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Unformatted text preview: 182 PROS. 5.9 PROB. 5.14 FRICTION H O M
5.9 5.12 U]
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’JI EWORK PROBLEMS Determine the force F required to cause motion in the system shOWn.
At which surfaces will sliding occur? The coefﬁcient of static friction
between the 2 kg block A and the 8 kg block B is p5 = 0.2 and the
coefﬁcient of static friction between block B and the horizontal plane
is [,ts = 0.1. The coefﬁcient of static friction between the person and the ﬂoor is
0.50, and the coefﬁcient of static friction between the crate and the
ﬂoor is 0.25. Determine the largest mass for the crate that the person
can move by pulling on the cable if the person’s mass is 70 kg. PROB. 5.10 PROB. 5.11 The coefﬁcient of static friction between each block and the surface
it contacts is 0.2. Block A weighs 41b and block B weighs 6 lbs.
Determine the largest angle (9 of the incline for which the blocks will
remain at rest. The masses of blocks A and B are 5 and 10kg, respectively. The
coefﬁcient of static friction between block A and its incline is 0.20.
Determine the minimum coefﬁcient of static friction between block B
and its incline required to maintain equilibrium. If this coefﬁcient is
not sufﬁciently large, in which direction will the blocks slide? Solve Problem 5.12 if block A has a mass of 10 kg and block B has
a mass of 5 kg. The masses of blocks A and C are 10 and 20 kg, respectively. These
blocks are interconnected by cords AB and BC. Knowing that the
system is in equilibrium, determine (a) the friction force acting on
each block, (b) the minimum allowable coefﬁcient of static friction
between each block and its surface for static equilibrium. Two 3 kg collars are connected by a cord and are in equilibrium in
the position shown. The coefﬁcient of static friction between collar A
and its inclined guide is 0.30. Determine the minimum allowable value
of the coefﬁcient of static friction between collar B and its guide. PROB. '5.15 PROB. 5.16 2ft B 0
__L PROBS. 5.20 AND 5.21 PROB. 5.22 A. DRY FRICTION “ 183 *5.16 *5.17 5.18 5.20 5.21 Three suitcases A, B, and C are placed on a chute. Their weights are
wA = wB = 30 lb, wc = 45 lb. The coefﬁcients of static_ friction between
the suitcases and the chute are [1,, = MB = 0.40, pc 2 0.20. Determine
which, if any, of the suitcases will slide down the chute. Hint: Succes
sively consider the possibility of impending motion of suitcase A ' alone, then of both suitcases A and B, and finally of all three suitcases. A 10 lb block resting on a plane inclined at 20" above the horizontal
is subjected to a horizontal force F parallel to the plane, as shown.
It is observed that the block will start to move if the magnitude of I—3
exceeds 3 lb. Determine (a) the coefﬁcient of static friction between
the block and the inclined plane, (b) the direction in which the block
starts to slide if the magnitude of F exceeds 3 lb. B y
. A gr
,1: A o ‘ PROB. 5.17 PROBS. 5.18 AND 5.19 The uniform 80 kg bar rests against the rough vertical wall. The
horizontal force I3 is 400 newtons acting to the right. Determine (a) the
friction force at end B, and (b) the minimum coefﬁcient of static friction
between the bar and the wall for which static equilibrium is possible.
