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Problem 1: A 1.50 m length of a piano wire with a diameter of 0.25 cm is stretched by attaching a 10 kg mass to one end. How far is the wire stretched?

Solution

Given

Length of the wire, L = 1.5 m

Diameter = 0.25 cm =  0.25 × 10-2 m

⇒ Radius = (0.25× 10-2)/2                             

Mass = 10 kg ⇒ W = 9.8× 10 = 98 N

Asked   Stretching, Δl

Formula

Now

And

Therefore, to solve the problem, we find the applied stress.

In order to calculate the cross-sectional area of the wire, we apply the formula, A = πr2. Hence,

 

 

Put in the formula for the stress, taking the weight as the force applied.

Similarly for strain,

 

Now use equations (1) and (2) in the formula for Y given above, remembering the value of Young modulus for steel is approximately 200 MPa (mega pascal) = 200 × 109 Pa, we have

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