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Unformatted text preview: CUSTOM GENERATED PROBLEMS 6—71. The three pinconnected members shown in the rat?
view support a downward force of 60 lb at G. If only virtlcad
forces are supported at the connections B, C, E an pa
supports A, D, F, determine the reactions at each pad. 6—72. The tractor boom supports the uniform mass of
500 kg in the bucket which has acenter of mass at G.
Determine the force in each hydraulic cylinder AB and CD
and the resultant force at pins E and F.The load IS supported
equally on each side of the tractor by a SlIl'Illal' mechanism. 0.4 m 0.3 m 6—73. The double tree AB is used to support the loading:
applied to each of the single trees. Determine the total load
that must be supported by the chain EG and its placement
for the double tree AB to remain horizontal. 8—1. If the horizontal force P : 801b, determine the
normal and frictional forces acting on the 300lb crate. Take #5 = 0.3, M = 0.2. Prob. 8—1 8—2. Determine the magnitude of force P needed to start
towing the 40kg crate. Also determine the location of the
resultant normal force acting on the crate. measured from
pointA.Take ,LLI = 0.3. mm Prob. 8—2 8—3. The spool of wire having a mass of 150 kg rests on the
ground at A and against the wall at B. Determine the force P required to begin pulling the wire horizontally off the spool.
The coefficient of static friction between the spool and its points of contact is #5 : 0.25. 8—4. The crate has a mass of 350 kg and is subjected to a
towing force P acting at a 20° angle with the horizontal. If the coefficient of static friction is #3 = 0.5, determine the magnitude of P to just start the crate moving down the
plane. CUSTOM GENERATED PROBLEMS 85. The motorcyclist travels with constant velocity along a
straight, horizontal, banked road. If he aligns his bike so that
the tires are perpendicular to the road at A, determine the
frictional force at A.The man has a mass of 60 kg and a mass center at GC. and the motorcycle has a mass of 120 kg and a mass center at G,,,. If the coefficient of static friction at A is
,uA = 0.4, will the bike slip? n 7 Prob. 8—5 8—6. The brook brake is used to stop the wheel from
rotating when the wheel is subjected to a couple moment M0. If the coefficient of static friction between the wheel
and the block is ,us, show that the brake is self locking, i.e., the required force P S 0, provided [3/6 S [1.5. CUSTOM GENERATED PROBLEMS *8—7. The block brake is used to stop the wheel from
rotating when the wheel is subjected to a couple moment M0” 1f the coefficient of static friction between the wheel
and the block is p.” determine the smallest force P that should be applied. Prob. 87 8—8. The block brake consists of a pinconnected lever and
friction block at B.The coefficient of static friction between the wheel and the lever is it, : 0.3, and a torque of 5 N m
is applied to the wheel. Determine if the brake can hold the wheel stationary when the force applied to the lever is (a)
P = 30N, (b) P = 70N.
5 N ' m 400 mm
Prob. 8—8 8—9. The block brake consists of a pinconnected lever and
friction block at B. The coefficient of static friction between the wheel and the lever is [1.5 = 0.3, and a torque of 5 N m
is applied to the wheel. Determine if the brake can hold the
wheel stationary when the force applied to the lever is (a) P = 30N, (b) P=70N. 8—10. The doorstep of negligible weight is pin connected at
A and the coefficient of static friction at B is as = 0.3. Determine the required distance 5 from A to the floor so
that the stop will resist opening of the door for any force P applied to the handle. *8—11. The chair has a weight of 10 lb and center of gravity
at G. It IS propped against the door as shown. If the coefficient of static friction at A is MA = 0.3, determine the smallest force P that must be a I‘edt [h
the door. Pp I 0 e handle to open Prob. 8—11 8—12. The uniform hoop of weight W is suspended from
the peg at and a horizontal force P is slowly applied at B.