The coefﬁcient of static friction between the 80 kg uniform bar and
the rough vertical wall is 0.3. Determine the smallest horizontal force
I3 at end A for which static equilibrium is possible. The uniform 20 lb bar is supported by a roller on the inclined wall
and by the rough horizontal surface. The bar is in static equilibrium
and 0 = 30°. Determine (a) the friction force acting on end A, and
(b) the minimum coefﬁcient of static friction between the bar and the
horizontal surface. The coefﬁcient of static friction between the uniform 20 lb bar and
the horizontal surface at end A is 0.40. The inclined‘surface at end B
is smooth. Determine the maximum angle 0 for which static equilib
rium is possible. The 3 ft diameter cylinder weighs 500 lb. The coefﬁcient of friction
between the cylinder and both surfaces is it, = 0.32. Determine the
maximum magnitude of the counterclockwise couple A7! for which
sliding will not occur. 184 PROB. 5.23 FRICTlON 5.23 5.25 *5.26
5.27 A 2 kN load is applied to the linkage, as shown. Knowing that the
system is in equilibrium, determine (a) the friction force acting on bar
AB at end A, (b) the minimum value of the coefﬁcient of static friction
for which static equilibrium is possible. The mass of the bars is
negligible. The semicylinder of mass m and radius R is in a condition of impending
motion. The coefﬁcient of static friction between the semicylinder
and the inclined planes are the identical values p, and point G is the
center of mass of the semicylinder. Determine u. PROB. 5.24 PROB. 5.25 The masses of the bars and the collar are negligible, and the system
is in static equilibrium. Determine (a) the friction and normal forces
acting on the collar, and (b) the minimum possible coefﬁcient of static
friction between the collar and the guide for which the system will
remain in static equilibrium. Solve Problem 5.25 if the mass of each bar is 20 kg. A cable is wrapped around the 50kg stepped drum and a tensile
force 1’3 is applied to the free end of the cable, as shown. The drum is
in static equilibrium. Determine (a) the magnitude of I3 and of the
friction force acting on the drum, (b) the direction in which the point
on the drum in contact with the inclined surface is tending to move,
and (c) the minimum value of the coefﬁcient of static friction for which
static equilibrium is possible. PROB. 5.27 PROB. 5.28 I PROB. 5.32 re————1ﬂ———>' A. DRY FRICTION 5.28 185 The 1000 lb stepped drum is held in static equilibrium by the tensile
force I5 applied to the cable. The drum is supported on its inner radius
by two rails (only one is visible in the side view shown). Determine
(a) the magnitude of 13, (b) the friction force exerted by each rail on
the drum, and (c) the minimum allowable coefﬁcient of static friction
between the drum and a rail. The coefﬁcients of static friction between the ladder and the wall,
and the ladder and the ground, are 0.2 and 0.3, respectively. Determine
the minimum horizontal distance d between the center of mass G of
the 60 kg worker and the wall for which the ladder will not slide. The
mass of the ladder is negligible. Solve Problem 5.29 if the mass of the ladder is 10 kg. PROB. 5.29 PROB. 5.31 The coefﬁcient of friction between the uniform 30 kg bar and both
surface is ,u: = 0.20. Is the system in static equilibrium? The coefﬁcient of friction between the uniform 5 lb bar and both
inclined walls is 0.30. Is the bar in static equilibrium in the horizontal
position shown? Point G is the center of mass of the 10 kg semicylinder. If the system
is in static equilibrium, determine (a) the angle 6, and (b) the minimum
allowable coefﬁcient of static friction between the semicylinder and
the ground. 4r/37r ‘<’ PROB. 5.33 186 200mm PROBS. 5.34 AND 5.35 Hydraulic
cylinder PROBS. 5.40 AND 5.41 FRICTION 5.34 The adjustable bracket is supported on the vertical guide by collars
at A and B. The coefﬁcient of static friction between each collar and
the guide is 0.20, and mass of the bracket is negligible. Determine the
magnitude of the vertical force F required to move the bracket upward
from rest. ’ 5.35 In Problem 5.34, determine the magnitude and sense of the vertical
force F required to move the bracket downward from the rest position. 5.36 The 200 lbin. couple is applied to rod AB in order to resist the 70 lb
force applied to piston C. Knowing that the linkage is in static equilib
rium at the position where 9 = 90°, determine (a) the friction force
acting on the piston, and (b) the minimum coefﬁcient of static friction
between the piston and its cylinder for which this situation is possible. 5.37 Solve Problem 5.36 for the position where 9 = 135°. 200mm PROBS. 5.36 AND 5.37 5.38 The coefﬁcient of static friction between collar B and bar CD is 0.25.
