Statics 2e 3
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4Solutions Manual
Accuracy of Numbers in Calculations
464 Solutions Manual
Chapter 4 Solutions
Problem 4.1
Compute the moment of force Fabout point B, using the following procedures.
(a) Determine the moment arm dand then evaluate MBDF d .
(b)
Resolve force
F
into
x
and
y
components at point
A
and use the principle
of moments.
(c) Use the principle of moments with Fpositioned at point C.
(d) Use the principle of moments with Fpositioned at point D.
(e) Use a vector approach.
Solution
Statics 2e 465
E
FD25 lb 3
5O{4
5O|:(9)
Problem 4.2
Compute the moment of force
F
about point
B
, using the following procedures.
(a) Determine the moment arm dand then evaluate MBDF d .
(b)
Resolve force
F
into
x
and
y
components at point
A
and use the principle
of moments.
(c) Use the principle of moments with Fpositioned at point C.
(d) Use the principle of moments with Fpositioned at point D.
(e) Use a vector approach.
Problem 4.3
The cover of a computer mouse is hinged at point
B
so that it may be clicked.
Repeat Prob. 4.1 to determine the moment about point B.
Solution
Problem 4.4
The cover of a computer mouse is hinged at point
B
so that it may be clicked.
Repeat Prob. 4.1 to determine the moment about point B.
Problem 4.5
An atomic force microscope (AFM) is a state-of-the-art device used to study
the mechanical and topological properties of surfaces on length scales as small
as the size of individual atoms. The device uses a flexible cantilever beam
AB
with a very sharp, stiff tip
BC
that is brought into contact with the surface to
be studied. Due to contact forces at
C
, the cantilever beam deflects. If the tip
of the AFM is subjected to the forces shown, determine the resultant moment of
both forces about point A. Use both scalar and vector approaches.
Problem 4.6
A large lever
AB
has a
5kN
force applied to it where the line of action of
this force passes through points
B
and
C
. Determine the moment of the force
about point
A
for any position of the lever where
0ı˛180ı
, and plot the
moment versus ˛.
Problem 4.7
A circular disk rotates on a bearing at point
A
, and has a string
BCD
attached
to it. The pulley at
C
is frictionless, and the string supports a weight
WD10 lb
.
Determine the moment of the force in segment
BC
of the string about point
A
for any position of the disk where
0ı360ı
, and plot the moment versus
. Neglect the size of the pulley.
Problem 4.8
The door of an oven has
22 lb
weight that acts vertically through point
D
. The
door is supported by a hinge at point
A
and two springs that are symmetrically
located on each side of the door. For the positions specified below, determine
the force needed in each of the two springs if the resultant moment about point
Aof the weight and spring forces is to be zero.
(a) ˛D45ı.
(b) ˛D90ı.
(c)
Based on your answers to Parts (a) and (b), determine the stiffness for
the springs.
Solution
Problem 4.9
The ball of a trailer hitch is subjected to a force
F
. If failure occurs when the
moment of
F
about point
A
reaches 10,000
in.lb
, determine the largest value
F
may have and the value of
˛
for which the moment about
A
is the largest.
Note that the value of
F
you determine must not produce a moment about
A
that exceeds 10,000 in.lb for any possible value of ˛.
Solution