Question

1.1 A steel wire with 3-m length and 1-mmcross-section is held between
rigid supports with a tension of 50 N. If the middle of the wire is pulled
5 mm sideways, calculate the change in tension. Also calculate change in
tension if temperature changes by 10 °C. (For steel, Y= 2 x 10" N m² and
a= 10-c-).
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Answer 1

Explanation:

The the length of wire l=2 m

The area of cross section A= 10⁻⁶ m²

The force acting on the system before F= 200N

The change in temperature is 5

The young modulus of steel be Y=2.2×10¹¹

To find:

The change in the tension after change in temperature

Solution:

The relation between the tension and length is

F'=ΔLAY/l

Putting the above values

F'= 0.005×10⁻⁶×2.2×10¹¹/2

F'=0.005×10⁵

F'=5×10² N

So the tension acting on it is 0.005 N

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