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56. Problem 13.55P (HRW) A 103 kg uniform log hangs by two steel wires, A and
B, both of radius 1.20 mm. Initially, wire A was 2.50 m long and
2.00 mm shorter than wire B. The log is now horizontal. What forces are
exerted on it by (a) wire A and (b) wire B? (c) What is the
ratio
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Solution: Click For PDF Version Let W be the weight of the log. Let the initial lengths of the wires
A and B be
and
Let
In the following we will approximate
Young’s modulus of steel
From Hook’s law of elasticity, we have
We, therefore, have
We thus find
(c) And,
(a) and (b) Force exerted on wire A is
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,
respectively. Let
be the
pull on wire A and
be the
pull on the wire B due to the weight of the log. From the data of the
problem we note the relations
,
be the
increase in length of wire A caused by the stress on it and let
be the corresponding increase in length of wire B. As the log becomes
horizontal because of the increase in lengths of wires A and B, we
have
Let area
of cross-section of wires A and B be
.