The bars have negligible mass. Determine the magnitude of the couple
IV! A for which bar AB will rotate clockwise from rest. 5.39 In Problem 5.38, determine the magnitude and sense of the couple
M A for which bar AB will rotate counterclockwise from rest. 5.40 A couple MC is applied to the brake drum C. Determine the smallest
force exerted by the hydraulic cylinder on brake arm AB for which
the brake drum will not rotate if MC is 300 Nm clockwise. The
coefﬁcient of static friction between the drum and the arm is 0.75. 5.41 Solve Problem 5.40 if MC is 300 Nm counterclockwise. *5.42 The coefﬁcient of static friction between the 2 kg bar and both surfaces
it contacts is 0.20. Determine the largest and smallest values of the
angle 6 for which the bar is in static equilibrium. PROBS. 5.38 AND 5.39 PROB. 5.42 PROB. 5.43 *5.43 The 3 lb bar AB is supported by the 2 lb bar CD. Determine the
minimum values of the coefﬁcients of static friction between each
pair of contact surfaces for which static equilibrium is possible. A. DRY FRICTION 1 87 50mm 40mm *5.44 A 50 mm diameter rod is being gripped by the Stilson wrench shown.
Members A ~and B may be regarded as a single rigid body connected
to member C only by pin D. It is observed that, regardless of the
magnitude of the force 13, the wrench does not slip over the rod (the
wrench is said to be selflocking). Determine the minimum coefficients
of static friction at both points of contact between the wrench and
the pipe. *5.45 A 5ft long bar is connected to the ﬂoor by a ballandsocket joint
that is 4 ft from the vertical wall supporting the other end of the bar.
The bar weighs 20 lb and the coefficient of static friction between the
bar and the wall is 0.35. Determine the maximum value of the angle 8
for which static equilibrium is possible. Hint: Because of the support
at end A, end B tends to move tangent to the dashed circle. PROB. 5.44 PROB. 5.45 PROB. 5.46 5.46 A 30 kg plank is resting on two horizontal joists, perpendicular to
the axis of the joists in the horizontal plane. The coefﬁcient of static
friction between the plank and the joists is 0.40. Determine the force 1—),
parallel to the joists, required to move the plank when d = 2 m. H int:
The friction forces acting on the plank may be considered to be
parallel to the joists. 3. Sliding or Tipping
The impending motion we have considered thus far originated from the
tendency of the pair of contacting surfaces to slide over each other. Another
type of impending motion that is possible is the tendency of the external
forces acting on a body to overturn (that is, tip over) the body. This type
of motion arises whenever the frictional and normal reactions cannot exert
a moment that is sufﬁcient to balance the moment of the external forces.
As an example, consider the horizontal force that the person in Figure 63
must apply to the ﬁle cabinet in order to move the cabinet. If the person
exerts a sufﬁciently large force close to the ground, as in Figure 6b, the 190 PROBS. 5.47 AND 5.48 FRICTION The value of P for tipping is smaller than that required to slide the crate.
Thus, we conclude that the crate will tip and P ax = 503 newtons . A m Additional Remarks It “Q11 be noted that we solved the case of impending slipping without em
ploying the moment equilibrium equation. This is a consequence of the
coefﬁcients of static friction at skids A and B being equal. If these coefficients
were diﬁerent, we would have needed 2 F , and Z M A, to ﬁnd the individual
values of NA and NB. An interesting aside to this problem is its similarity to the problem
posed in part (c) of Example 1. It can be seen that concern about the possibility
of impending tipping, which always requires that we consider moment
equilibrium, complicates the solution of problems involving impending
motion. HOMEWORK PROBLEMS 5.47 The coefﬁcient of static friction between the 1 ton granite block and
the ﬂoor is 0.35, and h = 2.5 ft. Determine the largest horizontal force
F that will not move the block. 5.48 The coefﬁcient of static friction between the 1 ton granite block and
the ﬂoor is 0.35. Determine the largest distance h for the horizontal
force F for which slipping will occur before tipping. 5.49 A 60 kg refrigerator, having center of mass G, is mounted on four
casters. The coefﬁcient of static friction between a locked caster and
the ﬂoor is 0.50, and the frictional resistance of a rolling caster is
negligible. Determine the magnitude of the horizontal force 15 required
