Unlock document.
This document is partially blurred.
Unlock all pages and 1 million more documents.
Get Access
PROBLEM 3.142* (Continued)
Copyright © McGraw-Hill Education. Permission required for reproduction or display.
PROBLEM 3.143*
Replace the wrench shown with an equivalent system consisting of two
forces perpendicular to the y-axis and applied respectively at A and B.
PROBLEM 3.144*
Show that, in general, a wrench can be replaced with two forces chosen in such a way that one force
passes through a given point while the other force lies in a given plane.
yy
PROBLEM 3.144* (Continued)
PROBLEM 3.145*
Show that a wrench can be replaced with two perpendicular forces, one of which is applied at a given
point.
xz
PROBLEM 3.145* (Continued)
Since the components of A must be real, a nontrivial solution is not possible. Thus, it is required that
0,
y
B≠
so that from Equation (4),
0.z=
To obtain one possible solution, arbitrarily let
0.
x
A=
(Note: Setting
, , or
yz z
AA B
equal to zero results in unacceptable solutions.)
22 2 22 2
2
22 2
z
aR M
BaR M
++
=+
PROBLEM 3.145* (Continued)
Copyright © McGraw-Hill Education. Permission required for reproduction or display.
In summary,
22 2
()
RM M aR
aR M
= −
+
A jk
2
22 2
()
aR aR M
aR M
= +
+
B jk
Which shows that it is possible to replace a wrench with two perpendicular forces, one of which is
applied at a given point.
Lastly, if
0R>
and
0,M>
it follows from the equations found for A and B that
0
y
A>
and
0.
y
B>
From Equation (6),
0x<
(assuming
0).a>
Then, as a consequence of letting
0,
x
A=
force A lies in a
plane parallel to the yz-plane and to the right of the origin, while force B lies in a plane parallel to the yz-
plane but to the left to the origin, as shown in the figure below.
PROBLEM 3.146*
Show that a wrench can be replaced with two forces, one of which has a prescribed line of action.
PROBLEM 3.146* (Continued)
z
λ
Note that for this case, the lines of action of both A and B intersect the x-axis.
PROBLEM 3.146* (Continued)
