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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