Problem 9.61
0.35 and: The drum rotates counterclockwise and PD20 lb.
MADT2.10 in:/ T1.10 in:/ (7)
Problem 9.62
0.1 and 0.09, respectively. The spring is initially unstretched.
(a) Determine the value of Pneeded to stretch the spring by 4mm.
(b)
Once the spring is stretched by
4mm
, determine the value to which
P
must be reduced so that the spring begins to contract.
Problem 9.63
Pulley
A
of the treadmill is driven by a motor that can supply a moment
MAD
200 in:lb
. Pulley
B
is frictionless, and its bearing slides in a frictionless slot
where force
P
tensions the belt. Both pulleys
A
and
B
have
1:5 in:
radius, and
the coefficient of static friction between pulley
A
and the belt is 0.3. Determine
the smallest value of Pneeded to prevent slip between pulley Aand the belt.
Problem 9.64
The winch is driven by an electric motor at
A
. The motor weighs
50 lb
with
center of gravity at the center of pulley
A
. The platform supporting the motor
has negligible weight and is hinged at
D
. The motor turns the pulley at
B
via
a belt between
A
and
B
. Pulley
B
has a spool upon which the rope BCG is
wrapped. The coefficient of static friction at
A
is 0.3 and at
B
is 0.2. Assuming
the motor has sufficient power, determine the largest weight
W
that may be
lifted if there is no slip between the belt and pulleys
A
and
B
.Hint: The use of
mathematical software is helpful, but not required.
Problem 9.65
Surfaces
A
,
B
, and
C
are cylindrical with the coefficients of static friction
shown. Object
B
can undergo vertical motion only. Determine the weight
of object
B
that causes it to have impending downward motion, and describe
which of surfaces A,B, and/or Cwill have impending slip.
Problem 9.66
In Prob. 9.65, determine the weight of object
B
that causes it to have impending
upward motion, and describe which of surfaces
A
,
B
, and/or
C
will have
impending slip.
Problem 9.67
An accessory belt for an engine is shown. Pulley
A
is attached to the engine’s
crankshaft and rotates clockwise. The belt tensioner consists of a frictionless
pulley at
B
that is mounted to a horizontal bar
G
that slides in a frictionless track
with a horizontal force
P
. Pulley
C
operates an alternator that requires
100 Nm
,
and pulley
D
operates a hydraulic pump that requires
300 Nm
. Pulley
E
is
frictionless. The coefficients of static friction for pulleys
A
,
C
, and
D
are 0.5,
and the radii of the pulleys are shown. Determine the minimum value of
P
that prevents the belt from slipping. Hint: The use of mathematical software is
helpful, but not required.
Problem 9.68
The portable winch shown consists of a rotating motor-powered drum that is
attached to a skid. Winches such as this were once used in logging operations
to move logs and to lift them onto trucks and railcars. To move the winch to a
new location, a worker stands on the skid and wraps a rope
ABCD
around the
drum. End
A
of the rope is attached to a fixed object, portion
AB
of the rope
is horizontal, and the rope makes less than one full turn around the drum. The
skid, drum, and worker weigh
800 lb
with center of gravity at point
G
, and the
drum has 10 in:radius.
(a) Assuming the skid does not tip, determine the smallest force the worker
must apply to portion CD of the rope so that the skid will slide.
(b)
Determine if the assumption in Part (a) that the skid does not tip is correct.
Problem 9.69
The schematic for a precision diamond wire saw that is used in a laboratory for
cutting very hard, brittle materials is shown. It consists of a wire with diamond
particles bonded to its entire surface. The wire wraps around a motor-driven
pulley at
A
that rotates counterclockwise, and frictionless pulleys at
B
and
D
.
At
C
is a fixed table where a workpiece is cut. Due to cutting, the workpiece
applies a
2
N vertical force to the wire in the direction shown. The wire is
tensioned by weight
W
. Portions
AB
and
BCD
of the wire are horizontal
and vertical, respectively. The angle of wrap at the motor is 150
ı
, and the
coefficients of static and kinetic friction between the motor pulley and the wire
are both 0.7. Neglecting all weight except
W
, determine the value of
W
so that
the wire does not slip on the pulley at A.
Problem 9.70
A simple bracket for supporting a can of paint or other items used during
construction consists of a member ABC and two short bars that are rigidly
connected to it. The bracket is slipped onto a wooden post and is held in place
by friction. Determine the minimum coefficient of static friction that prevents
the bracket from slipping regardless of the weight supported (this is called
self-locking).
Problem 9.71
Member CD is used to apply a horizontal force
P
to a uniform cylinder having
radius
r
and weight
W
. The contact surfaces at
A
and
B
have the same coefficient
of static friction
s
. Neglecting the weight of member CD, determine the force
P
necessary to cause impending motion of the cylinder. Express your answer in terms
of parameters such as W,r,s.
Problem 9.72
For a
3
m thick section of dam and water, determine the normal force and friction force
between the dam and foundation, specify the distance from point
A
to the location of
this force system, and determine the minimum value of the coefficient of friction so the
dam does not slide. The density of the dam is 2400 kg=m3, and the density of water is
1000 kg=m3.
Solution
The weight of the water in the FBD is
W2DwgVwD.1000 kg=m3/.9:81 m=s2/1
2.1 m/.1 m/.3 m/D14:72 kN:(4)
The equilibrium equations are
XFyD0W W1W2CND0; )ND156:0 kN, (5)
Problem 9.73
and 0.26, respectively. Determine the value of the horizontal force
P
necessary to
cause motion of the chest, and determine if the motion is sliding or tipping, if:
(a) All wheels are locked.
(b) The wheels at Aare locked and the wheels at Bcan rotate.
(c) The wheels at Acan rotate and the wheels at Bare locked.
