EulerFs formula c) =. 4. =ohnsonFs eAuation o
d) Secant formula
:ameFs eAuation is an eAuation for a thic%walled pressure c"linder. The other are for columns.
1+;.n 3>3 programming, which of the following J code commands is for dwell or rest a) J1 b) G5 c) J d) J' o
J- is for dwell or restG J1 is for linear interpolationG J' is for circular interpolation 3$G J is for circular interpolation 33$.
1+5.n 3>3 programming, which of the following M code commands is for a tool change a) M2 b) Mc) M d) M1 '-
Machine Design and Shop Practice (Problems and Elements)
o
M is for a tool changeG M is for spindle start 3$G M- is for spindle start 33$G M1 is for chuc% open.
1+*.$hich of the following is a material description referring to uniAue properties in three mutuall" perpendicular planes a) sotrop" b) #nisotrop" c) Orthotro"! d) sometr" #ns. rthotrop". E2ample is wood which shows uniAue properties in the three mutuall" perpendicular planes. 1.The true stressstrain cur/e in a stressstress diagram appears to be& a) :ower than the engineering stressstrain cur/e b) Hi#her than the en#ineerin# stress6strain %ur+e c) The same as the engineering stress strain cur/e d) S"mmetrical with the engineering stressstrain cur/e o
The true stressstrain cur/e uses the actual area of the specimen and is therefore higher than the engineering cur/e which is based on a constant (original) area of the specimen.
11.This is a hardening treatment for steels ha/ing low carbon content. a) Tempering b) Case hardenin# c) >ormali7ing
d) #nodi7ing
1'.$hat is a manufacturing process used for the production of aluminum a) 8orging b) E7trusion c) 4low molding
d) n0ection molding
1.This refers to a loss of material from the interface of two metal surfaces that are in intimate contact. !ow do "ou call this a) nterfacing b) nterference c) $ear d) 8rettin# %orrosion 1-.This is a t"pe of fit that reAuires heating the hub to e2pand its inside diameter. $hat do "ou call this t"pe of fit a) E2pansion fit b) 8orce fit c) Shrin' *it d) #n" of these 1+.#84M# is an acron"m for an association in/ol/ed in what machine elements a) Ball and roller &earin#s b) =ournal bearings c) 8lat belts and other belt t"pes d) #n" t"pe of gears o
#84M# means #nti8riction 4earing ManufacturersF #ssociation and is concerned with rolling element bearings such as ball, roller, and needle bearings.
1.$hat is the general description for mild steel a) Medium carbon steel b) Low %ar&on steel
c) !igh carbon steel
d) 3old rolled steel
#ns. Mild carbon steels are low carbon steels. 1;.
& O%tahedral shear6stress theor! d) Energ" distortion theor"
15.# t"pe of %e" in which width and thic%ness are eAual is called as& a) 8lat %e" & S4uare 'e! c) Pin %e"
d) 4arth %e"
1*.n the design of %e", the t"pical hub lengths are in accordance with the following relation where D is shaft diameter. a /90:D to 095D b) .+D to 1.'+D c) '.-D to .+D d) Depends on shaft diameter 1;.# coupling that allows a2ial fle2ibilit"?mo/ement in the operation. Made of alternate bolting of steel, leather, fabric and?or plastic material into two flanges. a) 8le2ible dis% coupling b) 8le2ible toroidal spring coupling % 8le7i&le Oldha$ %ou"lin# d) Elastic material bonded coupling 1;1.t is a machine member that supports another part that rotates, slides, or oscillates in or on it. a) Pulle" b) @e" % Bearin# d) Shaft '+
Machine Design and Shop Practice (Problems and Elements)
1;'.t is a bearing that permits constrained relati/e motion of rigid partsG lubricant is generall" inserted or supplied between the mating surfaces to reduce friction and wear, and to carr" awa" the heat generated. b) olling 3ontact 4earing a Slidin# Conta%t Bearin# c) Thrust 4earing d) =ournal 4earing 1;.These are surfaces that do not conform to each other /er" well as in the rollingelement bearings. a) 3onformal surfaces & Non6%on*or$al sur*a%es c) Sliding surfaces d) olling surfaces 1;-.The stud" of lubrication, friction, and wear of mo/ing or stationar" parts is %nown as& a) :ubrication & Tri&olo#! c) !"drod"namics d) !"drostatics 1;+.# bearing where surfaces are nonconformed and motion is primaril" rollingG it composed of rolling elements interposed between an outer ring and inner ring. a) Slidingelement bearing & Rollin#6ele$ent &earin# c) 3onformal surfaces bearing d) >onconformal surfaces bearing 1;.n a straight be/el gear, how do "ou call the angle between an element on the pitch cone and an element on the face cone a) 8ace angle b) Pitch angle % Addendu$ an#le d) Dedendum angle 1;;.t is a Jrashof fourbar mechanism in which the shortest lin% is the frame or fi2ed lin% and the other two cran%s completel" rotate with their a2es. !ow do "ou call this Jrashof fourbar mechanism a Dra#6lin' $e%hanis$ b) 3ran%roc%er mechanism c) Doubleroc%er mechanism d) Tripleroc%er mechanism 1;5. 8or a planar fourbar lin%age, the sum of the shortest and longest lengths cannot be greater than the sum of the remaining two lin% lengths if there is to be a continuous relati/e rotation between two members.I !ow do "ou call the preceding statement a) JrublerFs :aw b) 3oriolliFs :aw % Grasho*3s Law d) 8reudenteinFs :aw 1;*.