Question

copper wire of diameter 0.5 mm is stretched between two points at 25°C. Calculate the increase in tension in the wire if the temperature falls to 0°C Young's modulus for copper = 1.2 *10^11Nm^-2 linear expansivity for copper = 18*10^-6 K^-1

Answer 1

Diameter of copper wire (d) = 0.5 mm

Initial temperature (T1) = 25°C

Final temperature (T2) = 0°C

Young's modulus for copper (Y) = 1.2 x 10^11 Nm^-2

Linear expansivity for copper (α) = 18 x 10^-6 K^-1

Length of wire (L1) at 25°C can be calculated using: L1 = L0 (1 + αΔT) Where L0 is the original length at 0°C.

Let's assume an original length L0 = 10 m

Length at 25°C is: L1 = 10 (1 + 18x10^-6 x 25) = 10.0045 m

Length at 0°C (L2) is simply the original length L0 = 10 m

Using Young's modulus formula: Tension = (Y*ΔL)/L0 Where ΔL = Change in length

ΔL = L1 - L2 = 0.0045 m

Putting this in the formula: Tension = (1.2 x 10^11 x 0.0045)/10 Tension = 5.4 x 10^8 N

Therefore, the increase in tension is 5.4 x 10^8 N

Step-by-step explanation:

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