Problem 2.117
A cantilever I beam has a cable at end
B
that supports a force
E
F
, and
ErAB
is the
position vector from end
A
of the beam to end
B
. Position vectors
Er1
and
Er2
are
parallel to the flanges and web of the I beam, respectively. For determination
of the internal forces in the beam (discussed in Chapter 8), and for mechanics
of materials analysis, it is necessary to know the components of the force in
the axial direction of the beam (
AB
) and in directions parallel to the web and
flanges.
Determine the scalar and vector components of E
Fin direction Er2.
Problem 2.118
The gearshift lever
AB
for the transmission of a sports car has position vector
Er
whose line of action passes through points
A
and
B
. The driver applies a force
E
F
to the knob of the lever to shift gears. If the component of
E
F
perpendicular
to the gearshift lever must be
5
N to shift gears, determine the magnitude
F
of
the force.
Problem 2.119
A force of magnitude
8lb
is applied to line
AB
of a fishing rod
OA
. Determine
the vector components of the
8lb
force in directions parallel and perpendicular
to the rod.
Solution
176 Solutions Manual
Problem 2.120
Rod
AB
is the firing pin for the right-hand barrel of a side-by-side shotgun.
During firing, end
A
is struck by the hammer, which imparts a force
F
to the
firing pin. The force
F
lies in a plane parallel to the
xy
plane, but the firing pin
has a three-dimensional orientation as shown. Determine the components of
F
in directions parallel and perpendicular to the firing pin.
Problem 2.121
The collar
C
is fixed to rod
AB
and supports a weight
WD15
N, acting in the
negative
´
direction. Determine the vector components of the weight that are
parallel and perpendicular to rod AB.
(5)
As a partial check of the accuracy of our results, we use Eqs. (4) and (5) to evaluate the magnitudes Wkand
W?as
WkDq.5:185/2C.5:185/2C.9:074/2ND11:67 N;(6)
Problem 2.122
The collar
C
is fixed to rod
AB
using a glued bond that allows a maximum
force of
35
N parallel to the axis of the rod. The collar has weight
W
acting in
the negative
´
direction. Determine the weight
W
of the collar that will cause
the glued bond to break.
Problem 2.123
Components of a machine (not shown in the figure) are actuated by motion of a
threaded collar
C
that slides on a fixed bar
DEF GHI
. Segment
DE
of the bar
is straight and vertical, segment
F G
is straight where the coordinated of points
F
and
G
are given in the figure, and segment
HI
is straight and horizontal.
The collar’s motion is controlled by screw
AB
, which is turned by the motor at
point
A
. If the force in the screw is
50
N compression, use the dot product to
determine the component of the screw force in the direction of the bar for the
positions of the collar given below. Also determine the component of the screw
force perpendicular to the bar.
(a) Collar Cis 2mm below point E.
(b) Collar Cis 1/3 the distance from point Fto point G.
3.70 mm 25 mm/D40 mm:(7)
180 Solutions Manual
Thus
ErAC D.73 O{C40 O|/ mm;(8)
Problem 2.124
Components of a machine (not shown in the figure) are actuated by motion of a
threaded collar
C
that slides on a fixed bar
DEF GHI
. Segment
DE
of the bar
is straight and vertical, segment
F G
is straight where the coordinated of points
F
and
G
are given in the figure, and segment
HI
is straight and horizontal.
The collar’s motion is controlled by screw
AB
, which is turned by the motor at
point
A
. If the force in the screw is
50
N compression, use the dot product to
determine the component of the screw force in the direction of the bar for the
positions of the collar given below. Also determine the component of the screw
force perpendicular to the bar.
(a) Collar Cis 2/3 the distance from point Fto point G.
(b) Collar Cis 1/2 the distance from point Hto point I.
Solution
182 Solutions Manual
Part (b) When collar Cis 1=2the distance from point Hto point I, then
Problem 2.125
Components of a machine (not shown in the figure) are actuated by motion of a
threaded collar
C
that slides on a fixed bar
DEF GHI
. Segment
DE
of the bar
is straight and vertical, segment
F G
is straight where the coordinated of points
F
and
G
are given in the figure, and segment
HI
is straight and horizontal.
The collar’s motion is controlled by screw
AB
, which is turned by the motor at
point
A
. If the force in the screw is
50
N compression, use the dot product to
determine the component of the screw force in the direction of the bar for the
positions of the collar given below. Also determine the component of the screw
force perpendicular to the bar.