If the coeff1c1ent of static friction between the hoop and peg is it, = 0.2, determine ifit is possible for the angle 6 : 30°
before the hoop begins to slip. Prob. 8—12 CUSTOM GENERATED PROBLEMS 8—13. The coefficient of static friction between the shoes at
A and B of the tongs and the pallet is n} 2 0.5, and between the pallet and the floor as = 0.4. If a horizontal towing force of P = BOON is a l' 
pp led to the ton s, d t
largest mass that can be towed. g e ermine the Prob. 8—13 8—_14. A very thin bookmark having a width ofl in. is in the
lTllddlB‘Of a 10lb dictionary. If the pages are 8 in. by 10 in
determine the force P needed to start to pull the bookmark
out.The coefficient of static friction between the bookmark
and the paper is ,uI : 0.7. Assume the pressure on each
page and the bookmark is uniform. P CUSTOM GENERATED PROBLEMS 8—15. The uniform dresser has a weight of 90 lb and rests
on a tile ﬂoor for which pt, = 0.25. If the man pushes on it in the horizontal direction 0 2 0°, determine the smallest
magnitude of force F needed to move the dresser. Also, if the
man has a weight of 150 1b, determine the smallest
coefficient of static friction between his shoes and the floor
so that he does not slip. 8—16. The board can be adjusted vertically by tilting it up
and sliding the smooth pin A along the vertical guide G.
When placed horizontally, the bottom C then bears along the 817. A chain having a length of 20 ft and weight of 8 lb/ft
rests on a street for which the coefficient of static friction is
a, = 0.2. If a crane is used to hoist the chain, determine the
force P it applies to the chain if the length of chain
remaining on the ground begins to slip when the horizontal component of P becomes 10 lb. What length of chain
remains on the ground? *8—18. The fork lift has a weight of 2400 lb and a center of
gravity at G. If the rear wheels are powered, whereas the
front wheels are free to roll, determine the maximum
number of 3UO—lb crates the fork lift can push forward.The
coefficient of static friction between the wheels and the ground is [1.5 = 0.4, and between each crate and the ground 8—19. The SUDlblconcrete pipe is being lowered from the
truck bed when It is in the position shown. If the coefﬁcient
of static friction at the points of support A and B is #5 = 0.4, determine where it begins to slip first: at A or B
or both at A and B. , A Skg wedge is placed in the grooved slot of an
inclined plane. Determine the maximum angle 6 for the CUSTOM GENERATED PROBLEMS 8—2.1. man has a Weight of 200 lb, and the coefficient of
static friction between his shoes and the ﬂoor is p, = 0.5. Determine where he should position his center of gravity G at d In order to exert the maximum horizontal force on the
door. What is this force? edge of the guide, where ,u, = 0.4. Determine the largest dimension d which will support any applied force F without
causing the board to slip downward. incline without causing the wedge to slip.The coefficientof 8—22. The man havmg 3 “might of 150 static friction between the wedge and the surfaces of contact
is 11., = 0.2. lb pushes horizontally on the bottom of crate A, which is stacked on
top of crate B. Each crate has a weight of 100 lb. If the coefficient of static friction betWeen each crate is p, = 0 8
5 .
and between the bottom crate, his shoes, and the floor is
, g . .
u, — 0.3, determine if he can cause impending motion. .59} Top view H 0.75 in. mm
Side view CUSTOM GENERATED PROBLEMS 823. The crate has a weight of 200 lb and a center of
gravity at G. Determine the horizontal force P required_to
tow it. Also, determine the location of the resultant normal force measured from A. Take h = 4 ft and ,u, = 0.4. Prob. 8—23 8—24. The friction hook is made from a fixed frame which
is shown colored and a cylinder of negligible weight. A piece
of paper is placed between the smooth wall and the cylinder. If 6 : 20", determine the smallest coefficient of static
friction u at all points of contact so that any weight W of paper ,0 can be held. Prob. 8—24 8—25. The wheel weighs 20 lb and rests on a surface for
which my I 0.2. A cord wrapped around it is attached to
the top of the 30lb homogeneous block. If the coefficient Of
static friction at D is up = 0.3, determine the smallest vertical force that can be applied tangentially to the wheel
which will cause motion to impend. Prob. 8—25 8—26. Determine the smallest couple moment which can be
applied to the 20lb wheel that will cause impending motion.
