Final answer:
To find the tension in the wire, we can use Hooke's law. By calculating the cross-sectional area of the wire and the strain it experiences, we can then determine the tension using the formula: Tension = (Young's modulus) x (cross-sectional area) x (strain). The tension in the wire is approximately 4.66 N.
Step-by-step explanation:
To find the tension in the wire, we can use Hooke's law, which states that the force applied to a spring or elastic material is directly proportional to the displacement of the material from its equilibrium position. In this case, the weight attached to the wire is causing it to stretch by 1.12 mm. We can calculate the tension using the formula:
Tension = (Young's modulus) x (cross-sectional area) x (strain)
First, we need to find the cross-sectional area of the wire. The wire has a diameter of 0.556 mm, so its radius is half of that, which is 0.278 mm (or 2.78 x 10^(-4) m). Using the formula for the area of a circle, we get:
Area = π x (radius)^2
Plugging in the values, we find that the cross-sectional area of the wire is approximately 2.43 x 10^(-7) m^2.
Next, we need to find the strain. The wire originally had a length of 76.0 cm, and it stretched by 1.12 mm. The strain is given by:
Strain = (change in length) / (original length)
Plugging in the values, we find that the strain is approximately 1.47 x 10^(-3).
Now we can calculate the tension. Young's modulus, denoted as E, is a measure of the stiffness of a material. For copper, the Young's modulus is approximately 1.26 x 10^11 N/m^2. Plugging in the values, we get:
Tension = (1.26 x 10^11 N/m^2) x (2.43 x 10^(-7) m^2) x (1.47 x 10^(-3))
Calculating it gives us a tension of approximately 4.66 N.