Steel wire rope is used to lift a heavy object. We use a 3.1m steel wire that is 6.0mm in diameter and lift a 1700kg object. Then, the wire elongates
0.17m. Calculate the Young’s modulus for the rope material.

Young's modulus for the rope material is 20.8 MPa.    

Explanation:

The Young's modulus is given by:

Where:

F: is the force applied on the wire

L₀: is the initial length of the wire = 3.1 m

A: is the cross-section area of the wire

ΔL: is the change in the length = 0.17 m

The cross-section area of the wire is given by the area of a circle:

Now we need to find the force applied on the wire. Since the wire is lifting an object, the force is equal to the tension of the wire as follows:

Where:

: is the tension of the wire

: is the weigh of the object = mg

m: is the mass of the object = 1700 kg

g: is the acceleration due to gravity = 9.81 m/s²

Hence, the Young's modulus is:

Therefore, Young's modulus for the rope material is 20.8 MPa.                

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