The cord is attached to the 30lb block, and the coefficients of static friction are ,uB : 0.2 and an I 0.3. *827. The beam AB has a negligible mass and thickness
and is subjected to a triangular distributed loading. It is
supported at one end by a pin and at the other end by a post
having a mass of 50 kg and negligible thickness. Determine
the two coefficients of static friction at B and at C so that
when the magnitude of the applied force is increased to P : 150 N, the post slips at both B and C simultaneously. *8—28. Block C has a mass of 50 kg and is confined
between two walls by smooth rollers If the block rests on
top ofthe 40kg spool, determine the minimum cable force F
needed'to move the spool.The cable is wrapped around the
spool s inner core. The coefficients of static friction at A and B are [LA = 0.3 and as = 0.6. Prob. 8—28 8—29. Determine the minimum force P needed to push the
tube E up the incline.The tube has a mass of 75 kg and the
roller D has a mass of 100 kg. The force acts parallel to the
plane, and the coefficients of static friction at the contacting
surfaces are u,, : 0.3, ,uB = 0.25, and up = 0.4. Each
cylinder has a radius of 150 mm. 1 Prob. 8—29 CUSTOM GENERATED PROBLEMS *8—30. The uniform pole has a weight W and length L. lts end. B is tied to a supporting cord, and end A is placed
against the wall, for which the coefficient of static friction is pg. Determine the largest angle 9 at which the pole can be
placed without slipping. Prob. 8—30 31—31. The mine car and its contents have a total mass of 6
‘g and a center of gravrty at G. If the coefficient of static
friction between the wheels and the tracks is ,u.I : 0.4 when the wheels are locked, find the normal force acting on the
front wheels at B and the rear wheels at A when the brakes at both A and B are locked. Does the car move? Prob. 8—31 CUSTOM GENERATED PROBLEMS *8—32. The uniform pole has a weight of 30 lb and a length
of 26 ft. Determine the maximum distance d it can be placed
from the smooth wall and not slip. The coefficient of static friction between the floor and the pole is ,u: = 0.3. Prob. 8—32 8—33. An axial force of T = 800 lb is applied to the bar. If
the coefﬁcient of static friction at the jaws C and D is #5 = 0.5, determine the smallest normal force that the screw at A must exert on the smooth surface of the links at B
and C in order to hold the bar stationary. The links are pin—
connected at F and G. 8—34. The 15ft ladder has a uniform weight of 80 lb and
rests against the smooth wall at B. If the coefficient of static friction at A is ,uA = 0.4, determine if the ladder will slip.
Take 6 = 60°. Prob. 8—34 835. The log has a coefficient of static friction of ,trI : 0.3 with the ground and a weight of 40 lb/ft. Ifa man can pull on
the rope with a maximum force of 80 lb, determine the
greatest length l of log he can drag. Prob. 8—35 *8—36. The roll of paper of weight W rest between the two
supports at A and B. If the coefficient of static friction at these points is ,u, : 0.3, determine the horizontal force P
needed to cause motion. Prob. 8—36 8—37. 'The ZOOmm uniform rod has a weight W and is
placed in a glass as shown. If the smallest angle at which it can lean against the glass without slipping is 6 2 60°, determine the coefficient static friction between the glass
and rod. Neglect the thickneSS of the rod. Prob. 8—37 8—38. Determine the force P needed to lift the IOUlb load.
