Chapter 23
21
P23.56
This is the general version of the preceding problem. The known quantities are
A
,
B
,
m
,
g
, and
θ
. The
unknowns are
q
and
T
.
The approach to this problem should be the same as for the last problem, but without
numbers to substitute for the variables. Likewise, we can use the free body diagram given in the
solution to problem 55.
Again, Newton’s second law:
FT
q
A
x
∑
=−
+
=
sin
0
(1)
and
q
B
m
g
y
∑
=+
+
−
=
cos
0
(2)
(a)
Substituting
T
qA
=
sin
, into Eq. (2),
qA
qB
mg
cos
sin
+=
.
Isolating
q
on the left,
q
mg
AB
=
+
cot
af
.
(b)
Substituting this value into Eq. (1),
T
mgA
=
+
cos
sin
θθ
a
f
.
If we had solved this general problem first, we would only need to substitute the
appropriate values in the equations for
q
and
T
to find the numerical results needed for
problem 55. If you find this problem more difficult than problem 55, the little list at the first
step is useful. It shows what symbols to think of as known data, and what to consider
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This note was uploaded on 12/14/2011 for the course PHY 203 taught by Professor Staff during the Fall '11 term at Indiana State University .
 Fall '11
 Staff
 Physics

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