$hich of the following is not true for an instant center or centro of planar lin%ages a) 3entro is a point common to two bodies ha/ing the same /elocit" in each. & Centro is a "oint in one &od! a&out whi%h another &od! does not rotate . c) 3entro is a point in one bod" about which another bod" actuall" turns. d) 3entro is a point in one bod" about which another bod" tends to turn. 15.This is the most common wor% holding de/ice of a shaper machine with the base graduated in degrees that ma%e it possible to swi/el an" angle. $hat is this wor%ing de/ice a Sha"er +ise b) Parallel bars and hold down bars c) :athe holder d) Swi/el head 151.This is a shaper operation, which is shaping the gi/en stoc% and ha/ing the e2cess material remain with a tolerable allowance for finishing. !ow do "ou call this operation b) 8inishing c) #ngular cutting d) 3ontouring a Rou#hin# 15'.!ow do "ou call a cutting tool that has two or more cutting edges as in drill presses and milling machine cutters a) Jrinder b) Singlepoint cutting tool % Multi6"oint %uttin# tool d) Two point cutting tool 15.This is the trade name for a patented allo" made up chiefl" of cobalt, chromium, and tungsten in /ar"ing proportions. $hat is this trade name b) 3arbolo" c) Stainless steel d) 3opper a Stellite 15-.t is called as the transformation of concepts and ideas into useful machiner". $hat is this a Desi#n b) S"nthesis c) #nal"sis d) Theorem 15+.This is a combination of mechanisms and other components that transforms, transmits, or uses energ", load, or motion for a specific purpose. !ow do "ou call this a) Mechanism b) Engine d) :in%age % Ma%hine
'
Machine Design and Shop Practice (Problems and Elements)
15.t is defined as s"nergistic collection of machine elementsG s"nergistic because as a design it represents an idea or concept greater than the sum of the indi/idual pats. $hat is this s"stem a) S"stem of mechanisms c) Design s"stem d) E2pert s"stem & Me%hani%al s!ste$ 15;.t ma" be defined as the displacement per length produced in a solid and as the result of stress. !ow do "ou call this a) Deformation b) Elongation d) Stress % Strain 155.$hat is the combination of applied normal and shear stresses that produces ma2imum principal normal stress or minimum principal normal stress, with a third principal stress between or eAui/alent to the e2tremes a) Principal shear stress & Prin%i"al nor$al stress c) Ma2imum shear stress d) 4ending and shear stresses 15*.!ow do "ou call a load that is applied trans/ersel" to longitudinal a2is of member a) 3ombined loads b) 3oncentrated load % Bendin# load
d) Distributed load
1*.$hat is the abilit" of the material to absorb energ" up to fracture a Tou#hness b) igidit" c) esilience
d) Stiffness
1*1.$hat is the other term for the Ma2imumShearStress Theor", as a failure prediction theor" a) /on Mises criterion & Tres%a !ield %riterion c) 3oulombMohr theor" d) Modified Mohr theor" 1*'.t is a failure prediction theor", which states that a part sub0ected to an" combination of loads will fail (b" "ielding or fracturing) whene/er the ma2imum shear stress e2ceeds a critical /alue. !ow do "ou call this failure prediction theor" a) Distortionenerg" theor" & Ma7i$u$6shear6stress theor! c) nternal friction theor" d) Modified Mohr theor" 1*.This is a theor" in c"clic and impact loading, which states that damage at an" stress le/el, is proportional to number of c"cles. $hat is this theor" commonl" called a Miner3s Rule b) Paris Power :aw c) Joodman ule d) Manson3offin elationship 1*-.This is a lubrication where the loadcarr"ing surfaces of the bearing are separated b" a relati/el" thic% film of lubricant, so as to pre/ent metaltometal contactG and where the stabilit" of the film can be e2plained b" the laws of fluid mechanics. !ow do "ou call this t"pe of lubrication a) !"drostatic lubrication & H!drod!na$i% lu&ri%ation c) Elastoh"drod"namic lubrication d) 4oundar" lubrication 1*+.!ow do call the speed at which a rotating shaft becomes d"namicall" unstable a) >ormal speed b)
d) #/erage speed
1*.!ow do "ou call a ball bearing with race containing pronounced groo/e for rolling elements a) 3rown bearing & Conrad &earin# c) #ngularcontact bearing d) 3"lindrical bearing 1*;.This is a machining process for producing internal straight c"lindrical surface or profiles, with process characteristics and tooling similar to those for turning operations. $hat is this machining process a Borin# b) Drilling c) eaming d) Milling 1*5.$hat is a set of specification for parts, materials, or processes intended to achie/e uniformit", efficienc", and a specified Aualit" a) 3ode & Standard c) :aw d) Theorem 1**.This is a set of specifications for the anal"sis, design, manufacture, and construction of somethingG the purpose of which is to achie/e a specified degree of safet", efficienc", and performance or Aualit". !ow do "ou call this set of specifications a Code b) Standard c) :aw d) Theorem '.!ow do call the si7e to which limits or de/iations is assigned and is the same for both members of the fitG it is the e2act theoretical si7e ';
Machine Design and Shop Practice (Problems and Elements)
a) >ominal si7e
& Basi% si,e
c) Ma2imum si7e
d) Minimum si7e
'1.$hat is the algebraic difference between a si7e and the corresponding basic si7e a) Tolerance b) #llowance % De+iation
d) :imit
''.$hat is the difference between the ma2imum and minimum si7e limits of a part a) #llowance & Toleran%e c) De/iation
d) 4asic si7e
'.This is used either for /er" accurate angular measurements or for locating wor% at a gi/en angleG is used together with precision gage bloc%s. $hat is this a) Protractor b) 3ompound rest c) Sine &ar d) Micrometer
'5
