Question

This problem returns to the tightrope walker studied in Example 4.6, who created a tension of 3.94 times 10^3 , {N} in a wire making an angle 5.0^circ below the horizontal with each supporting pole. Calculate how much this tension stretches the steel wire if it was originally 15 , {m} long and 0.50 , {cm} in diameter.

A. 2.37 , {mm}
B. 3.15 , {mm}
C. 3.82 , {mm}
D. 4.59 , {mm}

Answer 1

To calculate how much the steel wire stretches due to tension, we would use Hooke's Law and the formula for Young's modulus, taking into account the tension, length, and diameter of the wire.

Step-by-step explanation:

The problem involves calculating how much tension stretches a steel wire in a tightrope walking scenario. The given parameters are the tension of 3.94 x 10³ N, the original length of the wire which is 15 m, and its diameter which is 0.50 cm. To find the elongation, we can use Hooke's Law alongside the formula for Young's modulus when dealing with a stress-strain relationship.

The tension applied to the wire only affects its length; since the angle given is below the horizontal, the entire tension can be considered to be acting along the wire's length. To calculate the elongation, we'll need to compute the cross-sectional area of the wire, the stress applied to it, and then use Young's modulus for steel to find the resultant strain, which would give us the elongation value.