Problem 9.30
A table saw for cutting wood is shown. The blade rotates counterclockwise,
and the operator pushes the wood into the blade using a stick to help keep his
or her hand away from the blade. Despite this safety precaution, it is possible
for the wood to be propelled by the blade with great force and speed into the
operator, causing injury. To help prevent this accident, the saw is outfitted with
an antikickback device, which weighs
0:3 lb
with center of gravity at point
B
.
Neglecting friction between the wood and saw table, determine the minimum
coefficient of friction between the wood and the antikickback device that will
prevent the wood workpiece from kicking back.
Problem 9.31
Bar
ABC
has square cross section and can slide in the square hole that is in
collar
D
. Collar
D
is supported by fixed vertical post
E
that is built in at its
base. The collar
D
can translate in the
´
direction and rotate about the
´
axis
without friction; other translations and rotations are constrained. End
C
of
the square cross section bar rests on a horizontal surface having coefficients of
friction
sD0:6
and
kD0:5
. If bar
ABC
is initially motionless, determine
the positive value of
P
that will cause impending motion. For this value of
P
,
also determine the reactions between bar ABC and the collar D.
Problem 9.32
Three books rest on a table. Books
A
,
B
, and
C
weigh 2, 3, and
4lb
, respec-
tively. Determine the horizontal force applied to book
A
that causes impending
motion of any of the books to the right, and determine which books move.
Problem 9.33
To glue blocks
B
and
C
to one another, the blocks are temporarily held together
until after a force
PD6lb
is applied. Both blocks weigh
2lb
. During the gluing
operation, the glue between blocks
B
and
C
acts as a lubricant, hence this surface
is frictionless. Using the coefficients of friction given in the figure, determine if
this gluing operation can be performed without either block sliding, and if sliding
does occur, determine which of the blocks will slide.
Problem 9.34
A portion of a machine that is used to lift an egg is shown. The clamps at
A
and
B
apply horizontal forces
P
to the egg, and the egg can have any of the three positions shown. If
PD0:5
N and an egg has
60
g
mass, determine the smallest value for the coefficient of friction at clamps
A
and
B
that will prevent the
egg from slipping.
(15). Hence,
Problem 9.35
A portion of a machine that is used to lift a stack of four identical books in
a printing factory is shown. The clamps at
A
and
B
apply horizontal forces
P
to the books. The coefficient of friction between a clamp and book is 0.6,
and the coefficient of friction between two books is 0.4. If each book weighs
8
N, determine the smallest value of
P
that will enable the stack of books to be
lifted.
Problem 9.36
In Prob. 9.35, if PD75 N, determine how many books may be lifted.
Problem 9.37
Block
A
and spool
B
weigh 8 and
6lb
, respectively. The spool has a string
wrapped around it to which a force
P
is applied. The coefficient of static friction
between the spool and the contact surfaces at
A
and
C
is 0.25. Determine the
value of
P
that causes impending motion, and determine if slip occurs at
A
, or
C
,
or both locations simultaneously.
Problem 9.38
Bars
AB
and
CD
are uniform and each weighs
7lb
. The coefficient of static
friction at surfaces Aand Bis the same.
If
PDQD0
, determine the minimum coefficient of static friction so that the
system has no motion.
Problem 9.39
Bars
AB
and
CD
are uniform and each weighs
7lb
. The coefficient of static
friction at surfaces Aand Bis the same.
If
QD0
and the coefficient of static friction for all surfaces is 0.6, determine
the value of Pthat causes impending motion of bar AB to the right.
Problem 9.40
Bars
AB
and
CD
are uniform and each weighs
7lb
. The coefficient of static
friction at surfaces Aand Bis the same.
If
PD0
and the coefficient of static friction for all surfaces is 0.6, determine
the value of Qthat causes impending motion of bar AB to the left.
Problem 9.41
Blocks
A
and
B
each have
2kg
mass. All contact surfaces have the same coefficient
of friction. Determine the force
P
needed to cause impending motion of block
B
to
the right if the coefficient of static friction is 0.4.
Problem 9.42
Blocks
A
and
B
each have
2kg
mass. All contact surfaces have the same coefficient
of friction. Determine the force
P
needed to cause impending motion of block
B
to
the right if the coefficient of static friction is 0.3.
Problem 9.43
A truck with
1500 kg
mass and center of gravity at point
C
is used to
pull a dumpster with
1700 kg
mass and center of gravity at point
G
. The
coefficient of static friction between the tires and pavement is 1.1, and
between the dumpster and pavement is 0.5. Assume the truck’s engine
has sufficient power and the dumpster does not tip. Hint: The use of
mathematical software is helpful, but not required. Determine if the truck
can pull the dumpster if:
The truck has rear-wheel drive.
Problem 9.44
A truck with
1500 kg
mass and center of gravity at point
C
is used to
pull a dumpster with
1700 kg
mass and center of gravity at point
G
. The
coefficient of static friction between the tires and pavement is 1.1, and
between the dumpster and pavement is 0.5. Assume the truck’s engine
has sufficient power and the dumpster does not tip. Hint: The use of
mathematical software is helpful, but not required. Determine if the truck
can pull the dumpster if:
The truck has four-wheel drive and end
E
of the cable is moved to
point H.
(1)
Wdumpster D.1700 kg/.9:81 m
s2/D16;680 ND16:68 kN:
(2)
The FBDs for the truck and dumpster are shown at the right. Our
strategy will be to determine
T
assuming the truck’s wheels slip,
and determine Tassuming the dumpster slips. The lower value of Tcorresponds to when slip will occur.
Truck: XMAD0WN2.2:8 m/.14:72 kN/.1:3 m/T1:5
If the trucks wheels slip, then
F1D1N1D.1:1/N1
and
F2D2N2D.1:1/N2
. Using these, we solve
Eqs. (3)–(7) to obtain Twith the result
Problem 9.45
Blocks
A
and
B
weigh 10 and
15
N, respectively. Point
C
is at the midpoint
of member BD, and both members AC and BD have negligible weight. The
coefficient of static friction for all contact surfaces is 0.3. Determine the positive
value of
P
that causes impending motion, and determine which of blocks
A
or
Bslides and the direction of motion.