to move the refrigerator when h = 1.0 m if all casters are locked. 5.50 Solve Problem 5.49 if only casters B are locked. mm mm PROB. 5.49 A. DRY FRICTION 191 r 5.51 In Problem 5.49, determine the largest value of hfor which the re
frigerator will not tip (a) if all casters are locked, (b) if only casters B
are locked. (c) Explain why it is impossible to tip the refrigerator over
with the force P when only casters A are locked. 5.52 A 60 kg cabinet whose center of mass is point G is supported by
skids along edges A and B. The coefﬁcients of static friction between
the skids and the incline are m = #3 = 0.75. Determine the largest
force F, parallel to the incline, for which the cabinet will not move. 5.53 Solve Problem 5.52 if [AA = 0.5 and p3 = 0.90. 5.54 Determine the magnitude and sense of the force 13 for which the
cabinet in Problem 5.52 is in a state of impending motion down the
incline. PROB. 5.52 5.55 The center of mass of the 120 lb table is point G. The table is supported
by four casters, each of which is locked. The coefﬁcient of static
friction between a locked caster and the incline is 0.60. Determine
the magnitude and sense of the horizontal force P for which the table
is in a state of impending motion down the incline. 5.56 Solve Problem 5.55 if only caster A are locked. The friction between
the unlocked casters B and the incline is negligible. PROB. 5.55 PROB. 5.57 5.57 The 25 kg door is mounted on the horizontal rail by means of runners
A and B. The coefﬁcients of friction for these runners are m = #3 = 0.15.
The door handle is pulled to the right to open the door. Determine
(a) the maximum distance d for the door handle for which the door
will not tip when it is opened, (b) the force required to open the door
if d equals the value found in part (a), and (c) the force required to
open the door if d equals onehalf the value found in part (a). Solve Problem 5.57 if [AA = 0.20, #3 = 0.10. The 8 lb thin semicylindrical shell is to be towed to the left. The
coefﬁcient of static friction between the shell and the surface is 0.35.
Determine the largest angle a for which the cable tension T will cause the shell to slide to the left without tipping. What is the corre
PROB. 5.59 sponding value of T? 192 PROB. 5.60 PROB. 5.63 FRICTION 5.60 *5.61 *5.62 *5.64 The angle [3 of the incline is very gradually increased until the block
of mass m moves. Develop formulas that indicate whether the block
slides or tips in terms of the coefﬁcient of friction u, the ratio b/h,
and the angle if at which movement occurs. The bar of mass m is supported in the vertical plane by pins A and B,
which are separated by a distance d. The coefﬁcient of static friction
between each pin and the bar is 0.70. Determine the largest value of d
for which static equilibrium is possible. 500mm PROB. 5.61 PROB. 5.62 A 500 kg electronic computer, having center of mass G, is placed on
the 20 kg dolly. The casters A of the dolly are locked. The coefﬁcients
of friction between the computer and the dolly, and between the
casters and the ﬂoor, are 0.50 and 0.30, respectively. Determine the
maximum force F that can be applied without causing the computer
to move. The 80 kg block rests against the vertical wall in the position shown.
Determine the largest horizontal force 175 for which the block will not
move if the coefﬁcient of friction between the ground and the block
is 0.50, and the vertical wall is smooth. Solve Problem 5.63 for the case where the coefﬁcient of friction between
the block and each surface it contacts is 0.5. 8. BASIC MACHINES HAVING FRICTION There are a multitude of simple mechanical devices, that we refer to as basic machines, that can be used to either move or prevent the motion of
physical objects. These devices can magnify or convert the input forces
applied to them into a different set of output forces that are applied to other
systems. For example, a wheel ﬁxed to an axle has the capability of trans
forming a torque exerted by its axle into a forward force that can propel
a vehicle. In Chapter 4, we developed the basic techniques for investigating the
equilibrium of machines. The common feature of the machines we shall
consider here is the important, and sometimes useful, effect of friction. ...
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This note was uploaded on 09/08/2010 for the course ME 270 taught by Professor Murphy during the Summer '08 term at Purdue.
 Summer '08
 MURPHY

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