Let the collar be positioned on the straight segment of the bar between points
F
and
G
. Determine the point along this segment of the bar where the force
from the screw in the direction of the bar is largest, and determine the value of
this force. Also determine the component of the screw force perpendicular to
the bar.
Problem 2.126
A winch at point
B
is used to slide a box up a chute
CD
in a warehouse. If the
component of the force from cable
AB
in the direction of the chute must be
400 lb
, determine the force in the cable for the position of the box given below.
The chute is parallel to the
x´
plane. Neglect the size of the box and the winch.
The box is at the base of the chute, point C.
Problem 2.127
A winch at point
B
is used to slide a box up a chute
CD
in a warehouse. If the
component of the force from cable
AB
in the direction of the chute must be
400 lb
, determine the force in the cable for the position of the box given below.
The chute is parallel to the
x´
plane. Neglect the size of the box and the winch.
The box is 1/3 the distance up the chute from point C.
Solution
Problem 2.128
A winch at point
B
is used to slide a box up a chute
CD
in a warehouse. If the
component of the force from cable
AB
in the direction of the chute must be
400 lb
, determine the force in the cable for the position of the box given below.
The chute is parallel to the
x´
plane. Neglect the size of the box and the winch.
The box is 3/4 the distance up the chute from point C.
Solution
When box Ais 3=4 the distance up the chute from point C; then the coordinates of the box Aare
Problem 2.129
The structure consists of a quarter-circular rod
AB
with
150 mm
radius that is
fixed in the
xy
plane. An elastic cord supporting a force of
100
N is attached to
a support at
D
and a bead at
C
. Determine the components of the cord force in
directions tangent and normal to the curved rod AB at point C.
Solution
Problem 2.130
Bead
A
has negligible weight and slides without friction on rigid fixed bar
BC
.
An elastic cord
AD
, which supports a
10 lb
tensile force, is attached to the
bead. At the instant shown, the bead has zero velocity. For the position of the
bead given below, determine the vector components of the cord tension that act
parallel and perpendicular to direction
BC
of the bar (your answers should be
vectors). Due to the cord tension, will the bead slide toward point Bor C?
Bead Ais positioned halfway between points Band C.
Problem 2.131
Bead
A
has negligible weight and slides without friction on rigid fixed bar
BC
.
An elastic cord
AD
, which supports a
10 lb
tensile force, is attached to the
bead. At the instant shown, the bead has zero velocity. For the position of the
bead given below, determine the vector components of the cord tension that act
parallel and perpendicular to direction
BC
of the bar (your answers should be
vectors). Due to the cord tension, will the bead slide toward point Bor C?
Bead Ais 1/4 the distance from point Bto point C.
Problem 2.132
Bead
B
has negligible weight and slides without friction on rigid fixed bar
AC
.
An elastic cord
BD
, which supports a
60
N tensile force, is attached to the bead.
At the instant shown, the bead has zero velocity. For the position of the bead
given below, determine the components of the cord tension that act parallel and
perpendicular to direction
AC
of the bar. Due to the cord tension, will the bead
slide toward point Aor C?
Bead Bis positioned halfway between points Aand C.
Problem 2.133
Bead
B
has negligible weight and slides without friction on rigid fixed bar
AC
.
An elastic cord
BD
, which supports a
60
N tensile force, is attached to the bead.
At the instant shown, the bead has zero velocity. For the position of the bead
given below, determine the components of the cord tension that act parallel and
perpendicular to direction
AC
of the bar. Due to the cord tension, will the bead
slide toward point Aor C?
Bead Bis 2/5 the distance from point Ato point C.
Solution
The position vector from Ato Cis
ErAC D.120 O{C60 O|C40 O
k/ mm, rAC Dq.120/2C.60/2C.40/2mm D140 mm. (1)
Since Bis 2=5 the distance from point Ato C, it follows that the position vector from Ato bead Bis
ErAB D2
k/ mm D.48 O{C24 O|C16 O
k/ mm:(2)
Problem 2.134
A sports car at point
A
drives down a straight stretch of road
CD
. A police car
at point
B
uses radar to measure the speed of the car, and obtains a reading of
80 km=h
. For the position of the car given below, determine the speed of the car.
Note that the
80 km=h
speed measured by the radar gun is the rate of change of
the distance between the car and the radar gun.
The car is 30% of the distance from point Cto point D.