# A 51 Kg bucket of concrete is suspended from a steel wire that is 1.2 mm in diameter and 11.2 m...

## Question:

A 51 Kg bucket of concrete is suspended from a steel wire that is 1.2 mm in diameter and 11.2 m long. What distance will the wire stretch? Young's modulus for steel is {eq}\rm 2.0 \times 10^{11} \ N/m^2 {/eq}.

## Young's Modulus:

The stress placed on material of constant cross-sectional area is proportional to the fractional change in length of the material. This is known as Young's Law, and the relationship between stress and strain defines Young's modulus. Young's modulus is important in engineering applications where the distance that materials stretch for a given force is important in the design of buildings, bridges, and other structures.

## Answer and Explanation:

The stress is related to the strain by Young's equation. For the stress, we use the weight of the bucket and the cross sectional area of the wire. We can then use the given values to solve for the change in length of the wire.

{eq}\sigma = E\epsilon\\ \dfrac{W}{A} = E\dfrac{\Delta L}{L_0}\\ \dfrac{(51 \ kg)(9.81 \ m/s^2)}{\pi (0.0006 \ m)^2} = (2.0\times 10^{11} \ N/m^2)\dfrac{\Delta L}{11.2 \ m}\\ 4.42\times 10^8 \ N/m^2 = (2.0\times 10^{11} \ N/m^2)\dfrac{\Delta L}{11.2 \ m}\\ \Delta L = 0.0248 \ m = 2.48 \ cm {/eq}

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