Smooth rollers are placed between the wedges. The
coefficient of static friction between A and C and between B and D is p5 = 0.3. Neglect the weight of each wedge. CUSTOM GENERATED PROBLEMS 8—39. The coefficient of static friction between the wedges
B and C is ,u.‘ : 0.6 and between the surfaces of contact B and A and Cand D, n,’ = 0.4. If P = 50 N, determine the largest allowable compression of the spring without causing wedge C to move to the left. Neglect the weight of the
wedges. k : 500 N/m 7 Prob. 839 8—40. If the coefficient of static friction between all the
surfaces of contact is #5, determine the forcePthat must be applied to the wedge in order to lift the brace that supports
the load F. CUSTOM GENERATED PROBLEMS 8—41. The column is used to support the upper floor. If a force F = 80 N is applied perpendicular to the handle to
tighten the screw, determine the compressive force in the
column. The squarethreaded screw on the jack has a coefficient of static friction of it, = 0.4, mean diameter of
25 mm, and a lead of3 mm. 8—42. If couple forces of F : 35N are applied to the
handle of the machinist’s vise, determine the compressive
force developed in the block. Neglect friction at the bearing
A. The guide at B is smooth. The single squarethreaded
screw has a mean radius Ofﬁ mm and a lead of8 mm,and the coefficient Of static friction is it, = 0.27. 843. If the required clamping force at the board A is to be
50 N, determine the torque M that must be applied to the
handle Of the “C” clamp to tighten it down. The single
squarethreaded screw has a mean radius of 10 mm, a lead of 3 mm, and the coefficient of static friction is ii, = 0.35. \ Prob. 843 *8—44. The two blocks under the double wedge are
brought together using a left and right square—threaded
screw. If the mean diameter is 20 mm, the lead is 5 mm, and the coefficient of static friction is it, = 0.4, determine the torque needed to spread the blocks apart. The coefficient of
static friction between each block and its surfaces of contact is it; = 0.4.
5 kN 8—45. Determine the minimum applied force P required to
move wedge A to the right. The spring is compressed a
distance of 175 mm. Neglect the weight of A and B The
coeffiCient of static friction for all contacting surfaces is its : 0.35. Neglect friction at the rollers. k :15 kN/m 346. Determine the largest weight of the wedge that can
e placed between the Slb cylinder and the wall without
upsetting eqmlibrium. The coefficient of static friction at A and Cis it, = 0.5 and at B, it; = 0.6. Prob. 8—46 CUSTOM GENERATED PROBLEMS 847. The beam is adjusted to the horizontal position by
means. of a wedge located at its right support. If the
coefficient of static friction between the wedge and the two surfaces of contact is piI = 0.25, determine the horizontal force P required to push the wedge forward. Neglect the weight and Size Of the wedge and the thickness of the beam.
3001b Prob. 847 If the beam AD is loaded as shown, determine the
horizontal force P which must be applied to the wed e in
order to remove it from under the beam. The COCfflClel'lng of
static friction at the wedge’s top and bottom surfaces are no. = 0.25 and it” = 0.35, respectively. If P : 0, is the wedge selflocking? Neglect the wei ht ‘
. and
wedge and the thickness of the beam. g 5126 0f the CUSTOM GENERATED PROBLEMS 8—49. The squarethreaded screw has a mean diameter of
20 mm and a lead of 4 mm. If the weight Of the plate A is 5 lb,
determine the smallest coefficient of static friction between
the screw and the plate so that the plate does not travel down the screw when the plate is suspended as shown. 850. The shaft has a squarethreaded screw with a lead of
8 mm and a mean radius of 15 mm. If it is in contact with a
plate gear having a mean radius of 30 mm, determine the
resisting torque M on the plate gear which can be overcome if a torque of 7 N m is applied to the shaft. The coefficient
of static friction at the screw is p3 = 0.2. Neglect friction of
the bearings located at A and B. IS mm Prob. 850 8—51. The two blocks used in a measuring device have
negligible weight. If the spring is compressed 5 in. when in
the position shown, determine the smallest axial force P
which the adjustment screw must exert on Bin order to start
the movement of B downward. The end of the screw is
smooth and the coefficient of static friction at all other points of contact is ,ur.5 = 0.3. k : 201mm. { Prob. 8—51 8—52. Determine the smallest force P needed to lift the
3000lb load.The coefficient of static friction between A and C and between B and D is as = 0.3, and between A and B
it; : 0.4. Neglect the weight of each wedge. Prob. 8—52 8—53. Determine the reversed horizontal force P
needed to pull out wedge A. The coefficient of static friction between A and C and between B and D is as = 0.2, and between A and B ,u; : 0.1. Neglect the weight of each
wedge. Prob. 853 *8—54. The squarethreaded bolt is used to join two plates
together. If the bolt has a mean diameter of d = 20 mm and a lead of 1: 3mm, determine the smallest torque M
required to loosen the bolt if the tension in the bolt is
T = 40 kN. The coefficient of static friction between the
threads and the bolt is ,uI = 0.15. CUSTOM GENERATED PROBLEMS 8—55. The hand clamp is constructed using a square
threaded screw having a mean diameter of 36 mm, a lead of
4 mm, and a coefficient of static friction at the screw of [.LS = 0.3. To tighten the Screw, a force of F = ZON is applied perpendicular to the handle. .Determine the
clamping force in the board AB. Prob. 8—55 8—56. The hand clamp is constructed using a square
threaded screw having a mean diameter of 36 mm, a lead of
4 mm, and a coefficient of static friction at the screw of M5 2 0.3. If the clamping force in the board AB is 300 N, determine the reversed force 7F that must be applied
perpendicular to the handle in order to loosen the screw. Prob. 8—56 8—57. The truck, which has a mass of 3.4 Mg, is to be
lowered down the slope by a rope that is wrapped around a
tree. If the wheels are free to roll and the man at A can resist
a pull of 300 N, determine the minimum number of turns the
rope should be wrapped around the tree to IOWer the truck
at a constant speed. The coefficient of kinetic friction between the tree and rope is uk 2 0.3. Prob. 8—57 CUSTOM GENERATED PROBLEMS 8—58. Determine the largest mass of cylinder A that can be supported from the drum if a force F = 20 N is applied to
the handle of the lever. The coefficient of static friction between the belt and the wheel is u, i 0.3. The drum is pin
supported at its center, B. Prob. 8—58 859. The uniform bar AB is supported by a rope that
passes over a frictionless pulley at C and a fixed peg at D. If
the coefficient Of static friction between the rope and the peg is n17 = 0.3, determine the smallest distance x from the end of the bar at which a 20N force may be placed and not
cause the bar to move. 1m Prob. 8—59 *8—60. Determine the torque M that can be resisted by the band brake if a force Of P = 30 N is applied to the handle
of the lever.The coefficient of static friction between the belt and the wheel is u, I 0.3. The wheel is pin connected at its
center, B. Prob. 8—60 8—61. Granular material, having a density Of 1.5 Mg/m3, is
transported on a conveyor belt that slides over the fixed
surface, having a coefficient of kinetic friction Of pk = 0.3. Operation of the belt is provided by a motor that supplies a
torque M to wheel A.The wheel at B is free to turn, and the
coefficient Of static friction between the wheel at A and the belt is W, = 0.4. If the belt is subjected to a pretension of 300 N when no load is on the belt, determine the greatest
volume V of material that is permitted on the belt at any
time without allowing the belt to stop. What is the torque M
required to drive the belt when it is subjected to this
maximum load? Fk=03 MA : 0.4 *8—_62. Blocks‘A and B weigh 50 lb and 30 lb, respectively.
Usmg the coefftcrents of static friction indicated, determine
the greatest ...
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 Spring '10
 Michael
 Force, Friction, UK

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